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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A string is called beautiful if no two consecutive characters are equal. For example, "ababcb", "a" and "abab" are beautiful strings, while "aaaaaa", "abaa" and "bb" are not. Ahcl wants to construct a beautiful string. He has a string s, consisting of only characters 'a', 'b', 'c' and '?'. Ahcl needs to replace each character '?' with one of the three characters 'a', 'b' or 'c', such that the resulting string is beautiful. Please help him! More formally, after replacing all characters '?', the condition s_i β‰  s_{i+1} should be satisfied for all 1 ≀ i ≀ |s| - 1, where |s| is the length of the string s. Input The first line contains positive integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Next t lines contain the descriptions of test cases. Each line contains a non-empty string s consisting of only characters 'a', 'b', 'c' and '?'. It is guaranteed that in each test case a string s has at least one character '?'. The sum of lengths of strings s in all test cases does not exceed 10^5. Output For each test case given in the input print the answer in the following format: * If it is impossible to create a beautiful string, print "-1" (without quotes); * Otherwise, print the resulting beautiful string after replacing all '?' characters. If there are multiple answers, you can print any of them. Example Input 3 a???cb a??bbc a?b?c Output ababcb -1 acbac Note In the first test case, all possible correct answers are "ababcb", "abcacb", "abcbcb", "acabcb" and "acbacb". The two answers "abcbab" and "abaabc" are incorrect, because you can replace only '?' characters and the resulting string must be beautiful. In the second test case, it is impossible to create a beautiful string, because the 4-th and 5-th characters will be always equal. In the third test case, the only answer is "acbac". Submitted Solution: ``` import random t = int(input()) for _ in range(t): txt = input() for i in range(len(txt)-1): chars = ['a', 'b', 'c'] if txt[i] != '?' and txt[i] == txt[i+1]: print(-1) break if txt[i] == '?': if i>0 and txt[i-1] != '?': chars.remove(txt[i-1]) if i<(len(txt)-1) and txt[i+1] != '?' and txt[i+1] in chars: chars.remove(txt[i+1]) k = random.randint(0, len(chars)-1) txt = txt[:i]+chars[k]+txt[i+1:] # txt[i] = chars[k] else: print(txt) ``` No
103,039
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A string is called beautiful if no two consecutive characters are equal. For example, "ababcb", "a" and "abab" are beautiful strings, while "aaaaaa", "abaa" and "bb" are not. Ahcl wants to construct a beautiful string. He has a string s, consisting of only characters 'a', 'b', 'c' and '?'. Ahcl needs to replace each character '?' with one of the three characters 'a', 'b' or 'c', such that the resulting string is beautiful. Please help him! More formally, after replacing all characters '?', the condition s_i β‰  s_{i+1} should be satisfied for all 1 ≀ i ≀ |s| - 1, where |s| is the length of the string s. Input The first line contains positive integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Next t lines contain the descriptions of test cases. Each line contains a non-empty string s consisting of only characters 'a', 'b', 'c' and '?'. It is guaranteed that in each test case a string s has at least one character '?'. The sum of lengths of strings s in all test cases does not exceed 10^5. Output For each test case given in the input print the answer in the following format: * If it is impossible to create a beautiful string, print "-1" (without quotes); * Otherwise, print the resulting beautiful string after replacing all '?' characters. If there are multiple answers, you can print any of them. Example Input 3 a???cb a??bbc a?b?c Output ababcb -1 acbac Note In the first test case, all possible correct answers are "ababcb", "abcacb", "abcbcb", "acabcb" and "acbacb". The two answers "abcbab" and "abaabc" are incorrect, because you can replace only '?' characters and the resulting string must be beautiful. In the second test case, it is impossible to create a beautiful string, because the 4-th and 5-th characters will be always equal. In the third test case, the only answer is "acbac". Submitted Solution: ``` def getChar(x, y): opts = ['a', 'b', 'c'] if x in opts: opts.remove(x) if y in opts: opts.remove(y) return opts[0] def findBS(s): length = len(s) opts = ['a', 'b', 'c'] if length == 1: if '?' in s: print(-1) else: print(s) return for i in range(len(opts)): if s[0] == '?' and s[1] != opts[i]: s[0] = opts[i] if s[length-1] == '?' and s[length-2] != opts[i]: s[length-1] = opts[i] for i in range(1, length-1): if s[i] == '?': s[i] = getChar(s[i-1], s[i+1]) if s[i] == s[i-1] or s[i] == s[i+1]: print('-1') return if '?' in opts: print(-1) print(''.join(s)) t = int(input()) for _ in range(t): s = list(input().rstrip()) findBS(s) ``` No
103,040
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A string is called beautiful if no two consecutive characters are equal. For example, "ababcb", "a" and "abab" are beautiful strings, while "aaaaaa", "abaa" and "bb" are not. Ahcl wants to construct a beautiful string. He has a string s, consisting of only characters 'a', 'b', 'c' and '?'. Ahcl needs to replace each character '?' with one of the three characters 'a', 'b' or 'c', such that the resulting string is beautiful. Please help him! More formally, after replacing all characters '?', the condition s_i β‰  s_{i+1} should be satisfied for all 1 ≀ i ≀ |s| - 1, where |s| is the length of the string s. Input The first line contains positive integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Next t lines contain the descriptions of test cases. Each line contains a non-empty string s consisting of only characters 'a', 'b', 'c' and '?'. It is guaranteed that in each test case a string s has at least one character '?'. The sum of lengths of strings s in all test cases does not exceed 10^5. Output For each test case given in the input print the answer in the following format: * If it is impossible to create a beautiful string, print "-1" (without quotes); * Otherwise, print the resulting beautiful string after replacing all '?' characters. If there are multiple answers, you can print any of them. Example Input 3 a???cb a??bbc a?b?c Output ababcb -1 acbac Note In the first test case, all possible correct answers are "ababcb", "abcacb", "abcbcb", "acabcb" and "acbacb". The two answers "abcbab" and "abaabc" are incorrect, because you can replace only '?' characters and the resulting string must be beautiful. In the second test case, it is impossible to create a beautiful string, because the 4-th and 5-th characters will be always equal. In the third test case, the only answer is "acbac". Submitted Solution: ``` def solve(p): if not p: return [] if len(p)==1: if p[0] == '?': return ['a'] else: return p s = set() s.add('a') s.add('b') s.add('c') for i in range(1,len(p)-1): if p[i] == '?': rem = list(s.difference(set([p[i-1], p[i+1], '?']))) if not rem: return -1 else: p[i] = rem[0] if p[0] == '?': p[0] = list(s.difference(set([p[1], '?'])))[0] if p[-1] == '?': p[-1] = list(s.difference(set([p[-2], '?'])))[0] for i in range(1, len(p)): if p[i]==p[i-1]: return -1 return p problems = [] for i in range(int(input())): problems += [list(input())] for p in problems: print(p) p = solve(p) if p!= -1: p = ''.join(p) print(p) ``` No
103,041
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Provide a correct Python 3 solution for this coding contest problem. Problem Jennifer and Marian presented Carla with the string S. However, Carla is not happy to receive the string S. I wanted the string T. The three decided to work together to change the string S to the string T. Jennifer first sorts the letters in any order. Marian then exchanges the lowercase letters of the two alphabets any number of times. This operation exchanges all the same characters in the string, for example: * aab-> Swap a and b-> bba * aab-> Swap a and c-> ccb Finally, Carla replaces one character with another and repeats until T. Jennifer and Marian decided to try to reduce the number of Carla replacements. Find the minimum number of replacements that Carla makes. Constraints * 1 ≀ n ≀ 105 * S and T contain only'a'~'z' * | S | = | T | = n Input n S T The length n of the string is given on the first line. The character string S is given on the second line, and the character string T is given on the third line. Output Print the minimum number of Carla replacements on one line. Examples Input 3 abc xyz Output 0 Input 5 aaabb xyxyz Output 1 "Correct Solution: ``` # AOJ 1568: String Conversion # Python3 2018.7.13 bal4u cha, chzn = ord('a'), ord('z')+1 S, T = [0]*128, [0]*128 input() a = input() for x in a: S[ord(x)] += 1 S = sorted(S[cha:chzn], reverse=True) a = input() for x in a: T[ord(x)] += 1 T = sorted(T[cha:chzn], reverse=True) ans = 0 for i in range(26): ans += abs(S[i]-T[i]) print(ans >> 1) ```
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Provide a correct Python 3 solution for this coding contest problem. Problem Jennifer and Marian presented Carla with the string S. However, Carla is not happy to receive the string S. I wanted the string T. The three decided to work together to change the string S to the string T. Jennifer first sorts the letters in any order. Marian then exchanges the lowercase letters of the two alphabets any number of times. This operation exchanges all the same characters in the string, for example: * aab-> Swap a and b-> bba * aab-> Swap a and c-> ccb Finally, Carla replaces one character with another and repeats until T. Jennifer and Marian decided to try to reduce the number of Carla replacements. Find the minimum number of replacements that Carla makes. Constraints * 1 ≀ n ≀ 105 * S and T contain only'a'~'z' * | S | = | T | = n Input n S T The length n of the string is given on the first line. The character string S is given on the second line, and the character string T is given on the third line. Output Print the minimum number of Carla replacements on one line. Examples Input 3 abc xyz Output 0 Input 5 aaabb xyxyz Output 1 "Correct Solution: ``` #!/usr/bin/env python3 # -*- coding: utf-8 -*- from collections import defaultdict N = int(input()) s1 = input() s2 = input() def make_appears(s): chars = list(map(ord, s)) hist = defaultdict(int) for ch in chars: hist[ch] += 1 appears = list(hist.values()) appears.sort() appears.reverse() return appears appears1 = make_appears(s1) appears2 = make_appears(s2) ans = 0 for i, j in zip(appears1, appears2): ans += abs(i - j) shorter = min(len(appears1), len(appears2)) ans += sum(appears1[shorter:]) + sum(appears2[shorter:]) print(ans//2) ```
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0
Provide a correct Python 3 solution for this coding contest problem. Problem Jennifer and Marian presented Carla with the string S. However, Carla is not happy to receive the string S. I wanted the string T. The three decided to work together to change the string S to the string T. Jennifer first sorts the letters in any order. Marian then exchanges the lowercase letters of the two alphabets any number of times. This operation exchanges all the same characters in the string, for example: * aab-> Swap a and b-> bba * aab-> Swap a and c-> ccb Finally, Carla replaces one character with another and repeats until T. Jennifer and Marian decided to try to reduce the number of Carla replacements. Find the minimum number of replacements that Carla makes. Constraints * 1 ≀ n ≀ 105 * S and T contain only'a'~'z' * | S | = | T | = n Input n S T The length n of the string is given on the first line. The character string S is given on the second line, and the character string T is given on the third line. Output Print the minimum number of Carla replacements on one line. Examples Input 3 abc xyz Output 0 Input 5 aaabb xyxyz Output 1 "Correct Solution: ``` from collections import Counter n = int(input()) counter1 = Counter(input()) counter2 = Counter(input()) values1 = [0] * (26 - len(counter1)) + sorted(counter1.values()) values2 = [0] * (26 - len(counter2)) + sorted(counter2.values()) print(sum([abs(i - j) for i, j in zip(values1, values2)]) // 2) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Problem Jennifer and Marian presented Carla with the string S. However, Carla is not happy to receive the string S. I wanted the string T. The three decided to work together to change the string S to the string T. Jennifer first sorts the letters in any order. Marian then exchanges the lowercase letters of the two alphabets any number of times. This operation exchanges all the same characters in the string, for example: * aab-> Swap a and b-> bba * aab-> Swap a and c-> ccb Finally, Carla replaces one character with another and repeats until T. Jennifer and Marian decided to try to reduce the number of Carla replacements. Find the minimum number of replacements that Carla makes. Constraints * 1 ≀ n ≀ 105 * S and T contain only'a'~'z' * | S | = | T | = n Input n S T The length n of the string is given on the first line. The character string S is given on the second line, and the character string T is given on the third line. Output Print the minimum number of Carla replacements on one line. Examples Input 3 abc xyz Output 0 Input 5 aaabb xyxyz Output 1 Submitted Solution: ``` #!/usr/bin/env python3 # -*- coding: utf-8 -*- from collections import defaultdict N = int(input()) s1 = input() s2 = input() chars1 = list(map(ord, s1)) chars2 = list(map(ord, s2)) hist1 = defaultdict(int) hist2 = defaultdict(int) for ch in chars1: hist1[ch] += 1 for ch in chars2: hist2[ch] += 1 appears1 = list(hist1.values()) appears2 = list(hist2.values()) ans = 0 for i, j in zip(appears1, appears2): ans += abs(i - j) longer = max(len(appears1), len(appears2)) ans += sum(appears1[longer:]) + sum(appears2[longer:]) print(ans) ``` No
103,622
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two integers l and r. Let's call an integer x modest, if l ≀ x ≀ r. Find a string of length n, consisting of digits, which has the largest possible number of substrings, which make a modest integer. Substring having leading zeros are not counted. If there are many answers, find lexicographically smallest one. If some number occurs multiple times as a substring, then in the counting of the number of modest substrings it is counted multiple times as well. Input The first line contains one integer l (1 ≀ l ≀ 10^{800}). The second line contains one integer r (l ≀ r ≀ 10^{800}). The third line contains one integer n (1 ≀ n ≀ 2 000). Output In the first line, print the maximum possible number of modest substrings. In the second line, print a string of length n having exactly that number of modest substrings. If there are multiple such strings, print the lexicographically smallest of them. Examples Input 1 10 3 Output 3 101 Input 1 11 3 Output 5 111 Input 12345 12346 6 Output 1 012345 Note In the first example, string Β«101Β» has modest substrings Β«1Β», Β«10Β», Β«1Β». In the second example, string Β«111Β» has modest substrings Β«1Β» (3 times) and Β«11Β» (2 times). Submitted Solution: ``` n = int(input()) x = [int(x) for x in input().split()] h = x[0] l = x[0] a = 0 for i in range(0,n): if x[i] > h: h = x[i] a+=1 if x[i] < l: l = x[i] a+=1 print(a) ``` No
103,731
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Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` n,k=map(int, input().split()) s=input() a=0 b=0 ans=0 x=0 for i in range(n): if s[i]=='a': a+=1 else: b+=1 if(min(a,b)<=k): ans=max(ans,a+b) else: if s[x]=='a': a-=1 else: b-=1 x+=1 print(ans) ```
104,075
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0
Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` def executa(n, k, letra, s): r = 0 tk = k p = 0 for i in range(n): while r < n and tk >= 0: if a[r] == letra: if tk == 0: break tk -= 1 r += 1 p += 1 s = max(s, p) p -= 1 if a[i] == letra: tk += 1 if r == n: break return s if __name__ == '__main__': entrada = input() entrada_str = list(entrada.split(" ")) entrada_int = list(map(int, entrada_str)) n = entrada_int[0] k = entrada_int[1] a = input() soma = executa(n, k, "b", 0) soma = executa(n, k, "a", soma) print(soma) ```
104,076
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Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` n, k = list(map(int, input().split())) s = input() res = 0 count_a = 0 count_b = 0 left = 0 right = 0 while True: if s[right] == 'a': count_a += 1 else: count_b += 1 if count_a <= k or count_b <= k: if right - left + 1 > res: res = right - left + 1 else: if s[left] == 'a': count_a -= 1 else: count_b -= 1 left += 1 right += 1 if n - left < res or right == n: break print(res) ```
104,077
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Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` def answer(n,k,A): if n==1: return 1 dp=[0]*(n+1) for i in range(1,n+1): if A[i-1]=="a": dp[i]=dp[i-1]+1 else: dp[i]=dp[i-1] l=0;r=0 maxi=0 while r>=l and r<n: x=dp[r+1]-dp[l] if min(x, r+1-l-x)<=k: r+=1 else: maxi=max(maxi,r-l) l+=1 maxi=max(maxi,r-l) return maxi n,k=map(int,input().split()) A=input() print(answer(n,k,A)) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` le, ch = map(int, input().split()) st = input() ca, cb, si, mx = [0] * 4 for x in st: if x == 'a': ca += 1 else: cb += 1 if min(ca, cb) > ch: if st[si] == 'a': ca -= 1 else: cb -= 1 si += 1 else: mx += 1 print(mx) ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` from sys import stdin,stdout def fn(a,ch): # print(a) ans=0 for i in range(n): l,r=i,n-1 while l<=r: mid=(l+r)>>1 req=a[i]+k-int(s[i]!=ch) if a[mid]<=req:l=mid+1 else:r=mid-1 # print(i,r) ans=max(ans,r-i+1) return ans for _ in range(1):#int(stdin.readline())): # n=int(stdin.readline()) n,k=list(map(int,stdin.readline().split())) s=input() make_a=[];make_b=[] make_a+=[int(s[0]=='a')] make_b+=[int(s[0]=='b')] for i in range(1,n): make_a+=[make_a[-1]+int(s[i]=='a')] make_b+=[make_b[-1]+int(s[i]=='b')] # print(make_a) # print(make_b) ans=max(fn(make_a,'b'),fn(make_b,'a')) print(ans) ''' 10 1 bbabbabbba ''' ```
104,080
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0
Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` num = input() n, k = num.split() n = int(n) k = int(k) string = input() count_a = 0 count_b = 0 def check(ch): i = 0 j = 0 count = 0 answer = 0 for i in range(n): if(string[i] == ch): count += 1 if(count > k): while(count > k): if(string[j] == ch): count -= 1 j += 1 answer = max(answer, i-j +1) return answer max_a = check('a') max_b = check('b') print(max(max_a, max_b)) ```
104,081
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0
Provide tags and a correct Python 3 solution for this coding contest problem. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Tags: binary search, dp, strings, two pointers Correct Solution: ``` read = lambda: map(int, input().split()) n, k = read() s = input() i = j = 0 cur = k while cur and j < n: if s[j] == 'a': cur -= 1 j += 1 while j < n and s[j] == 'b': j += 1 ans = j while j < n: while i < n and s[i] == 'b': i += 1 i += 1 j += 1 while j < n and s[j] == 'b': j += 1 ans = max(ans, j - i) i = j = 0 cur = k while cur and j < n: if s[j] == 'b': cur -= 1 j += 1 while j < n and s[j] == 'a': j += 1 ans = max(ans, j) while j < n: while i < n and s[i] == 'a': i += 1 i += 1 j += 1 while j < n and s[j] == 'a': j += 1 ans = max(ans, j - i) print(ans) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` z,zz=input,lambda:list(map(int,z().split())) zzz=lambda:[int(i) for i in stdin.readline().split()] szz,graph,mod,szzz=lambda:sorted(zz()),{},10**9+7,lambda:sorted(zzz()) from string import * from re import * from collections import * from queue import * from sys import * from collections import * from math import * from heapq import * from itertools import * from bisect import * from collections import Counter as cc from math import factorial as f from bisect import bisect as bs from bisect import bisect_left as bsl from itertools import accumulate as ac def lcd(xnum1,xnum2):return (xnum1*xnum2//gcd(xnum1,xnum2)) def prime(x): p=ceil(x**.5)+1 for i in range(2,p): if (x%i==0 and x!=2) or x==0:return 0 return 1 def dfs(u,visit,graph): visit[u]=True for i in graph[u]: if not visit[i]: dfs(i,visit,graph) ###########################---Test-Case---################################# """ """ ###########################---START-CODING---############################## n,k=zz() s=z() m=k a=s[:k].count('a') b=k-a l=0 for i in range(k,n): if s[i]=='a':a+=1 else:b+=1 while min(a,b)>k: if s[l]=='a':a-=1 else:b-=1 l+=1 m=max(m,i-l+1) print(m) ``` Yes
104,083
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` n, m = input().split(' ') n, m = int(n), int(m) ans = 0 s = input() for i in range(2): left, used = 0, 0 for right in range(n): if ord(s[right]) != ord('a') + i: used += 1 while used > m: if ord(s[left]) != ord('a') + i: used -= 1 left += 1 ans = max(ans, right - left + 1) print(ans) ``` Yes
104,084
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` def main(): n, k = liee() s = input() l, ans, h = 1, 0, n while l <= h: m = (l + h) // 2 if fun(m, n, s, k): ans, l = m, m + 1 else: h = m - 1 print(ans) def fun(m, n, s, k): a, b = s[0:m].count('a'), s[0:m].count('b') if max(a, b) + k >= m: return 1 for i in range(m, n): if s[i - m] == 'a': a -= 1 else: b -= 1 if s[i] == 'a': a += 1 else: b += 1 if max(a, b) + k >= m: return 1 return 0 def fun2(s): cnt, num = 0, s.count('0') for i in s[1:]: if i == '1': cnt += 1 elif num == 1: cnt += 1 break else: break return cnt from sys import * import inspect import re from math import * import threading from collections import * from pprint import pprint as pp mod = 998244353 MAX = 10**5 def lie(): return int(input()) def liee(): return map(int, input().split()) def array(): return list(map(int, input().split())) def deb(p): for line in inspect.getframeinfo(inspect.currentframe().f_back)[3]: m = re.search(r'\bdeb\s*\(\s*([A-Za-z_][A-Za-z0-9_]*)\s*\)', line) print('%s %d' % (m.group(1), p)) def vector(size, val=0): vec = [val for i in range(size)] return vec def matrix(rowNum, colNum, val=0): mat = [] for i in range(rowNum): collumn = [val for j in range(colNum)] mat.append(collumn) return mat def dmain(): setrecursionlimit(100000000) threading.stack_size(40960000) thread = threading.Thread(target=main) thread.start() if __name__ == '__main__': # main() dmain() ``` Yes
104,085
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") #################################################################################### n,k=map(int,input().split()) from bisect import bisect s=input() l1=[] l2=[] l3=[] l4=[] c,d=0,0 for i in range(n): if s[i]=='a': l1.append(i) d+=1 else: c+=1 l3.append(i) l2.append(c) l4.append(d) if len(l1)!=0 and c!=0: ans=0 ans1=0 for i in l1: a=bisect(l2,l2[i]+k) ans=max(ans,a-i) for i in l3: a=bisect(l4,l4[i]+k) ans1=max(ans1,a-i) if l1[0]==0: a=bisect(l4,k) ans1=max(ans1,a) if l3[0]==0: a=bisect(l2,k) ans=max(ans,a) else: ans=len(s) ans1=len(s) print(max(ans,ans1)) ``` Yes
104,086
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` aplha=[chr(i) for i in range(ord('a'),ord('z')+1)] #for _ in range(int(input())): n,k=map(int,input().split()) s=list(input()) out=0 for i in aplha: l=0 r=0 t=k while l<n and r<n: if s[r]==i: r+=1 else: if t>0: t-=1 r+=1 continue else: if s[l]==i: l+=1 else: t+=1 l+=1 out=max(out,r-l) print(out) ``` No
104,087
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` # !/bin/env python3 # encoding: UTF-8 # βœͺ H4WK3yEδΉ‘ # Mohd. Farhan Tahir # Indian Institute Of Information Technology and Management,Gwalior # Question Link # https://codeforces.com/problemset/problem/676/C # # ///==========Libraries, Constants and Functions=============/// import sys inf = float("inf") mod = 1000000007 def get_array(): return list(map(int, sys.stdin.readline().split())) def get_ints(): return map(int, sys.stdin.readline().split()) def input(): return sys.stdin.readline() # ///==========MAIN=============/// def solve(c, s, k): ans = 0 r = 0 balance = 0 for i in range(len(s)): while r < len(s) and (s[r] == c or balance < k): if s[r] != c: balance += 1 r += 1 ans = max(ans, r-i) if s[i] != c: balance -= 1 return ans def main(): n, k = get_ints() s = input() print(max(solve('a', s, k), solve('b', s, k))) if __name__ == "__main__": main() ``` No
104,088
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` from collections import Counter def good(s, k, l): c = Counter() for i in range(len(s)): c[s[i]] += 1 if i - l >= 0: c[s[i - l]] -= 1 if i + 1 >= l: if min(c.values()) <= k: return True return False def solve(s, k): low = 1 high = 1 while good(s, k, high): high *= 2 while low + 1 < high: mid = (low + high) // 2 if good(s, k, mid): low = mid else: high = mid return low n, k = map(int, input().split()) s = input() print(solve(s, k)) ``` No
104,089
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters. Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve? Input The first line of the input contains two integers n and k (1 ≀ n ≀ 100 000, 0 ≀ k ≀ n) β€” the length of the string and the maximum number of characters to change. The second line contains the string, consisting of letters 'a' and 'b' only. Output Print the only integer β€” the maximum beauty of the string Vasya can achieve by changing no more than k characters. Examples Input 4 2 abba Output 4 Input 8 1 aabaabaa Output 5 Note In the first sample, Vasya can obtain both strings "aaaa" and "bbbb". In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa". Submitted Solution: ``` n, k = [int(i) for i in input().split()] s = input() def beauty (x): ret = 0 cnt = 0 r = 0 for l in range(n): while r < n and (cnt < k or s[r] != x): if s[r] == x: cnt += 1 r += 1 if r == x: cnt -= 1 ret = max(ret, r-l) return ret print(max(beauty('a'), beauty('b'))) exit(0) ``` No
104,090
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Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` s = input() n = len(s) max_palin = [[0 for i in range(n + 1)] for j in range(n + 1)] count = [0 for i in range(n + 1)] for sub_len in range(1, n + 1): for left in range(0, n - sub_len + 1): right = left + sub_len - 1 if sub_len == 1: max_palin[left][right] = 1 elif sub_len == 2: if s[left] == s[right]: max_palin[left][right] = 2 else: max_palin[left][right] = 0 else: if s[left] == s[right] and max_palin[left + 1][right - 1] > 0: mid = (left + right) // 2 if sub_len % 2 == 0: max_palin[left][right] = max_palin[left][mid] + 1 else: max_palin[left][right] = max_palin[left][mid - 1] + 1 count[max_palin[left][right]] += 1 for i in range(n - 1, 0, -1): count[i] += count[i + 1] for i in range(1, n + 1): print(count[i], end=' ') print() ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` class HString: def __init__(self, string, base=257, modulo=1000000007): self.__base, self.__modulo = base, modulo self.__prefix_hash, self.__base_pow, self.__size = [], [1], 0 self += string def __add__(self, string): for ch in string: self.__base_pow.append((self.__base_pow[-1] * self.__base) % self.__modulo) if self.__size == 0: self.__prefix_hash.append(ord(ch)) else: self.__prefix_hash.append((self.__prefix_hash[-1] * self.__base + ord(ch)) % self.__modulo) self.__size += 1 return self def size(self): return self.__size def getModulo(self): return self.__modulo def getHashValue(self, st, en): value = self.__prefix_hash[en] if st > 0: value -= ((self.__prefix_hash[st-1] * self.__base_pow[en-st+1]) % self.__modulo) if value < 0: value += self.__modulo return value def palindromic_characteristics(s): n, org, rev = len(s), HString(s), HString(s[::-1]) palindrome_level = [[0 for _ in range(n)] for _ in range(n)] palindrome_level_count = [0 for _ in range(n + 1)] for i in range(n): for j in range(i, n): if org.getHashValue(i, j) == rev.getHashValue(n-1-j, n-1-i): mid = (i + j) // 2 + (i + j) % 2 if i > mid-1: palindrome_level[i][j] = 1 else: palindrome_level[i][j] = palindrome_level[i][mid-1] + 1 palindrome_level_count[palindrome_level[i][j]] += 1 for i in range(n-1, 0, -1): palindrome_level_count[i] += palindrome_level_count[i+1] return palindrome_level_count[1:] s = input() print(' '.join(map(str, palindromic_characteristics(s)))) ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` def PanlidromicCharacteristics(string): n = len(string) res = [[0 for i in range (n)] for j in range (n)] count = [0 for i in range (n + 1)] # for i in range (n): # res[i][i] = 1 # count[1] += 1 for length in range (1, n + 1): for i in range (n-length + 1): j = i + length - 1 if length == 1: res[i][j] = 1 elif length == 2 and string[i] == string[j]: res[i][j] = 2 elif string[i] == string[j] and res[i + 1][j - 1] > 0: res[i][j] = res[i][i + length//2 - 1] + 1 count[res[i][j]] += 1 # k-palindrome is also a (k - 1)-palindrome for i in range (len(count) - 1, 0, -1): count[i - 1] += count[i] for i in range (1, len(count)): print(count[i], end = " ") return string = input() PanlidromicCharacteristics(string) ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` s = input() n = len(s) isPalindrome = [[False for i in range(n)] for i in range(n)] for i in range(n): isPalindrome[i][i] = True for i in range(n - 1, -1, -1): for j in range(i + 1, n): if (s[i] == s[j] and (i + 1 == j or isPalindrome[i + 1][j - 1] == True)): isPalindrome[i][j] = True degreePalindrome = [[0 for i in range(n)] for i in range(n)] #degreePalindrome[i][j] = degreePalindrome[i][mid] + 1 res = [0] * (n + 1) for i in range(n): for j in range(i, n): if (i == j): degreePalindrome[i][j] = 1 elif isPalindrome[i][j]: mid = (i + j - 1) // 2 degreePalindrome[i][j] = degreePalindrome[i][mid] + 1 res[degreePalindrome[i][j]] += 1 for i in range( n - 2, 0, -1): res[i] += res[i + 1] print(*res[1::]) ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` s = input() n = len(s) dp = [[0 for i in range(n - le + 1)] for le in range(n + 1)] ans = [0 for i in range(n + 1)] for le in range(1, n + 1): for l in range(0, n - le + 1): r = l + le if s[l] != s[r - 1]: continue if le == 1: dp[1][l] = 1 ans[1] += 1 elif le == 2: ans[2] += 1 dp[2][l] = 2 elif dp[le - 2][l + 1]: v = 1 m = (l + r) // 2 st = m + 1 if le & 1 else m le2 = m - l q = dp[le2][l] if q: v = q + 1 ans[v] += 1 dp[le][l] = v for i in range(n - 1, 0, -1): ans[i] += ans[i + 1] print(*ans[1:]) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` s = input() size = len(s) dp = [[0 for l in range(size)] for li in range(size)] ans = [0]*(size+1) for i in range(1, size+1): if i == 1: for j in range(0, size): dp[j][j] = 1 ans[1] += 1 elif i == 2: for j in range(0, size-1): if s[j+1] == s[j]: dp[j][j+1] = 2 ans[1] += 1 ans[2] += 1 else: dp[j][j+1] = 0 else: for j in range(0, size-i+1): if s[j] != s[j+i-1] or dp[j+1][j+i-2] == 0: dp[j][j+i-1] = 0 else: dp[j][j+i-1] = dp[j][int((j+j+i-2)/2)] + 1 for p in range(1, dp[j][j+i-1]+1): ans[p] += 1 for i in range(1, size): print(ans[i], end="") print(" ", end="") print(ans[size]) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` def main(): s = input() n = len(s) isPalindrome = [[False for i in range(n + 1)] for i in range(n + 1)] for i in range(n): isPalindrome[i][i] = True for i in range(n - 1, -1, -1): for j in range(i + 1, n): if (s[i] == s[j] and (i + 1 == j or isPalindrome[i + 1][j - 1] == True)): isPalindrome[i][j] = True degreePalindrome = [[0 for i in range(n)] for i in range(n)] #degreePalindrome[i][j] = degreePalindrome[i][mid] + 1 res = [0] * (n + 1) for i in range(n): for j in range(i, n): if (i == j): degreePalindrome[i][j] = 1 elif isPalindrome[i][j]: mid = (i + j - 1) // 2 degreePalindrome[i][j] = degreePalindrome[i][mid] + 1 res[degreePalindrome[i][j]] += 1 for i in range( n - 2, 0, -1): res[i] += res[i + 1] print(*res[1::]) if __name__ == "__main__": main() ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Tags: brute force, dp, hashing, strings Correct Solution: ``` s = input() dp = [[0]*5005 for _ in range(5005)] n = len(s) ans = [0 for _ in range(5005)] for length in range(1,n+1): for l in range(n-length+1): r = l+length if(length == 1): dp[l][r] = 1 continue elif(length == 2): dp[l][r] = 2 if(s[l] == s[r-1]) else 0 continue if(s[l] != s[r-1] or dp[l+1][r-1] == 0): continue dp[l][r] = 1 m = (l+r) // 2 if(length&1): if(dp[l][m] and dp[m+1][r]): dp[l][r] = dp[l][m]+1 else: if(dp[l][m] and dp[m][r]): dp[l][r] = dp[l][m]+1 for length in range(1,n+1): for l in range(n-length+1): ans[dp[l][l+length]] += 1 for i in range(n-1,0,-1): ans[i] += ans[i+1] for i in range(1,n+1): print(ans[i],end=' ') print() ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Submitted Solution: ``` class HString: def __init__(self, string, base=257, modulo=1000000007): self.__base, self.__modulo = base, modulo self.__prefix_hash, self.__base_pow, self.__size = [], [1], 0 self += string def __add__(self, string): for ch in string: self.__base_pow.append((self.__base_pow[-1] * self.__base) % self.__modulo) if self.__size == 0: self.__prefix_hash.append(ord(ch)) else: self.__prefix_hash.append((self.__prefix_hash[-1] * self.__base + ord(ch)) % self.__modulo) self.__size += 1 return self def size(self): return self.__size def getModulo(self): return self.__modulo def getHashValue(self, st, en): value = self.__prefix_hash[en] if st > 0: value -= ((self.__prefix_hash[st-1] * self.__base_pow[en-st+1]) % self.__modulo) if value < 0: value += self.__modulo return value def palindromic_characteristics(s): n, org, rev = len(s), HString(s), HString(s[::-1]) palindrome_level = [[0 for _ in range(n)] for _ in range(n)] palindrome_level_count = [0 for _ in range(n + 1)] i, j = 0, 0 while i < n: j = i while j < n: if org.getHashValue(i, j) == rev.getHashValue(n-1-j, n-1-i): mid = (i + j) // 2 + (i + j) % 2 if i > mid-1: palindrome_level[i][j] = 1 else: palindrome_level[i][j] = palindrome_level[i][mid-1] + 1 palindrome_level_count[palindrome_level[i][j]] += 1 j += 1 i += 1 for i in range(n-1, 0, -1): palindrome_level_count[i] += palindrome_level_count[i+1] return palindrome_level_count[1:] s = input() print(' '.join(map(str, palindromic_characteristics(s)))) ``` Yes
104,144
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Submitted Solution: ``` s = input() n = len(s) max_palin = [[0 for i in range(n + 1)] for j in range(n + 1)] count = [0 for i in range(n + 1)] for sub_len in range(1, n + 1): for left in range(0, n - sub_len + 1): right = left + sub_len - 1 if sub_len == 1: max_palin[left][right] = 1 elif sub_len == 2: if s[left] == s[right]: max_palin[left][right] = 2 else: max_palin[left][right] = 0 else: if s[left] == s[right] and max_palin[left + 1][right - 1] > 0: max_palin[left][right] = max_palin[left][left + sub_len // 2 - 1] + 1 count[max_palin[left][right]] += 1 for i in range(n - 1, 0, -1): count[i] += count[i + 1] for i in range(1, n + 1): print(count[i], end=' ') print() ``` Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Submitted Solution: ``` def main(): s = input() n = len(s) dp = [[0 for i in range(n + 1)] for j in range(n + 1)] count = [0 for i in range(n + 1)] for sub_len in range(1, n + 1): for left in range(0, n - sub_len + 1): right = left + sub_len - 1 if sub_len == 1: dp[left][right] = 1 elif sub_len == 2: if s[left] == s[right]: dp[left][right] = 2 else: if s[left] == s[right] and dp[left + 1][right - 1] > 0: dp[left][right] = dp[left][left + sub_len // 2 - 1] + 1 count[dp[left][right]] += 1 for i in range(n - 1, 0, -1): count[i] += count[i + 1] for i in range(1, n + 1): print(count[i], end=' ') print() if __name__ == "__main__": main() ``` Yes
104,146
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Submitted Solution: ``` P = 311 # we use two mods to reduce the chance of collision MOD1 = int(1e9) + 7 MOD2 = int(1e9) + 9 def main(): s = input() n = len(s) # Pre-compute power_1 = [0 for i in range(n + 1)] power_2 = [0 for i in range(n + 1)] mod_inv_1 = [0 for i in range(n + 1)] mod_inv_2 = [0 for i in range(n + 1)] power_1[0] = 1 power_2[0] = 1 mod_inv_1[0] = 1 mod_inv_2[0] = 1 for i in range(1, n + 1): power_1[i] = power_1[i - 1] * P % MOD1 power_2[i] = power_2[i - 1] * P % MOD1 mod_inv_1[i] = bin_exp(power_1[i], MOD1 - 2, MOD1) mod_inv_2[i] = bin_exp(power_2[i], MOD2 - 2, MOD2) # Compute hash values hash_1 = 0 hash_2 = 0 forward_hash_1 = [0 for i in range(n + 1)] forward_hash_2 = [0 for i in range(n + 1)] for i in range(1, n + 1): hash_1 += ord(s[i - 1]) * power_1[i] hash_2 += ord(s[i - 1]) * power_2[i] hash_1 %= MOD1 hash_2 %= MOD2 forward_hash_1[i] = hash_1 forward_hash_2[i] = hash_2 hash_1 = 0 hash_2 = 0 backward_hash_1 = [0 for i in range(n + 1)] backward_hash_2 = [0 for i in range(n + 1)] for i in range(1, n + 1): hash_1 += ord(s[n - i]) * power_1[i] hash_2 += ord(s[n - i]) * power_2[i] hash_1 %= MOD1 hash_2 %= MOD2 backward_hash_1[i] = hash_1 backward_hash_2[i] = hash_2 dp = [[0 for i in range(n + 1)] for j in range(n + 1)] count = [0 for i in range(n + 1)] for sub_len in range(1, n + 1): for left in range(0, n - sub_len + 1): right = left + sub_len - 1 if sub_len == 1: dp[left][right] = 1 elif sub_len == 2: if s[left] == s[right]: dp[left][right] = 2 else: if s[left] == s[right] and dp[left + 1][right - 1] > 0: dp[left][right] = dp[left][left + sub_len // 2 - 1] + 1 count[dp[left][right]] += 1 for i in range(n - 1, 0, -1): count[i] += count[i + 1] for i in range(1, n + 1): print(count[i], end=' ') print() def bin_exp(a, x, mod): res = 1 while x > 0: if x & 1: res *= a res %= mod a *= a a %= mod x >>= 1 return res def get_forward_hash(forward_hash, mod_inv, left, right, mod): return (forward_hash[right + 1] - forward_hash[left] + mod) * mod_inv[left] % mod def get_backward_hash(backward_hash, mod_inv, n, left, right): r_left = n - left - 1 r_right = n - right - 1 return (backward_hash[r_left + 1] - backward_hash[r_right] + mod) * mod_inv[r_right] % mod if __name__ == "__main__": main() ``` Yes
104,147
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Submitted Solution: ``` def palh(s): if s[:(len(s)//2)]==s[-(len(s)//2):]: return palh(s[:(len(s)//2)])+1 else: return 0 S=input() N=len(S) R=[0 for i in range(N+1)] for l in range(0, N): for r in range(l+1, N): for i in range(0, palh(S[l:r])+1): R[i]+=1 print(*R[:-1]) ``` No
104,148
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0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes. A string is 1-palindrome if and only if it reads the same backward as forward. A string is k-palindrome (k > 1) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty (k - 1)-palindromes. The left half of string t is its prefix of length ⌊|t| / 2βŒ‹, and right half β€” the suffix of the same length. ⌊|t| / 2βŒ‹ denotes the length of string t divided by 2, rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. Input The first line contains the string s (1 ≀ |s| ≀ 5000) consisting of lowercase English letters. Output Print |s| integers β€” palindromic characteristics of string s. Examples Input abba Output 6 1 0 0 Input abacaba Output 12 4 1 0 0 0 0 Note In the first example 1-palindromes are substring Β«aΒ», Β«bΒ», Β«bΒ», Β«aΒ», Β«bbΒ», Β«abbaΒ», the substring Β«bbΒ» is 2-palindrome. There are no 3- and 4-palindromes here. Submitted Solution: ``` s = input() size = len(s) dp = [[0 for l in range(size)] for l in range(size)] ans = [0]*(size+1) for i in range(1, size+1): if i == 1: for j in range(0, size): dp[j][j] = 1 ans[1] += 1 elif i == 2: for j in range(0, size-1): if s[j+1] == s[j]: dp[j][j+1] = 2 ans[1] += 1 ans[2] += 1 else: dp[j][j+1] = 0 else: for j in range(0, size-i+1): if s[j] != s[j+i-1] or dp[j+1][j+i-2] == 0: dp[j][j+i-1] = 0 else: dp[j][j+i-1] = dp[j][int((j+j+i-2)/2)] + 1 ans[dp[j][j+i-1]] += 1 for i in range(1, size): print(ans[i], end="") print(" ", end="") print(ans[size]) ``` No
104,149
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0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Suppose you have two strings s and t, and their length is equal. You may perform the following operation any number of times: choose two different characters c1 and c2, and replace every occurence of c1 in both strings with c2. Let's denote the distance between strings s and t as the minimum number of operations required to make these strings equal. For example, if s is abcd and t is ddcb, the distance between them is 2 β€” we may replace every occurence of a with b, so s becomes bbcd, and then we may replace every occurence of b with d, so both strings become ddcd. You are given two strings S and T. For every substring of S consisting of |T| characters you have to determine the distance between this substring and T. Input The first line contains the string S, and the second β€” the string T (1 ≀ |T| ≀ |S| ≀ 125000). Both strings consist of lowercase Latin letters from a to f. Output Print |S| - |T| + 1 integers. The i-th of these integers must be equal to the distance between the substring of S beginning at i-th index with length |T| and the string T. Example Input abcdefa ddcb Output 2 3 3 3 Submitted Solution: ``` class UnionFind: def __init__(self, n): self.parent = [-1] * n self.cnt = n def root(self, x): if self.parent[x] < 0: return x else: self.parent[x] = self.root(self.parent[x]) return self.parent[x] def merge(self, x, y): x = self.root(x) y = self.root(y) if x == y: return if self.parent[x] > self.parent[y]: x, y = y, x self.parent[x] += self.parent[y] self.parent[y] = x self.cnt -= 1 def is_same(self, x, y): return self.root(x) == self.root(y) def get_cnt(self): return self.cnt s = [ord(char) - 97 for char in input()] t = [ord(char) - 97 for char in input()][::-1] s_ = [0] * 6 t_ = [0] * 6 st = [[0] * 6 for _ in range(6)] for i, val in enumerate(s): s_[val] |= 1 << i for i, val in enumerate(t): t_[val] |= 1 << i for ind_s in range(6): for ind_t in range(6): if ind_s == ind_t: continue st[ind_s][ind_t] = bin(s_[ind_s] * t_[ind_t])[2:][::-1] + "0" * (len(s) + len(t) + 100) length = len(t) - 1 ans = [] for i in range(len(s) - len(t) + 1): shift = length + i uf = UnionFind(6) for ind_s in range(6): for ind_t in range(6): if ind_s == ind_t: continue if st[ind_s][ind_t][shift] == "1": uf.merge(ind_s, ind_t) ans.append(6 - uf.get_cnt()) print(*ans) ``` No
104,168
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0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Suppose you have two strings s and t, and their length is equal. You may perform the following operation any number of times: choose two different characters c1 and c2, and replace every occurence of c1 in both strings with c2. Let's denote the distance between strings s and t as the minimum number of operations required to make these strings equal. For example, if s is abcd and t is ddcb, the distance between them is 2 β€” we may replace every occurence of a with b, so s becomes bbcd, and then we may replace every occurence of b with d, so both strings become ddcd. You are given two strings S and T. For every substring of S consisting of |T| characters you have to determine the distance between this substring and T. Input The first line contains the string S, and the second β€” the string T (1 ≀ |T| ≀ |S| ≀ 125000). Both strings consist of lowercase Latin letters from a to f. Output Print |S| - |T| + 1 integers. The i-th of these integers must be equal to the distance between the substring of S beginning at i-th index with length |T| and the string T. Example Input abcdefa ddcb Output 2 3 3 3 Submitted Solution: ``` import sys input = sys.stdin.readline class UnionFind: def __init__(self, n): self.parent = [-1] * n self.cnt = n def root(self, x): if self.parent[x] < 0: return x else: self.parent[x] = self.root(self.parent[x]) return self.parent[x] def merge(self, x, y): x = self.root(x) y = self.root(y) if x == y: return if self.parent[x] > self.parent[y]: x, y = y, x self.parent[x] += self.parent[y] self.parent[y] = x self.cnt -= 1 def is_same(self, x, y): return self.root(x) == self.root(y) def get_cnt(self): return self.cnt s = [ord(char) - 97 for char in input()[:-1]] t = [ord(char) - 97 for char in input()[:-1]][::-1] s_ = [0] * 6 t_ = [0] * 6 st = [[0] * 6 for i in range(6)] for i, val in enumerate(s): s_[val] |= 1 << i for i, val in enumerate(t): t_[val] |= 1 << i for ind_s in range(6): for ind_t in range(6): if ind_s == ind_t: continue st[ind_s][ind_t] = bin(s_[ind_s] * t_[ind_t])[2:][::-1] + "0" * (len(s) + len(t)) length = len(t) - 1 ans = [] for i in range(len(s) - len(t) + 1): shift = length + i uf = UnionFind(6) for ind_s in range(6): for ind_t in range(6): if ind_s == ind_t: continue if st[ind_s][ind_t][shift] == "1": uf.merge(ind_s, ind_t) ans.append(6 - uf.get_cnt()) print(*ans) ``` No
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0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Suppose you have two strings s and t, and their length is equal. You may perform the following operation any number of times: choose two different characters c1 and c2, and replace every occurence of c1 in both strings with c2. Let's denote the distance between strings s and t as the minimum number of operations required to make these strings equal. For example, if s is abcd and t is ddcb, the distance between them is 2 β€” we may replace every occurence of a with b, so s becomes bbcd, and then we may replace every occurence of b with d, so both strings become ddcd. You are given two strings S and T. For every substring of S consisting of |T| characters you have to determine the distance between this substring and T. Input The first line contains the string S, and the second β€” the string T (1 ≀ |T| ≀ |S| ≀ 125000). Both strings consist of lowercase Latin letters from a to f. Output Print |S| - |T| + 1 integers. The i-th of these integers must be equal to the distance between the substring of S beginning at i-th index with length |T| and the string T. Example Input abcdefa ddcb Output 2 3 3 3 Submitted Solution: ``` class UnionFind: def __init__(self, n): self.parent = [-1] * n self.cnt = n def root(self, x): if self.parent[x] < 0: return x else: self.parent[x] = self.root(self.parent[x]) return self.parent[x] def merge(self, x, y): x = self.root(x) y = self.root(y) if x == y: return if self.parent[x] > self.parent[y]: x, y = y, x self.parent[x] += self.parent[y] self.parent[y] = x self.cnt -= 1 def is_same(self, x, y): return self.root(x) == self.root(y) def get_cnt(self): return self.cnt s = [ord(char) - 97 for char in input()] t = [ord(char) - 97 for char in input()][::-1] s_ = [0] * 6 t_ = [0] * 6 st = [[0] * 6 for _ in range(6)] for i, val in enumerate(s): s_[val] |= 1 << i for i, val in enumerate(t): t_[val] |= 1 << i for ind_s in range(6): for ind_t in range(6): if ind_s == ind_t: continue st[ind_s][ind_t] = bin(s_[ind_s] * t_[ind_t])[2:][::-1] + "0" * (len(s) + len(t) + 100) length = len(t) - 1 ans = [] for i in range(len(s) - len(t) + 1): shift = length + i uf = UnionFind(6) for ind_s in range(6): for ind_t in range(6): if ind_s == ind_t: continue if st[ind_s][ind_t][shift] == "1": uf.merge(ind_s, ind_t) ans.append(6 - uf.get_cnt()) if len(s) > 100: print(len(s)) print(len(t)) print(*ans) ``` No
104,170
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` """ NTC here """ from sys import stdin # import threading # setrecursionlimit(10**6) # threading.stack_size(2**26) def iin(): return int(stdin.readline()) def lin(): return list(map(int, stdin.readline().split())) # range = xrange # input = raw_input md=10**9+7 def main(): t=iin() while t: t-=1 x=iin() s=list(input()) l=len(s) ans=l i=0 while i<x: i+=1 ch=int(s[i-1]) ans=(i+ch*(ans-i))%md if l>=x:continue incr=l ss=[] for _ in range(ch): for j in range(i,l): if incr<ans and incr<x: ss.append(s[j]) incr+=1 else: break l=incr for k in ss:s.append(k) #print(ans, l, s) print(ans%md) main() #threading.Thread(target=main).start() ```
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` M = int(1e9+7) n = int(input()) while n>0: n -= 1 x = int(input()) s = input() idx = 0 length = len(s) while length < x: t = ord(s[idx])-ord('1') s += s[idx+1:]*t length += (length-idx-1)*t idx += 1 while idx != x: t = ord(s[idx])-ord('1') length += ((length-idx-1)*t)%M idx += 1 print(length%M) ```
104,540
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` for _ in range(int(input())): x = int(input()) s = list(input()) l = 0 ans = len(s) while(l<x): if(ans>=x): break temp = len(s) ans+=(int(s[l])-1)*(temp-l-1) for i in range(int(s[l])-1): if(len(s)>x): break for j in range(l+1,temp): s.append(s[j]) if(len(s)>x): break l+=1 while(l<x): temp = ans ans+=(int(s[l])-1)*(temp-l-1) ans = ans%(10**9+7) l+=1 print(ans) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` M = 1000000007 t = int(input()) while t: t += -1 x = int(input()) s = input() i = 0 while len(s) < x: s += s[i + 1: ] * (int(s[i]) - 1) i += 1 n = len(s) for j in range(i, x): tmp = n - (j + 1) n = j + 1 + tmp * (int(s[j])) n = n % M print(n % M) ```
104,542
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` def main(): TT = int(input()) for _ in range(TT): x = int(input()) s = [int(c) for c in input().strip()] ans = len(s) for l in range(0, x): ans += (ans - l - 1) * (s[l] - 1) ans %= 1000000007 end = len(s) for _ in range(1, s[l]): if len(s) > x + 1: break for c in range(l + 1, end): if len(s) > x + 1: break s.append(s[c]) print(ans) if __name__ == '__main__': main() ```
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` ttt = int(input()) mod = 10**9 + 7 s = "#"*(10**6 + 1500) s=list(s) for bo in range(ttt): x=int(input()) st=input() s[1:len(st)+1]=list(st) siz=len(st) p = 0 while siz < x: p += 1 whe = siz for de4d in range(int(s[p])-1): for k in range(p+1,whe+1): siz += 1 s[siz] = s[k] if (siz>x): break if (siz>x): break if (siz>x): break ans = len(st) for i in range(1,x+1): ans = i + (ans-i)*int(s[i]) ans = ans%mod print(ans) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` t = int(input()) ans = [] arr = [None] * (10 ** 6) cur = 0 MOD = 10 ** 9 + 7 for _ in range(t): x, s = int(input()), list(map(int, str(input()))) max_p = cur + x for i in range(cur, min(max_p, cur + len(s))): arr[i] = s[i - cur] def copy(start, length, times): b = start + length for i in range(times): for j in range(length): if b >= max_p: return arr[b] = arr[start + j] b += 1 val = len(s) cnt = 1 while x: if arr[max_p - 1] is None and arr[cur] > 1: copy(cur + 1, val - cnt, arr[cur] - 1) val = (cnt + (val - cnt) * arr[cur]) % MOD cnt += 1 cur += 1 x -= 1 ans.append(val) for a in ans: print(a) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Tags: implementation, math Correct Solution: ``` def solve(s,x): n = len(s) mod = 10**9 + 7 for i in range(x): n += (n-i-1)*(int(s[i])-1) n %= mod if len(s) < x: s += s[i+1:]*(int(s[i])-1) return n for _ in range(int(input())): x = int(input()) s = input() print(solve(s,x)) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` for _ in range(int(input())): x=int(input()) a=input() l=len(a) a=[i for i in a] ans=l p=0 m=10**9+7 while ans<x: for j in range(int(a[p])-1): for i in range(p+1,ans): a.append(a[i]) ans+=(int(a[p])-1)*((ans-p-1+m)%m) p+=1 for j in range(p,x): ans+=(int(a[j])-1)*((ans-j-1+m)%m) ans%=m print(ans) ``` Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` #TLE # import sys, os.path # import math # from collections import defaultdict,deque # input = sys.stdin.readline # I = lambda : list(map(int,input().split())) # S = lambda : list(map(str,input())) # def main(): # # s1 = [0]*((2*(10**6))+1) # t,=I() # for t1 in range(t): # x, = I() # s1 = str(input()).rstrip('\n') # # for i in range(len(s2)): # # s1[i] = int(s2[i]) # l = 0 # count = 0 # count1 = len(s1) # count1%=((10**9)+7) # for i in range(x): # k = int(s1[i]) # count1-=1 # count1%=((10**9)+7) # if count1>x: # count1*=k # count1%=((10**9)+7) # else: # l1 = len(s1) # for j in range(k-1): # for l in range(i+1,l1): # s1+=s1[l] # count1*=k # count1%=((10**9)+7) # count1+=x # count1%=((10**9)+7) # print(count1) # main() # import sys, os.path import math from collections import defaultdict,deque input = sys.stdin.readline I = lambda : list(map(int,input().split())) S = lambda : list(map(str,input())) def main(): # s1 = [0]*((2*(10**6))+1) t,=I() for t1 in range(t): x, = I() s2 = str(input()).rstrip('\n') s1 = [] for i in range(len(s2)): if i>x: break s1.append(int(s2[i])) count1 = len(s2) count1%=((10**9)+7) for i in range(x): k = int(s1[i]) count1-=1 count1%=((10**9)+7) if len(s1)>x: count1*=k count1%=((10**9)+7) else: if k==1: continue X = s1[i+1:] l1 = len(s1) for j in range(k-1): if len(s1)<x: s1.extend(X) count1*=k count1%=((10**9)+7) count1+=x count1%=((10**9)+7) print(count1) main() # import sys # input = sys.stdin.readline # mod = 10 ** 9 + 7 # t = int(input()) # for _ in range(t): # x = int(input()) # s = input().rstrip('\n') # X = [] # for i, si in enumerate(s): # if i == x: # break # X.append(int(s[i])) # ans = len(s) # for i in range(x): # ans = (ans + (ans - i - 1) * (X[i] - 1)) % mod # if len(X) < x: # if X[i] == 1: # continue # X_ = X[i + 1:] # for j in range(X[i] - 1): # if len(X) < x: # X.extend(X_) # print(ans) ``` Yes
104,548
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` import time import sys MOD = 1e9 + 7 # f = open('test.txt', 'w+') # f.write("1\n333047\n") # f.write('1'*300 + '2' + '1'*20 + '2') # f.seek(0) f = sys.stdin t1 = time.time() for t in range(int(f.readline())): x, s = int(f.readline().rstrip()), f.readline().rstrip() i = 0 while len(s) < x: i += 1 s += s[i:] * (int(s[i - 1])-1) answer = len(s) while i < x: i += 1 answer = (answer + (answer - i) * (int(s[i - 1]) - 1)) % MOD print(int(answer)) # print("--- %s seconds ---" % (time.time() - t1)) ``` Yes
104,549
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` import sys T = int(sys.stdin.readline().strip()) for _ in range(T): x = int(sys.stdin.readline().strip()) s = list(sys.stdin.readline().strip()) ls = len(s) for l in range(x): t = ord(s[l]) - ord('0') - 1 ls = (ls + (ls - l - 1)*t) % ((10**9)+7) e = len(s) while len(s) <= x and t > 0: s += s[l+1:e] t -= 1 print(ls) ``` Yes
104,550
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` t=int(input()) for i in range(t): x=int(input()) s=input() p=s l=0 while(l!=x): r=int(p[0]) p=p[1:] if r>1: p+=p if r>2: p+=p if (len(p)+l+1)>=x: l+=1 break l+=1 j=0 res=l y=len(p) while(l!=x): y-=1 y=y*int(p[j]) l+=1 res+=1 j+=1 print((res+y)%(10**9+7)) ``` No
104,551
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` for _ in range(int(input())): x = int(input()) s = list(map(int, input())) ans = len(s) for i in range(1, x+1): ans = (i + (ans-i) * s[i-1])%1000000007 for _ in range(s[i-1]-1): if len(s) < x: s += s[i:] else: break print(ans) ``` No
104,552
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` t=int(input()) for i in range(t): x=int(input()) y=input() s=[] for j in y: s.append(j) l=0 res=len(s) while(l!=x): if len(s)<x: for p in range(int(s[l])-1): for j in range(l + 1, len(s)): s.append(s[j]) res=(res+(res-l-1)*(int(s[l])-1))%(10**9+7) l+=1 print(res%(10**9+7)) ``` No
104,553
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i. There is one cursor. The cursor's location β„“ is denoted by an integer in \{0, …, |s|\}, with the following meaning: * If β„“ = 0, then the cursor is located before the first character of s. * If β„“ = |s|, then the cursor is located right after the last character of s. * If 0 < β„“ < |s|, then the cursor is located between s_β„“ and s_{β„“+1}. We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor. We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions: * The Move action. Move the cursor one step to the right. This increments β„“ once. * The Cut action. Set c ← s_right, then set s ← s_left. * The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c. The cursor initially starts at β„“ = 0. Then, we perform the following procedure: 1. Perform the Move action once. 2. Perform the Cut action once. 3. Perform the Paste action s_β„“ times. 4. If β„“ = x, stop. Otherwise, return to step 1. You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7. It is guaranteed that β„“ ≀ |s| at any time. Input The first line of input contains a single integer t (1 ≀ t ≀ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases. The first line of each test case contains a single integer x (1 ≀ x ≀ 10^6). The second line of each test case consists of the initial string s (1 ≀ |s| ≀ 500). It is guaranteed, that s consists of the characters "1", "2", "3". It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that β„“ ≀ |s| at any time. Output For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7. Example Input 4 5 231 7 2323 6 333 24 133321333 Output 25 1438 1101 686531475 Note Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, β„“ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above: * Step 1, Move once: we get β„“ = 1. * Step 2, Cut once: we get s = 2 and c = 31. * Step 3, Paste s_β„“ = 2 times: we get s = 23131. * Step 4: β„“ = 1 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 2. * Step 2, Cut once: we get s = 23 and c = 131. * Step 3, Paste s_β„“ = 3 times: we get s = 23131131131. * Step 4: β„“ = 2 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 3. * Step 2, Cut once: we get s = 231 and c = 31131131. * Step 3, Paste s_β„“ = 1 time: we get s = 23131131131. * Step 4: β„“ = 3 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 4. * Step 2, Cut once: we get s = 2313 and c = 1131131. * Step 3, Paste s_β„“ = 3 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 4 not= x = 5, so we return to step 1. * Step 1, Move once: we get β„“ = 5. * Step 2, Cut once: we get s = 23131 and c = 13113111311311131131. * Step 3, Paste s_β„“ = 1 times: we get s = 2313113113111311311131131. * Step 4: β„“ = 5 = x, so we stop. At the end of the procedure, s has length 25. Submitted Solution: ``` import sys import math from collections import defaultdict,Counter,deque # input=sys.stdin.readline # def print(x): # sys.stdout.write(str(x)+"\n") import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # sys.stdout=open("CP2/output.txt",'w') # sys.stdin=open("CP2/input.txt",'r') mod=pow(10,9)+7 t=int(input()) for i in range(t): x=int(input()) s=list(map(int,input())) cur=0 ans=0 tot=len(s)-1 while cur<x: tot=(s[cur]*tot)%mod if len(s)<x: s+=s[cur+1:]*(s[cur]-1) else: # print(len(s)) if cur+1+tot>=mod: ans=cur+1+tot-mod else: ans=cur+1+tot if tot==0: tot=10**9-1 else: tot-=1 cur+=1 print(len(s)) print(ans) ``` No
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` import math import sys for _ in range(int(input())): n,m=(map(int,sys.stdin.readline().split())) k=n-m p=m+1 c=(k//p) ans=(n*(n+1))//2 rem=k%p ans1=(rem*((c+1)*(c+2)))//2 ans2=0 ans2=(c*(c+1)*(p-rem))//2 print(ans-ans1-ans2) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` import sys input = sys.stdin.readline t = int(input()) C = [list(map(int,input().split())) for i in range(t)] # ANS = [0] * t # t = 10**5 # C = [[523422132331, 102342223434] for i in range(t)] def c(x, y): if x % 2 == 0: return (x//2) * y else: return (y//2) * x for i in range(t): n = C[i][0] o = C[i][1] z = n-o al = c(n, (n-1)) + n # print("al",al) if z-1 <= o: print(al - z) # ANS[i] = al-z # v=0 else: a = z // (o+1) b = z % (o+1) # print(a,b) mi = c((a+1), (a+2)) * b + c(a, (a+1)) * (o+1-b) print(al - mi) # ANS[i] = al-mi # for i in ANS: # print(i) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` import sys input=sys.stdin.readline for _ in range(int(input())): n,m=map(int,input().split()) grps=m+1 zeach=(n-m)//grps extras=(n-m)%grps print( (n*(n+1)//2)- (zeach*(zeach+1)//2)*grps -(extras)*(zeach+1) ) ```
104,557
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Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` import os import sys from io import BytesIO, IOBase from collections import Counter BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) def gcd(a, b): if a == 0: return b return gcd(b % a, a) def lcm(a, b): return (a * b) / gcd(a, b) def main(): for _ in range(int(input())): n,m=map(int, input().split()) ans=n*(n+1)//2 #print(ans) k=(n-m)//(m+1) f=k k=(n-m)%(m+1) ans-=(m+1-k)*(f*(f+1)//2) #print(ans) f+=1 ans-=(k)*(f*(f+1)//2) print(ans) return if __name__ == "__main__": main() ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` import sys input = sys.stdin.readline T = int(input()) for _ in range(T): n, m = list(map(int, input().split())) S = 0 x = (n - m) // (m + 1) z = (n - m) % (m + 1) S += (m + 1 - z) * (x * (x + 1)) // 2 S += z * (x + 1) * (x + 2) // 2 print(n * (n + 1) // 2 - S) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` """ // Author : snape_here - Susanta Mukherjee """ from __future__ import division, print_function import os,sys from io import BytesIO, IOBase if sys.version_info[0] < 3: from __builtin__ import xrange as range from future_builtins import ascii, filter, hex, map, oct, zip def ii(): return int(input()) def si(): return input() def mi(): return map(int,input().split()) def li(): return list(mi()) def gcd(x, y): while y: x, y = y, x % y return x def read(): sys.stdin = open('input.txt', 'r') sys.stdout = open('output.txt', 'w') import math mod=1000000007 def day(d, m, y): t = [ 0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4 ] y -= m < 3 return (( y + int(y / 4) - int(y / 100) + int(y / 400) + t[m - 1] + d) % 7) def isl(y): if y%400==0: return True elif y%4==0 and y%100!=0: return True return False def main(): for i in range(ii()): n,m=mi() if m==0: ans=0 else: tot=(n*(n+1))//2 s=(n-m)//(m+1) b=(m+1-(n-m)%(m+1))*s*(s+1)//2 + ((n-m)%(m+1))*(s+1)*(s+2)//2 ans=tot-b print(ans) # region fastio# BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") def print(*args, **kwargs): """Prints the values to a stream, or to sys.stdout by default.""" sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout) at_start = True for x in args: if not at_start: file.write(sep) file.write(str(x)) at_start = False file.write(kwargs.pop("end", "\n")) if kwargs.pop("flush", False): file.flush() if sys.version_info[0] < 3: sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout) else: sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # endregion if __name__ == "__main__": #read() main() #Comment read() ```
104,560
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Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` import sys inf = 1 << 64 def input(): return sys.stdin.readline().rstrip() def slv(): n, m = map(int, input().split()) u, v = divmod(n - m, m + 1) ans = n * (n + 1)//2 - v*(u + 1)*(u + 2)//2 - (m + 1 - v)*u*(u + 1)//2 print(ans) return t = int(input()) for i in range(t): slv() ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Tags: binary search, combinatorics, greedy, math, strings Correct Solution: ``` import sys input=sys.stdin.readline t=int(input()) for i in range(t): n,m=map(int,input().split()) zeros=n-m if zeros==0: print((n*(n+1))//2) else: div=zeros//(m+1) rem=zeros%(m+1) print(n*(n+1)//2-rem*(div+1)*(div+2)//2-(m+1-rem)*((div+1)*div)//2) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` from sys import stdin, stdout def total(k): return (k*(k+1)) // 2 ans = [] t= int(stdin.readline()) for line in stdin: n, m = tuple(map(int,line.split())) if m==0: ans.append( str(0) ) else: al = total(n) zeros = n-m #divide into m+1 groups k, extra = zeros//(m+1), zeros%(m+1) zero_blocks = extra*(k+1) + (m+1)*total(k) ans.append(str(al-zero_blocks)) stdout.write('\n'.join(ans)) ``` Yes
104,563
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` import sys lines = list(sys.stdin.readlines()) t = int(lines[0]) def count(x): return x * (x+1)//2 for i in range(t): n, ones = map(int, lines[i+1].split()) zeros = n - ones if zeros==0: print(count(n)) continue used_ones = min(ones, zeros-1) groups = used_ones+1 smal_size = zeros//groups larg_size = smal_size + 1 larg_count = zeros%groups total = count(n) total -= count(smal_size) * (groups-larg_count) total -= count(larg_size) * larg_count print(total) ``` Yes
104,564
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` import sys def fastio(): from io import StringIO from atexit import register global input sys.stdin = StringIO(sys.stdin.read()) input = lambda : sys.stdin.readline().rstrip('\r\n') sys.stdout = StringIO() register(lambda : sys.__stdout__.write(sys.stdout.getvalue())) fastio() for _ in range(int(input())): n,m=list(map(int,input().split())) l=n if m==0 else (n-2*m if m<=n//2 else 0) s1=n-m-l if l==n: print(0) else: p=(n-m)//(m+1);r=(n-m)%(m+1) k=(n*(n+1))//2-(m+1-r)*(p*(p+1)//2)-r*(p+1)*(p+2)//2 print(k) ``` Yes
104,565
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` # import sys # import math # from collections import defaultdict,Counter # input=sys.stdin.readline # def print(x): # sys.stdout.write(str(x)+"\n") import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # sys.stdout=open("CP3/output.txt",'w') # sys.stdin=open("CP3/input.txt",'r') # m=pow(10,9)+7 t=int(input()) for i in range(t): n,m=map(int,input().split()) if m==0: print(0) elif n-m<=m: print(n*(n+1)//2-(n-m)) else: d=n-m k=d//(m+1) d1=d%(m+1) print(n*(n+1)//2-(m+1)*(k*(k+1)//2)-(k+1)*d1) ``` Yes
104,566
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` import math def main(): num = int(input()) for _ in range(num): n, m = map(int, input().split()) if m == 0: print(0) continue b = n - m a = n // 2 if m == 1: d = math.ceil(n/2) ans = d ** 2 elif a < b: ans = n * (n + 1) // 2 d = math.ceil(n/2) amari = m - d ans -= amari * (amari + 1) * 2 + d else: ans = n * (n + 1) // 2 ans -= b print(ans) main() ``` No
104,567
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` def solve_c(): n = int(input()) for _ in range(n): c() def c(): n, m = [int(x) for x in input().split()] if m == 0: print(0) return if m == 1: print(2*n-2) else: print(n*(n+1)//2+m-n) solve_c() ``` No
104,568
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` # -*- coding: utf-8 -*- import bisect import heapq import math import random import sys from collections import Counter, defaultdict, deque from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal from functools import lru_cache, reduce from itertools import combinations, combinations_with_replacement, product, permutations from operator import add, mul, sub sys.setrecursionlimit(100000) input = sys.stdin.readline # -*- coding: utf-8 -*- sys.setrecursionlimit(100000) input = sys.stdin.readline INF = 2**62-1 def read_int(): return int(input()) def read_int_n(): return list(map(int, input().split())) def read_float(): return float(input()) def read_float_n(): return list(map(float, input().split())) def read_str(): return input().strip() def read_str_n(): return list(map(str, input().split())) def error_print(*args): print(*args, file=sys.stderr) def mt(f): import time def wrap(*args, **kwargs): s = time.time() ret = f(*args, **kwargs) e = time.time() error_print(e - s, 'sec') return ret return wrap def slv(N, M): if M == 0: return 0 if M == N: return ((N+1) * N ) // 2 ans = ((N+1) * N) // 2 r = N - M d = r // (M+1) e = r % (M+1) if d != 0: ans -= (((d+1) * d) // 2) * (M+1 - e) ans -= (((d-1) * d) // 2) * (e) else: ans -= r return ans def main(): T = read_int() for _ in range(T): N, M = read_int_n() print(slv(N, M)) if __name__ == "__main__": main() ``` No
104,569
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1". More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≀ l ≀ r ≀ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5). Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s). Mahmoud couldn't solve the problem so he asked you for help. Can you help him? Input The input consists of multiple test cases. The first line contains a single integer t (1 ≀ t ≀ 10^5) β€” the number of test cases. The description of the test cases follows. The only line for each test case contains two integers n, m (1 ≀ n ≀ 10^{9}, 0 ≀ m ≀ n) β€” the length of the string and the number of symbols equal to "1" in it. Output For every test case print one integer number β€” the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1". Example Input 5 3 1 3 2 3 3 4 0 5 2 Output 4 5 6 0 12 Note In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4. In the second test case, the string s with the maximum value is "101". In the third test case, the string s with the maximum value is "111". In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0. In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. Submitted Solution: ``` """ Author : thekushalghosh Team : CodeDiggers """ import sys,math input = sys.stdin.readline ############ ---- USER DEFINED INPUT FUNCTIONS ---- ############ def inp(): return(int(input())) def inlt(): return(list(map(int,input().split()))) def insr(): s = input() return(s[:len(s) - 1]) def invr(): return(map(int,input().split())) ################################################################ ############ ---- THE ACTUAL CODE STARTS BELOW ---- ############ t = 1 t = inp() def qw(n): return(n * (n + 1) // 2) for tt in range(t): n,m = invr() q = n - m if m == 0: print(0) continue ww = (n * (n + 1) // 2) w = q % ww qq = q // ww ww = ww - (w * qw(qq + 1)) - ((m + 1 - w) * qw(qq)) print(ww) ``` No
104,570
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Once Bob saw a string. It contained so many different letters, that the letters were marked by numbers, but at the same time each letter could be met in the string at most 10 times. Bob didn't like that string, because it contained repeats: a repeat of length x is such a substring of length 2x, that its first half coincides character by character with its second half. Bob started deleting all the repeats from the string. He does it as follows: while it's possible, Bob takes the shortest repeat, if it is not unique, he takes the leftmost one, and deletes its left half and everything that is to the left of this repeat. You're given the string seen by Bob. Find out, what it will look like after Bob deletes all the repeats in the way described above. Input The first input line contains integer n (1 ≀ n ≀ 105) β€” length of the string. The following line contains n space-separated integer numbers from 0 to 109 inclusive β€” numbers that stand for the letters of the string. It's guaranteed that each letter can be met in the string at most 10 times. Output In the first line output the length of the string's part, left after Bob's deletions. In the second line output all the letters (separated by a space) of the string, left after Bob deleted all the repeats in the described way. Examples Input 6 1 2 3 1 2 3 Output 3 1 2 3 Input 7 4 5 6 5 6 7 7 Output 1 7 Tags: greedy, hashing, string suffix structures Correct Solution: ``` def pow(x, exp, mod): res = 1 while exp: if exp & 1: res = (res * x) % mod x = (x * x) % mod exp >>= 1 return res MOD = 2 ** 121 - 1 M = int(1e9) + 1 n = int(input()) vals = list(map(int, input().split())) groups = dict() for i in range(n): groups.setdefault(vals[i], []).append(i) powsA = [1] for i in range(n): powsA.append((powsA[-1] * M) % MOD) hashes = [0] * (n + 1) for i in range(n): hashes[i + 1] = (hashes[i] * M + vals[i]) % MOD def get_hash(p, l): res = hashes[p + l] - (hashes[p] * powsA[l]) % MOD if res < 0: res += MOD elif res > MOD: res -= MOD return res best = 0 i = 0 while i < n: val = vals[i] for j in groups[val]: if j <= i: continue l = j - i if j + l <= n and get_hash(i, l) == get_hash(j, l): best = max(best, j) i = j - 1 break i += 1 res = vals[best:] print(len(res)) print(" ".join(map(str, res))) ```
104,730
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Once Bob saw a string. It contained so many different letters, that the letters were marked by numbers, but at the same time each letter could be met in the string at most 10 times. Bob didn't like that string, because it contained repeats: a repeat of length x is such a substring of length 2x, that its first half coincides character by character with its second half. Bob started deleting all the repeats from the string. He does it as follows: while it's possible, Bob takes the shortest repeat, if it is not unique, he takes the leftmost one, and deletes its left half and everything that is to the left of this repeat. You're given the string seen by Bob. Find out, what it will look like after Bob deletes all the repeats in the way described above. Input The first input line contains integer n (1 ≀ n ≀ 105) β€” length of the string. The following line contains n space-separated integer numbers from 0 to 109 inclusive β€” numbers that stand for the letters of the string. It's guaranteed that each letter can be met in the string at most 10 times. Output In the first line output the length of the string's part, left after Bob's deletions. In the second line output all the letters (separated by a space) of the string, left after Bob deleted all the repeats in the described way. Examples Input 6 1 2 3 1 2 3 Output 3 1 2 3 Input 7 4 5 6 5 6 7 7 Output 1 7 Submitted Solution: ``` n = int(input()) number = [int(x) for x in input().split()] x = list(set(number)) print(len(x)) for i in x: print(i,end=" ") ``` No
104,731
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Once Bob saw a string. It contained so many different letters, that the letters were marked by numbers, but at the same time each letter could be met in the string at most 10 times. Bob didn't like that string, because it contained repeats: a repeat of length x is such a substring of length 2x, that its first half coincides character by character with its second half. Bob started deleting all the repeats from the string. He does it as follows: while it's possible, Bob takes the shortest repeat, if it is not unique, he takes the leftmost one, and deletes its left half and everything that is to the left of this repeat. You're given the string seen by Bob. Find out, what it will look like after Bob deletes all the repeats in the way described above. Input The first input line contains integer n (1 ≀ n ≀ 105) β€” length of the string. The following line contains n space-separated integer numbers from 0 to 109 inclusive β€” numbers that stand for the letters of the string. It's guaranteed that each letter can be met in the string at most 10 times. Output In the first line output the length of the string's part, left after Bob's deletions. In the second line output all the letters (separated by a space) of the string, left after Bob deleted all the repeats in the described way. Examples Input 6 1 2 3 1 2 3 Output 3 1 2 3 Input 7 4 5 6 5 6 7 7 Output 1 7 Submitted Solution: ``` n = int(input()) a = list(map(int,input().split()))[:n] b = [] for i in range(len(a)): if a[i] not in b: b.append(a[i]) print(len(b)) print(*b) ``` No
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Once Bob saw a string. It contained so many different letters, that the letters were marked by numbers, but at the same time each letter could be met in the string at most 10 times. Bob didn't like that string, because it contained repeats: a repeat of length x is such a substring of length 2x, that its first half coincides character by character with its second half. Bob started deleting all the repeats from the string. He does it as follows: while it's possible, Bob takes the shortest repeat, if it is not unique, he takes the leftmost one, and deletes its left half and everything that is to the left of this repeat. You're given the string seen by Bob. Find out, what it will look like after Bob deletes all the repeats in the way described above. Input The first input line contains integer n (1 ≀ n ≀ 105) β€” length of the string. The following line contains n space-separated integer numbers from 0 to 109 inclusive β€” numbers that stand for the letters of the string. It's guaranteed that each letter can be met in the string at most 10 times. Output In the first line output the length of the string's part, left after Bob's deletions. In the second line output all the letters (separated by a space) of the string, left after Bob deleted all the repeats in the described way. Examples Input 6 1 2 3 1 2 3 Output 3 1 2 3 Input 7 4 5 6 5 6 7 7 Output 1 7 Submitted Solution: ``` def get_pow_list(x, exp, mod): res = [1] for i in range(exp): res.append((res[-1] * x) % mod) return res MOD = 2 ** 61 - 1 n = int(input()) orig_vals = list(map(int, input().split())) sv = list(set(orig_vals)) sv_inv = {sv[i]: i + 1 for i in range(len(sv))} vals = [sv_inv[x] for x in orig_vals] groups = dict() for i in range(n): groups.setdefault(vals[i], []) groups[vals[i]].append(i) pows = [get_pow_list(x, n, MOD) for x in [2, len(sv) + 1]] logs = [-1] while len(logs) - 1 < n: logs.extend([logs[-1] + 1] * len(logs)) hashes = [[0] * (4 * n) for i in range(logs[n] + 1)] for i in range(n): hashes[0][i] = vals[i] for l in range(1, len(hashes)): e = pows[0][l - 1] for i in range(n): hashes[l][i] = hashes[l - 1][i] * pows[1][e] + hashes[l - 1][i + e] def get_hash(h, p, l, mod): if l == 0: return 0 elif ((l - 1) & l) == 0: return h[logs[l]][p] else: nl = pows[0][logs[l]] return get_hash(h, p, nl, mod) * pows[1][l - nl] + get_hash( h, p + nl, l - nl, mod ) best = 0 for i in range(n - 1, -1, -1): val = vals[i] for jj in range(len(groups[val])): j = groups[val][jj] if i == j: break l = i - j if get_hash(hashes, i, l, MOD) == get_hash(hashes, j, l, MOD): best = max(best, j) if best != 0: break res = orig_vals[best:] print(len(res)) print(" ".join(map(str, res))) ``` No
104,733
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Once Bob saw a string. It contained so many different letters, that the letters were marked by numbers, but at the same time each letter could be met in the string at most 10 times. Bob didn't like that string, because it contained repeats: a repeat of length x is such a substring of length 2x, that its first half coincides character by character with its second half. Bob started deleting all the repeats from the string. He does it as follows: while it's possible, Bob takes the shortest repeat, if it is not unique, he takes the leftmost one, and deletes its left half and everything that is to the left of this repeat. You're given the string seen by Bob. Find out, what it will look like after Bob deletes all the repeats in the way described above. Input The first input line contains integer n (1 ≀ n ≀ 105) β€” length of the string. The following line contains n space-separated integer numbers from 0 to 109 inclusive β€” numbers that stand for the letters of the string. It's guaranteed that each letter can be met in the string at most 10 times. Output In the first line output the length of the string's part, left after Bob's deletions. In the second line output all the letters (separated by a space) of the string, left after Bob deleted all the repeats in the described way. Examples Input 6 1 2 3 1 2 3 Output 3 1 2 3 Input 7 4 5 6 5 6 7 7 Output 1 7 Submitted Solution: ``` def pow(x, exp, mod): res = 1 while exp: if exp & 1: res = (res * x) % mod x = (x * x) % mod exp >>= 1 return res MOD = 2 ** 121 - 1 M = int(1e9) + 1 n = int(input()) vals = list(map(int, input().split())) groups = dict() for i in range(n): groups.setdefault(vals[i], []).append(i) powsA = [1] for i in range(n): powsA.append((powsA[-1] * M) % MOD) hashes = [0] * (n + 1) for i in range(n): hashes[i + 1] = (hashes[i] * M + vals[i]) % MOD def get_hash(p, l): res = hashes[p + l] - (hashes[p] * powsA[l]) % MOD if res < 0: res += MOD elif res > MOD: res -= MOD return res best = 0 for i in range(n - 1, -1, -1): val = vals[i] for j in groups[val]: if i == j: break l = i - j if i + l <= n and get_hash(i, l) == get_hash(j, l): best = max(best, i) if best != 0: break res = vals[best:] print(len(res)) print(" ".join(map(str, res))) ``` No
104,734
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0
Provide tags and a correct Python 3 solution for this coding contest problem. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Tags: brute force, hashing, implementation, strings Correct Solution: ``` def solve(): read=lambda:list(map(int,input().split())) from collections import Counter as co k,n=read() s=input() repeated=(len(s)!=len(set(s))) etalon=co(s) a=[] kk=[] ap=a.append for i in range(k-1): ap(input()) if co(a[-1])!=etalon: print(-1) exit() ss=False for i in a: if i!=s: ss=i for j in range(len(s)): if s[j]!=ss[j]: kk.append(j) break if len(kk)>4: print(-1) exit() if ss: if repeated: for i in a: k = 0 for j in range(len(i)): if s[j] != i[j]: k += 1 if k != 0 and k != 2: break else: print(s) exit() if len(kk)!=2: for i in range(len(kk)): for j in range(i): stry=s[:kk[j]]+s[kk[i]]+s[kk[j]+1:kk[i]]+s[kk[j]]+s[kk[i]+1:] for u in a: k = 0 for j in range(len(u)): if stry[j] != u[j]: k += 1 if not(k==0 and repeated) and k != 2: break else: print(stry) exit() if len(kk)==2: for change in kk: for i in range(len(s)): if change==i: continue if i >change: stry = s[:change] + s[i] + s[change + 1:i] + s[change] + s[i + 1:] else: stry = s[:i] + s[change] + s[i + 1:change] + s[i] + s[change + 1:] for u in a: k = 0 for j in range(len(u)): if stry[j] != u[j]: k += 1 if not(k==0 and repeated) and k != 2: break else: print(stry) exit() print(-1) else: if repeated: print(s) exit() print(s[1]+s[0]+s[2:]) solve() ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Tags: brute force, hashing, implementation, strings Correct Solution: ``` read=lambda:list(map(int,input().split())) from collections import Counter as co k,n=read() s=input() repeated=(len(s)!=len(set(s))) etalon=co(s) a=[] kk=[] ap=a.append for i in range(k-1): ap(input()) if co(a[-1])!=etalon: print(-1) exit() ss=False for i in a: if i!=s: ss=i for j in range(len(s)): if s[j]!=ss[j]: kk.append(j) break if len(kk)>4: print(-1) exit() if ss: if repeated: for i in a: k = 0 for j in range(len(i)): if s[j] != i[j]: k += 1 if k != 0 and k != 2: break else: print(s) exit() if len(kk)!=2: for i in range(len(kk)): for j in range(i): stry=s[:kk[j]]+s[kk[i]]+s[kk[j]+1:kk[i]]+s[kk[j]]+s[kk[i]+1:] #print(stry) for u in a: k = 0 for j in range(len(u)): if stry[j] != u[j]: k += 1 #print(stry,i,k) if not(k==0 and repeated) and k != 2: break else: print(stry) exit() if len(kk)==2: for change in kk: for i in range(len(s)): if change==i: continue if i >change: stry = s[:change] + s[i] + s[change + 1:i] + s[change] + s[i + 1:] else: stry = s[:i] + s[change] + s[i + 1:change] + s[i] + s[change + 1:] for u in a: k = 0 for j in range(len(u)): if stry[j] != u[j]: k += 1 #print(stry,i,k) if not(k==0 and repeated) and k != 2: break else: print(stry) exit() print(-1) else: if repeated: print(s) exit() print(s[1]+s[0]+s[2:]) ```
105,010
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0
Provide tags and a correct Python 3 solution for this coding contest problem. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Tags: brute force, hashing, implementation, strings Correct Solution: ``` import collections def swapCharacters(strings, k, n): """ Time: O(n^2 * k) Space: O(1) """ if k == 1: s0 = list(strings[0]) s0[0], s0[1] = s0[1], s0[0] return ''.join(s0) # Initial check for validity freq = collections.Counter(strings[0]) canSame = (max(freq.values()) >= 2) # could swap two of the same characters ==> same string for s in strings: if collections.Counter(s) != freq: return -1 # Find diff indices between first two strings max_dist = 0 max_dist_s = None s0 = strings[0] for s1 in strings[1:]: dist = HammingDistance(s0, s1, n) if dist > max_dist: max_dist = dist max_dist_s = s1 # Hamming distance <= 2*2 between input strings to be valid if max_dist > 4: return -1 diffs = [i for i in range(n) if s0[i] != s1[i]] # Checks all possible strings which match first two -- Finding strings (O(N)), testing string (O(KN)) s0 = list(s0) for i in diffs: for j in range(n): # try swapping s0[i], s0[j] = s0[j], s0[i] # see if matches second string now #dist = sum([s0[i] != s1[i] for i in diffs]) dist = HammingDistance(s0, s1, n) if dist == 2 or (dist == 0 and canSame): cand = ''.join(s0) if verifyAll(strings, k, n, cand, canSame): return cand # revert s0[i], s0[j] = s0[j], s0[i] # nothing works return -1 def HammingDistance(s0, s1, n): count = 0 for i in range(n): if s0[i] != s1[i]: count += 1 return count def verifyAll(strings, k, n, cand, canSame): for s in strings: dist = HammingDistance(s, cand, n) if (dist != 0 or not canSame) and dist != 2: return False return True k, n = [int(x) for x in input().split()] strings = set() # discard duplicates for _ in range(k): strings.add(input()) strings = list(strings) k = len(strings) res = swapCharacters(strings, k, n) print(res) ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Tags: brute force, hashing, implementation, strings Correct Solution: ``` def solve(): read=lambda:list(map(int,input().split())) from collections import Counter as co k,n=read() s=list(input()) repeated=(len(s)!=len(set(s))) etalon=co(s) a=[] kk=[] ap=a.append for i in range(k-1): ap(list(input())) if co(a[-1])!=etalon: print(-1) exit() ss=False for i in a: if i!=s: ss=i for j in range(len(s)): if s[j]!=ss[j]: kk.append(j) break if len(kk)>4: print(-1) exit() if ss: if repeated: for i in a: k = 0 for j in range(len(i)): if s[j] != i[j]: k += 1 if k != 0 and k != 2: break else: print(''.join(s)) exit() if len(kk)!=2: for i in range(len(kk)): for j in range(i): stry=s[:kk[j]]+[s[kk[i]]]+s[kk[j]+1:kk[i]]+[s[kk[j]]]+s[kk[i]+1:] for u in a: k = 0 for j in range(len(u)): if stry[j] != u[j]: k += 1 if not(k==0 and repeated) and k != 2: break else: print(''.join(stry)) exit() if len(kk)==2: for change in kk: for i in range(len(s)): if change==i: continue if i >change: stry = s[:change] + [s[i]] + s[change + 1:i] + [s[change]] + s[i + 1:] else: stry = s[:i] + [s[change]] + s[i + 1:change] + [s[i]] + s[change + 1:] for u in a: k = 0 for j in range(len(u)): if stry[j] != u[j]: k += 1 if not(k==0 and repeated) and k != 2: break else: print(''.join(stry)) exit() print(-1) else: if repeated: print(''.join(s)) exit() print(s[1]+s[0]+''.join(s[2:])) solve() ```
105,012
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0
Provide tags and a correct Python 3 solution for this coding contest problem. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Tags: brute force, hashing, implementation, strings Correct Solution: ``` #!/usr/bin/env python3 n,k = map(int, input().split()) nn = [] ans = '' for i in range(n): mid = input() if mid in nn: ans = mid continue nn.append(mid) n = len(nn) if len(nn) == 1: ans = nn[0] ans = list(ans) ans[0],ans[1] = ans[1],ans[0] print(''.join(ans)) else: diff = [] check = True cnt = {chr(97+i):0 for i in range(26)} for v in range(k): cnt[nn[0][v]] += 1 for i in range(n): cnt2 = {chr(97+i):0 for i in range(26)} for j in range(k): cnt2[nn[i][j]] += 1 if cnt != cnt2: print('-1') check = False break if check: check = False for i in range(n): check = False for j in range(i,n): diff = [l for l in range(k) if nn[i][l] != nn[j][l]] if len(diff) > 4: check = True print('-1') break; if check: break diff = [l for l in range(k) if nn[0][l] != nn[1][l]] mid = [] check2 = False for i in range(k): if nn[0][i] in mid: check2 = True break mid.append(nn[0][i]) #print(diff) if not check: res = list(nn[0]) check = False for i in range(len(diff)): if check: break for j in range(k): if i == j: continue res[diff[i]],res[j] = res[j], res[diff[i]] ans = ''.join(res) #print(ans) check = True for x in range(n): mid = [ans[y] for y in range(k) if nn[x][y] != ans[y]] #print(len(diff)) if len(mid) == 2: continue elif len(mid) == 0 and check2: continue else: check = False if check: print(ans) check = True break res[diff[i]],res[j] = res[j],res[diff[i]] if not check: print('-1') ```
105,013
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0
Provide tags and a correct Python 3 solution for this coding contest problem. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Tags: brute force, hashing, implementation, strings Correct Solution: ``` import sys k, n = map(int, input().split()) s = [list(word.rstrip()) for word in sys.stdin] double = True if max(s[0].count(chr(i+97)) for i in range(26)) > 1 else False diff = [set() for _ in range(k)] diff_cnt = [0]*k for i in range(1, k): for j in range(n): if s[0][j] != s[i][j]: diff[i].add(j) diff_cnt[i] += 1 if diff_cnt[i] > 4: print(-1) exit() for i in range(n): for j in range(i+1, n): s[0][i], s[0][j] = s[0][j], s[0][i] for x in range(1, k): w = [y for y in diff[x] | {i, j} if s[0][y] != s[x][y]] if double and len(w) == 0: continue if len(w) == 2 and s[0][w[0]] == s[x][w[1]] and s[0][w[1]] == s[x][w[0]]: continue break else: print(''.join(s[0])) exit() s[0][i], s[0][j] = s[0][j], s[0][i] print(-1) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Submitted Solution: ``` import collections def swapCharacters(strings, k, n): """ Time: O(n^2 * k) Space: O(1) """ if k == 1: return strings[0] # Initial check for validity freq = collections.Counter(strings[0]) for s in strings: if collections.Counter(s) != freq: return -1 # Find diff indices between first two strings max_dist = 0 max_dist_s = None s0 = strings[0] for s1 in strings[1:]: dist = HammingDistance(s0, s1, n) if dist > max_dist: max_dist = dist max_dist_s = s1 # Hamming distance <= 2*2 between input strings to be valid if max_dist > 4: return -1 diffs = [i for i in range(n) if s0[i] != s1[i]] # Checks all possible strings which match first two -- Finding strings (O(N)), testing string (O(KN)) s0 = list(s0) for i in diffs: for j in range(n): # try swapping s0[i], s0[j] = s0[j], s0[i] # see if matches second string now #dist = sum([s0[i] != s1[i] for i in diffs]) dist = HammingDistance(s0, s1, n) if dist == 0 or dist == 2: cand = ''.join(s0) if verifyAll(strings, k, n, cand): return cand # revert s0[i], s0[j] = s0[j], s0[i] # nothing works return -1 def HammingDistance(s0, s1, n): count = 0 for i in range(n): if s0[i] != s1[i]: count += 1 return count def verifyAll(strings, k, n, cand): for s in strings: dist = HammingDistance(s, cand, n) if dist != 0 and dist != 2: return False return True k, n = [int(x) for x in input().split()] strings = [] for _ in range(k): strings.append(input()) res = swapCharacters(strings, k, n) print(res) ``` No
105,015
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Submitted Solution: ``` k, n = map(int, input().split()) se = None for _ in range(k): s = input() nse = set([s]) for i in range(n-1): for j in range(i+1, n): ns = [] for k in range(n): if k != i and k != j: ns.append(s[k]) elif k == i: ns.append(s[j]) else: ns.append(s[i]) nse.add(''.join(ns)) print(nse) if se is None: se = nse else: se &= nse if len(se) == 0: print(-1) exit() se = list(se) print(se[0]) ``` No
105,016
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0
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Submitted Solution: ``` from itertools import permutations class UniqueElement: def __init__(self, value, occurrences): self.value = value self.occurrences = occurrences def perm_unique(elements): e_set = set(elements) list_unique = [UniqueElement(i, elements.count(i)) for i in e_set] u = len(elements) return perm_unique_helper(list_unique, [0] * u, u - 1) def perm_unique_helper(list_unique, result_list, d): if d < 0: yield tuple(result_list) else: for i in list_unique: if i.occurrences > 0: result_list[d] = i.value i.occurrences -= 1 for g in perm_unique_helper(list_unique, result_list, d - 1): yield g i.occurrences += 1 def count(s): counter = {} for ch in s: if ch not in counter: counter[ch] = 0 counter[ch] += 1 return counter def hamming_distance(s1, s2, get_diff=False): assert len(s1) == len(s2) diff = [] for ch1, ch2 in zip(s1, s2): if ch1 != ch2: diff.append(1) else: diff.append(0) if not get_diff: return sum(diff) else: return sum(diff), diff def final_check(ss, ans): for s in ss: if hamming_distance(s, ans) not in {0, 2}: return False return True def main(): k, n = tuple(int(s) for s in input().split()) ss = [input() for _ in range(k)] if k == 1: s = list(ss[0]) s[0], s[1] = s[1], s[0] print(''.join(s)) return counter = count(ss[0]) for s in ss[1:]: if counter != count(s): print(-1) return dis, diff = hamming_distance(ss[0], ss[1], get_diff=True) if dis > 4: print(-1) return diff_chs = [ch for ch, is_diff in zip(ss[0], diff) if is_diff] for perm in permutations(diff_chs): asd = 0 new_str = [] for ch, is_diff in zip(ss[0], diff): if is_diff: new_str.append(perm[asd]) asd += 1 else: new_str.append(ch) new_str = ''.join(new_str) if final_check(ss, new_str): print(new_str) return print(-1) if __name__ == '__main__': main() ``` No
105,017
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string). You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, kΒ·n ≀ 5000). Input The first line contains two integers k and n (1 ≀ k ≀ 2500, 2 ≀ n ≀ 5000, k Β· n ≀ 5000) β€” the number of strings we obtained, and the length of each of these strings. Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters. Output Print any suitable string s, or -1 if such string doesn't exist. Examples Input 3 4 abac caab acba Output acab Input 3 4 kbbu kbub ubkb Output kbub Input 5 4 abcd dcba acbd dbca zzzz Output -1 Note In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character. In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 β€” by swapping the second and the fourth, and s3 β€” by swapping the first and the third. In the third example it's impossible to obtain given strings by aforementioned operations. Submitted Solution: ``` n,jks=map(int,input().split()) m=[] m.append(input()) c=set(m[0]) def Tr(s): for w in m: f=[] for i in range(jks): if w[i]!=s[i]: f.append(i) if len(f)==2 and w[f[0]]==s[f[1]] and w[f[1]]==s[f[0]]: pass elif len(f)==0 and len(set(s))!=len(s): pass else: return False return True for i in range(1,n): m.append(input()) # if c!=set(m[i]): # print(-1) # break #else: a=m[0] b=m[1] f=[] for i in range(jks): if a[i]!=b[i]: f.append(i) if len(f)>4: print(-1) else: for a in m[:2]: sl=list(a) for x in f: for i in range(jks): if i==x: continue slc=sl.copy() slc[x],slc[i]=slc[i],slc[x] sls=''.join(slc) if Tr(sls): print(sls) break else: continue break else: continue break else: print(-1) ``` No
105,018
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` # Template 1.0 import sys, re, math from collections import deque, defaultdict, Counter, OrderedDict from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, gcd from heapq import heappush, heappop, heapify, nlargest, nsmallest def STR(): return list(input()) def INT(): return int(input()) def MAP(): return map(int, input().split()) def LIST(): return list(map(int, input().split())) def list2d(a, b, c): return [[c] * b for i in range(a)] def sortListWithIndex(listOfTuples, idx): return (sorted(listOfTuples, key=lambda x: x[idx])) def sortDictWithVal(passedDic): temp = sorted(passedDic.items(), key=lambda kv: (kv[1], kv[0]))[::-1] toret = {} for tup in temp: toret[tup[0]] = tup[1] return toret def sortDictWithKey(passedDic): return dict(OrderedDict(sorted(passedDic.items()))) sys.setrecursionlimit(10 ** 9) INF = float('inf') mod = 10 ** 9 + 7 def calcNext(num): for i in range(num+1, 2**m): if(i not in vis): return i return -1 def calcPrev(num): for i in range(num-1, -1, -1): if (i not in vis): return i return -1 t = INT() while (t != 0): n, m = MAP() currLen = 2**m currMed = (2**m-1)//2 vis = set() # vis.add(currMed) for _ in range(n): torem = int(input(), 2) if(currLen%2==0): currLen-=1 vis.add(torem) if(torem<=currMed): currMed = calcNext(currMed) else: currLen-=1 vis.add(torem) if(torem>=currMed): currMed = calcPrev(currMed) # print(currMed) # print(bin(currMed).replace("0b", "")) print(format(currMed, '0'+str(m)+'b')) t-=1 ''' 1 4 3 000 111 100 011 1 2 3 4 5 6 ''' ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` t=int(input()) for _ in range(t): n,m=map(int,input().split()) arr=[] for i in range(n): arr.append(input().strip()) arr1=[] for i in arr: arr1.append(int(i,2)) a=(2**m-n-1)//2 arr1.sort() for i in arr1: if i<=a: a+=1 ans=bin(a).replace("0b","") ans="0"*(m-len(ans))+ans print(ans) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` import sys max_int = 1000000001 # 10^9+1 min_int = -max_int t = int(input()) for _t in range(t): n, m = map(int, sys.stdin.readline().split()) to_skip = [] for _n in range(n): s = int(sys.stdin.readline()[:-1], base=2) to_skip.append(s) to_skip.sort() mid = (2 ** m - n - 1) // 2 for elem in to_skip: if elem <= mid: mid += 1 else: break print(("{0:0>" + str(m) + "b}").format(mid)) ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` ''' Auther: ghoshashis545 Ashis Ghosh College: jalpaiguri Govt Enggineerin College Date:24/05/2020 ''' import sys from collections import deque,defaultdict as dd from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right from itertools import permutations from datetime import datetime from math import ceil,sqrt,log,gcd def ii():return int(input()) def si():return input() def mi():return map(int,input().split()) def li():return list(mi()) abc='abcdefghijklmnopqrstuvwxyz' abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25} mod=1000000007 #mod=998244353 inf = float("inf") vow=['a','e','i','o','u'] dx,dy=[-1,1,0,0],[0,0,1,-1] def read(): tc=0 if tc: input=sys.stdin.readline else: sys.stdin=open('input1.txt', 'r') sys.stdout=open('output1.txt','w') def solve(): for _ in range(ii()): n,m=mi() tot=pow(2,m)-n x=(tot-1)//2 a=[] for i in range(n): s=si() a.append(int(s,2)) a.sort() cnt=bisect(a,x) x+=cnt c=cnt while(cnt): cnt=bisect(a,x)-c x+=cnt c+=cnt s=bin(x)[2:] print('0'*(m-len(s))+s) if __name__ =="__main__": # read() solve() ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` tc = int(input()) for _ in range(tc): n,m = map(int,input().split()) cache = {} curr = (2**m - 1)//2 for i in range(n): s = input() x = int(s,2) cache[x] = 1 if i%2 == 0: if x<=curr: while(len(cache)!=0 and curr+1 in cache): curr += 1 curr += 1 else: if x>=curr: while(len(cache)!=0 and curr-1 in cache): curr -= 1 curr -= 1 temp = bin(curr)[2:] if m!=len(temp): temp = "0"*abs(m-len(temp)) + temp print(temp) ```
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Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` def solve(): n, m = [int(x) for x in input().split()] a = [] for i in range(n): a.append(input()) a = [int(x, 2) for x in a] need = ((1 << m) - n - 1)//2 + 1 cur = (1 << (m-1)) - 1 while True: left = cur+1 flag = bool(cur in a) for s in a: if s <= cur: left -= 1 if left == need and not flag: ans = bin(cur).split('b')[1] if len(ans) < m: ans = '0'*(m-len(ans)) + ans print(ans) return elif left < need: cur += 1 else: cur -= 1 t = int(input()) while t > 0: t -= 1 solve() ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` import math import string t = int(input()) for tt in range(t): n, m = map(int, input().split()) a = [] for i in range(n): a.append(int(input(), 2)) need = (2 ** m - n - 1) // 2 l = 0 r = 2 ** m while(r - l > 1): mid = (l + r) // 2 x = mid for i in range(n): if(a[i] < mid): x -= 1 if(x > need): r = mid else: l = mid ans = [] for i in range(m): ans.append(l % 2) l //= 2 ans.reverse() for i in range(m): print(ans[i], end="") print() ```
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0
Provide tags and a correct Python 3 solution for this coding contest problem. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Tags: binary search, bitmasks, brute force, constructive algorithms Correct Solution: ``` def dd(i,nn): s=bin(i).replace("0b", "") l=len(s) #print(l,nn) kk="" for i in range (nn-l): kk=kk+'0' print(kk+s) t=int(input()) for i in range(t): n,m=map(int,input().split()) aa=[] for pp in range(n): pp=input() aa.append(int(pp,2)) y=2**(m-1) - 1 a=max(0,y-n) b=min(y+n,2**m -1) for i in range(a,b+1): l=i r=2**m -1-i #print(l,r) flag=1 for k in aa: if(k==i): flag=0 break if(k<i): l=l-1 else: r=r-1 if(flag==0): continue if(n%2==0 and l==r-1): dd(i,m) if(n%2!=0 and l==r): dd(i,m) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` from sys import stdin,stdout import math from bisect import bisect_left def main(): t = int(stdin.readline()) for _ in range (t): n,m = list(map(int, stdin.readline().split())) total = pow(2,m) - 1 med = math.floor((total) / 2) arr = [] for _ in range(n): num = int(stdin.readline(),2) arr.append(num) arr.sort() ite = min(total+1,200) ans = 0 for x in range(max(0, med - int(ite/2)),min(total+1, med + int(ite/2)+1)): pos = bisect_left(arr, x) if pos != len(arr) and arr[pos] == x: continue # use pos to calculate left and right quantity # if n % 2 == 1 then exclude current # else then include currente elif n % 2 == 1: left = x - pos right = total - x - (n - pos) if left == right: ans = x break else: left = x - pos + 1 right = total - x - (n - pos) if left == right: ans = x break ans = bin(ans).replace("0b", "") if len(ans) < m: ans = "0" * (m - len(ans)) + ans stdout.write(ans + "\n") main() ``` Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # ------------------------------ from math import factorial, floor from collections import Counter, defaultdict, deque from heapq import heapify, heappop, heappush def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0 def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0 def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2) mod = 998244353 INF = float('inf') # ------------------------------ from bisect import bisect def main(): for _ in range(N()): n, mm = RL() arr = [int(input(), 2) for _ in range(n)] arr.sort() now = (2**mm)-n res = (now-1)//2 for i in arr: if i<=res: res+=1 # print(res) res = bin(res)[2:].zfill(mm) print(res) if __name__ == "__main__": main() ``` Yes
105,430
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` import sys, heapq from collections import * from functools import lru_cache sys.setrecursionlimit(10**6) def main(): # sys.stdin = open('input.txt', 'r') t = int(input()) for _ in range(t): n, m = map(int,input().split(' ')) total = 2**m mid = (total-1)//2 removes = set() for _ in range(n): s = input() cur = 0 for ch in s: cur = cur<<1 if ch == '1': cur += 1 removes.add(cur) removed = set() for r in removes: if total & 1 and r >= mid: while mid-1 in removed: mid -= 1 mid -= 1 elif total & 1 == 0 and r <= mid: while mid+1 in removed: mid += 1 mid += 1 total -= 1 removed.add(r) res = [] for i in range(m): if mid & (1<<i): res.append('1') else: res.append('0') # print(''.join(res[::-1]),mid) print(''.join(res[::-1])) if __name__ == "__main__": main() ``` Yes
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Consider all binary strings of length m (1 ≀ m ≀ 60). A binary string is a string that consists of the characters 0 and 1 only. For example, 0110 is a binary string, and 012aba is not. Obviously, there are exactly 2^m such strings in total. The string s is lexicographically smaller than the string t (both have the same length m) if in the first position i from the left in which they differ, we have s[i] < t[i]. This is exactly the way strings are compared in dictionaries and in most modern programming languages when comparing them in a standard way. For example, the string 01011 is lexicographically smaller than the string 01100, because the first two characters are the same, and the third character in the first string is less than that in the second. We remove from this set n (1 ≀ n ≀ min(2^m-1, 100)) distinct binary strings a_1, a_2, …, a_n, each of length m. Thus, the set will have k=2^m-n strings. Sort all strings of the resulting set in lexicographical ascending order (as in the dictionary). We number all the strings after sorting from 0 to k-1. Print the string whose index is ⌊ (k-1)/(2) βŒ‹ (such an element is called median), where ⌊ x βŒ‹ is the rounding of the number down to the nearest integer. For example, if n=3, m=3 and a=[010, 111, 001], then after removing the strings a_i and sorting, the result will take the form: [000, 011, 100, 101, 110]. Thus, the desired median is 100. Input The first line contains an integer t (1 ≀ t ≀ 1000) β€” the number of test cases. Then, t test cases follow. The first line of each test case contains integers n (1 ≀ n ≀ min(2^m-1, 100)) and m (1 ≀ m ≀ 60), where n is the number of strings to remove, and m is the length of binary strings. The next n lines contain a_1, a_2, …, a_n β€” distinct binary strings of length m. The total length of all given binary strings in all test cases in one test does not exceed 10^5. Output Print t answers to the test cases. For each test case, print a string of length m β€” the median of the sorted sequence of remaining strings in the corresponding test case. Example Input 5 3 3 010 001 111 4 3 000 111 100 011 1 1 1 1 1 0 3 2 00 01 10 Output 100 010 0 1 11 Note The first test case is explained in the statement. In the second test case, the result after removing strings and sorting is [001, 010, 101, 110]. Therefore, the desired median is 010. Submitted Solution: ``` for _ in range(int(input())): n,m=map(int,input().split()) x=(2**m-n-1)//2 arr=[] for i in range(n): arr.append(int(input(),2)) arr.sort() for i in range(0,n): if(arr[i]<=x): x+=1 if x in arr: x+=1 y=bin(x)[2:] print('0'*(m-len(y))+y) ``` Yes
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