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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 bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each). You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows. The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring. The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?. It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible. Example Input 9 6 4 100110 3 2 1?1 3 2 1?0 4 4 ???? 7 4 1?0??1? 10 10 11??11??11 4 2 1??1 4 4 ?0?0 6 2 ????00 Output YES YES NO YES YES NO NO YES NO Note For the first test case, the string is already a 4-balanced bitstring. For the second test case, the string can be transformed into 101. For the fourth test case, the string can be transformed into 0110. For the fifth test case, the string can be transformed into 1100110. Submitted Solution: ``` for _ in range(int(input())): n,k = map(int,input().split()) a = list(input()) flag = False dic = [-1 for i in range(k)] for i in range(n): if a[i] == '1' and dic[i%k] != 0: dic[i%k] = 1 elif a[i] == '0' and dic[i%k] != 1: dic[i%k] = 0 elif a[i] == '?': if dic[i%k] != -1: continue else: dic[i%k] = '?' else: flag = True break if flag: print('NO') else: s = count = 0 for i in dic: if i == '?': count += 1 elif i == 1: s += 1 if s > k//2 or (s<k//2 and count == 0): print('NO') elif s == k//2 and count ==0: print('YES') elif count != 0: if s == k//2: print('YES') elif (k//2)-s <= count: print('YES') else: print('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. A bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each). You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows. The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring. The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?. It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible. Example Input 9 6 4 100110 3 2 1?1 3 2 1?0 4 4 ???? 7 4 1?0??1? 10 10 11??11??11 4 2 1??1 4 4 ?0?0 6 2 ????00 Output YES YES NO YES YES NO NO YES NO Note For the first test case, the string is already a 4-balanced bitstring. For the second test case, the string can be transformed into 101. For the fourth test case, the string can be transformed into 0110. For the fifth test case, the string can be transformed into 1100110. Submitted Solution: ``` import sys input = sys.stdin.readline for _ in range(int(input())): N, K = map(int, input().split()) a = list(input())[: -1] cs = 0 q = 0 for i in range(K): t = 0 if a[i] == "1": t = 1 elif a[i] == "0": t = -1 else: q += 1 cs += t q -= abs(cs) if q < 0: print("NO") continue for i in range(N - K): if a[i] != "?" and (a[i + K] != "?") and (a[i] != a[i + K]): print("NO") break elif a[i] != a[i + K]: if a[i] == "0": a[i + K] = "0" elif a[i] == "1": a[i + K] = "1" elif a[i + K] == "0": a[i] = "0" elif a[i + K] == "1": a[i] = "1" else: cs = 0 q = 0 for i in range(K): t = 0 if a[i] == "1": t = 1 elif a[i] == "0": t = -1 else: q += 1 cs += t q -= abs(cs) if q < 0: print("NO") continue for i in range(N - K): if a[i] != "?" and (a[i + K] != "?") and (a[i] != a[i + K]): print("NO") break elif a[i] != a[i + K]: if a[i] == "0": a[i + K] = "0" elif a[i] == "1": a[i + K] = "1" elif a[i + K] == "0": a[i] = "0" elif a[i + K] == "1": a[i] = "1" else: cs = [0] * (N + 1) qs = [0] * (N + 1) for i in range(N): t = 0 if a[i] == "1": t = 1 elif a[i] == "0": t = -1 else: qs[i + 1] += 1 cs[i + 1] = cs[i] + t qs[i + 1] += qs[i] for i in range(N - K + 1): if (abs(cs[i + K] - cs[i]) - (qs[i + K] - qs[i])) % 2: print("NO") break elif (abs(cs[i + K] - cs[i]) - (qs[i + K] - qs[i])) > 0: print("NO") break else: 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. A bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each). You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows. The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring. The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?. It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible. Example Input 9 6 4 100110 3 2 1?1 3 2 1?0 4 4 ???? 7 4 1?0??1? 10 10 11??11??11 4 2 1??1 4 4 ?0?0 6 2 ????00 Output YES YES NO YES YES NO NO YES NO Note For the first test case, the string is already a 4-balanced bitstring. For the second test case, the string can be transformed into 101. For the fourth test case, the string can be transformed into 0110. For the fifth test case, the string can be transformed into 1100110. Submitted Solution: ``` from sys import stdin N = int(stdin.readline()) for case in range(N): length, k = map(int, stdin.readline().split()) string = str(stdin.readline()) count = { "1":0, "0":0, "?":0 } flag = True for i in range(k): res = string[i] for j in range(i+k, length, k): if res != "?" and string[j] != res and string[j] != "?": flag = False break if res == "?" and string[j] != "?": res = string[j] if flag: count[res] += 1 if count["1"] <= k//2 and count["0"] <= k//2 and flag: print("YES") else: print("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. A bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each). You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows. The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring. The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?. It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible. Example Input 9 6 4 100110 3 2 1?1 3 2 1?0 4 4 ???? 7 4 1?0??1? 10 10 11??11??11 4 2 1??1 4 4 ?0?0 6 2 ????00 Output YES YES NO YES YES NO NO YES NO Note For the first test case, the string is already a 4-balanced bitstring. For the second test case, the string can be transformed into 101. For the fourth test case, the string can be transformed into 0110. For the fifth test case, the string can be transformed into 1100110. Submitted Solution: ``` # -*- coding: utf-8 -*- """ Created on Sun Sep 6 21:22:04 2020 @author: Dark Soul """ t=int(input('')) arr=[] s=[] for i in range(t): arr.append(list(map(int,input().split()))) s.append(input('')) for j in range(t): [n,k]=arr[j] tst=list(s[j]) flag=0 f1=0 f2=0 q=0 for i in range(k): if tst[i]=='1': f1+=1 elif tst[i]=='0': f2+=1 else: q+=1 if q==0: if f1!=k//2 or f2!=k//2: flag=1 if f1>k//2 or f2>k//2: flag=1 if flag: print('NO') continue if q: if f1==k//2: for i in range(k): if tst[i]=='?': tst[i]='0' if i+k<n: if tst[i+k]!=tst[i]: flag=1 break elif f2==k//2: for i in range(k): if tst[i]=='?': tst[i]='1' if i+k<n: if tst[i+k]!=tst[i]: flag=1 break else: f1=abs(f1-k//2) f2=abs(f2-k//2) for i in range(k): if tst[i]=='?': if i+k<n: if tst[i+k]!='?': tst[i]=tst[i+k] else: if f1: tst[i]='1' f1-=1 elif f2: tst[i]='0' f2-=1 else: flag=1 break else: if f1: tst[i]='1' f1-=1 elif f2: tst[i]='0' f2-=1 else: flag=1 break if flag: print('NO') continue for i in range(n-k): if tst[i]!=tst[i+k]: if tst[i+k]=='?': tst[i+k]=tst[i] else: flag=1 break if flag: print('NO') else: 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. A bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each). You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows. The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring. The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?. It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible. Example Input 9 6 4 100110 3 2 1?1 3 2 1?0 4 4 ???? 7 4 1?0??1? 10 10 11??11??11 4 2 1??1 4 4 ?0?0 6 2 ????00 Output YES YES NO YES YES NO NO YES NO Note For the first test case, the string is already a 4-balanced bitstring. For the second test case, the string can be transformed into 101. For the fourth test case, the string can be transformed into 0110. For the fifth test case, the string can be transformed into 1100110. Submitted Solution: ``` #------------------------template--------------------------# import os import sys from math import * from collections import * from fractions import * from bisect import * from heapq import* from io import BytesIO, IOBase def vsInput(): sys.stdin = open('input.txt', 'r') sys.stdout = open('output.txt', 'w') 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") ALPHA='abcdefghijklmnopqrstuvwxyz' M=998244353 EPS=1e-6 def value():return tuple(map(int,input().split())) def array():return [int(i) for i in input().split()] def Int():return int(input()) def Str():return input() def arrayS():return [i for i in input().split()] #-------------------------code---------------------------# # vsInput() def check(): return True for _ in range(Int()): n,k=value() s=[i for i in input()] ok="YES" ind=[i for i in range(n) if s[i]=='?'] id=0 need=0 have=0 # INITIALS ------------------------------------/ for i in range(k): if(s[i]=='1'):need+=1 elif(s[i]=='0'):need-=1 else:have+=1 if(abs(need)>have or (have-abs(need))%2): ok="NO" elif(have==abs(need)): for i in range(have): s[ind[id]]=str(int(need<0)) id+=1 have=0 need=0 # SLIDE ---------------------------------------/ # print(ok) for i in range(1,n-k+1): if(id<len(ind) and ind[id]<i): id=bisect_left(ind,i) if(s[i-1]=='0'): need+=1 elif(s[i-1]=='1'): need-=1 else: have-=1 if(s[i+k-1]=='0'):need-=1 elif(s[i+k-1]=='1'):need+=1 else: have+=1 # print(id,have,need,ind) if(abs(need)>have or (have-abs(need))%2): ok="NO" break elif(have==abs(need)): for i in range(have): s[ind[id]]=str(int(need<0)) id+=1 have=0 need=0 # print(s) print(ok) ```
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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 bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each). You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows. The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring. The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?. It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible. Example Input 9 6 4 100110 3 2 1?1 3 2 1?0 4 4 ???? 7 4 1?0??1? 10 10 11??11??11 4 2 1??1 4 4 ?0?0 6 2 ????00 Output YES YES NO YES YES NO NO YES NO Note For the first test case, the string is already a 4-balanced bitstring. For the second test case, the string can be transformed into 101. For the fourth test case, the string can be transformed into 0110. For the fifth test case, the string can be transformed into 1100110. Submitted Solution: ``` t=int(input()) for _ in range(t): n,k=map(int,input().split()) a=list(input()) flag=1 for i in range(n): if(a[i]=="?"): if(i+k<n): a[i]=a[i+k] else: if(a[i]=="0"): if(i+k<n): if(a[i]!=a[i+k] and a[i+k]=="1"): flag=0 break a[i+k]=a[i] if(i-k>=0 ): if(a[i]!=a[i-k]and a[i-k]=="1"): flag=0 break a[i-k]=a[i] else: if(i+k<n): if(a[i]!=a[i+k]and a[i+k]=="0"): flag=0 break a[i+k]=a[i] #print(i+k) if(i-k>=0): if(a[i]!=a[i-k]and a[i-k]=="1"): flag=0 break a[i-k]=a[i] #print(a) one=0 zero=0 doubt=0 #print(a) for i in range(k): if(a[i]=="1"): one+=1 elif(a[i]=="0"): zero+=1 else: doubt=0 if(one>k/2 or zero>k/2): print("NO") continue oneneed=k/2-one zeroneed=k/2-zero for i in range(k,n): if(a[i-k]=='1'): one-=1 if(a[i-k]=='0'): zero-=1 if(a[i]=='1'): one+=1 else: zero+=1 if(one>k/2 or zero>k/2): flag=0 break if(flag==0): print("NO") else: 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. A bitstring is a string consisting only of the characters 0 and 1. A bitstring is called k-balanced if every substring of size k of this bitstring has an equal amount of 0 and 1 characters (k/2 of each). You are given an integer k and a string s which is composed only of characters 0, 1, and ?. You need to determine whether you can make a k-balanced bitstring by replacing every ? characters in s with either 0 or 1. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. Input Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows. The first line of each test case contains two integers n and k (2 ≤ k ≤ n ≤ 3 ⋅ 10^5, k is even) — the length of the string and the parameter for a balanced bitstring. The next line contains the string s (|s| = n). It is given that s consists of only 0, 1, and ?. It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, print YES if we can replace every ? in s with 0 or 1 such that the resulting bitstring is k-balanced, or NO if it is not possible. Example Input 9 6 4 100110 3 2 1?1 3 2 1?0 4 4 ???? 7 4 1?0??1? 10 10 11??11??11 4 2 1??1 4 4 ?0?0 6 2 ????00 Output YES YES NO YES YES NO NO YES NO Note For the first test case, the string is already a 4-balanced bitstring. For the second test case, the string can be transformed into 101. For the fourth test case, the string can be transformed into 0110. For the fifth test case, the string can be transformed into 1100110. Submitted Solution: ``` import sys, os, io def rs(): return sys.stdin.readline().rstrip() def ri(): return int(sys.stdin.readline()) def ria(): return list(map(int, sys.stdin.readline().split())) def ws(s): sys.stdout.write(s + '\n') def wi(n): sys.stdout.write(str(n) + '\n') def wia(a): sys.stdout.write(' '.join([str(x) for x in a]) + '\n') import math,datetime,functools,itertools,operator,bisect,fractions from collections import deque,defaultdict,OrderedDict,Counter from fractions import Fraction from decimal import Decimal def main(): starttime=datetime.datetime.now() if(os.path.exists('input.txt')): sys.stdin = open("input.txt","r") sys.stdout = open("output.txt","w") for _ in range(ri()): n,k=ria() a=rs() a=list(a) q=deque(a[:k]) n1=0 nq=0 n0=0 for i in q: if i=='?': nq+=1 if i=='1': n1+=1 if i=='0': n0+=1 if max(n1,n0)>k//2: print("NO") else: t=0 if n1==k//2: for e in range(k): if q[e]=='?': q[e]='0' n0=nq nq=0 t=1 if n0==k//2 and t==0: for e in range(k): if q[e]=='?': q[e]='1' n1=nq nq=0 c=True for i in range(k,n): if q[0]=='?': nq-=1 if q[0]=='1': n1-=1 if q[0]=='0': n0-=1 q.popleft() q.append(a[i]) if q[-1]=='?': nq+=1 if q[-1]=='1': n1+=1 if q[-1]=='0': n0+=1 if max(n1,n0)>k//2: c=False break t=0 if n1==k//2: for e in range(k): if q[e]=='?': q[e]='0' n0=nq nq=0 t=1 if n0==k//2 and t==0: for e in range(k): if q[e]=='?': q[e]='1' n1=nq nq=0 if c: print("YES") else: print("NO") #<--Solving Area Ends endtime=datetime.datetime.now() time=(endtime-starttime).total_seconds()*1000 if(os.path.exists('input.txt')): print("Time:",time,"ms") class FastReader(io.IOBase): newlines = 0 def __init__(self, fd, chunk_size=1024 * 8): self._fd = fd self._chunk_size = chunk_size self.buffer = io.BytesIO() def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size)) 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, size=-1): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, self._chunk_size if size == -1 else size)) 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() class FastWriter(io.IOBase): def __init__(self, fd): self._fd = fd self.buffer = io.BytesIO() self.write = self.buffer.write def flush(self): os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class FastStdin(io.IOBase): def __init__(self, fd=0): self.buffer = FastReader(fd) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") class FastStdout(io.IOBase): def __init__(self, fd=1): self.buffer = FastWriter(fd) self.write = lambda s: self.buffer.write(s.encode("ascii")) self.flush = self.buffer.flush if __name__ == '__main__': sys.stdin = FastStdin() sys.stdout = FastStdout() main() ```
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25,299
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,654
0
25,308
Tags: dp, strings Correct Solution: ``` def make_array(n, m): new_arr = [] for _ in range(n): new_arr += [[0] * m] return new_arr def catching_cheaters(): n, m = [int(x) for x in input().split(' ')] str_a = input() str_b = input() dp = make_array(n + 1, m + 1) ans = 0 for i in range(1, n + 1): for j in range(1, m + 1): if str_a[i - 1] == str_b[j - 1]: dp[i][j] = dp[i - 1][j - 1] + 2 else: dp[i][j] = max(0, max(dp[i - 1][j], dp[i][j - 1]) - 1) ans = max(ans, dp[i][j]) print(ans) if __name__ == "__main__": catching_cheaters() ```
output
1
12,654
0
25,309
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,655
0
25,310
Tags: dp, strings Correct Solution: ``` import sys import os from io import BytesIO, IOBase #Fast IO Region 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, m = map(int, input().split()) a, b = input(), input() dp = [[0] * (m+2) for _ in range(n+2)] ans = 0 for i in range(n-1, -1, -1): for j in range(m-1, -1, -1): if a[i] == b[j]: dp[i][j] = dp[i+1][j+1] + 2 else: dp[i][j] = max(0, max(dp[i][j+1], dp[i+1][j]) -1) ans = max(ans, dp[i][j]) print(ans) ```
output
1
12,655
0
25,311
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,656
0
25,312
Tags: dp, strings Correct Solution: ``` from collections import deque n,m = list(map(int,input().split())) a = input() b = input() l1 = len(a) l2 = len(b) dp = [[0 for j in range(l2+1)] for i in range(l1+1)] mv = 0 for i in range(1,l1+1): for j in range(1,l2+1): if a[i-1]==b[j-1]: dp[i][j] = dp[i-1][j-1]+2 else: dp[i][j] = max(max(dp[i-1][j],dp[i][j-1])-1,0) mv = max(mv,dp[i][j]) print(mv) ```
output
1
12,656
0
25,313
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,657
0
25,314
Tags: dp, strings Correct Solution: ``` # coding: utf-8 n, m = map(int, input().split()) a = input() b = input() dp = [[0 for j in range(m + 1)] for i in range(n + 1)] maximal = 0 for i in range(1, n + 1): for j in range(1, m + 1): dp[i][j] = max(dp[i - 1][j] - 1, dp[i][j - 1] - 1, dp[i - 1][j - 1] + 2 if a[i - 1] == b[j - 1] else 0) maximal = max(maximal, dp[i][j]) print(maximal) ```
output
1
12,657
0
25,315
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,658
0
25,316
Tags: dp, strings Correct Solution: ``` n,m=map(int,input().split()) a=input() b=input() dp=[[0 for i in range(m+1)] for j in range(n+1)] ans=0 for i in range(1,n+1): for j in range(1,m+1): if a[i-1]==b[j-1]: dp[i][j]=max(dp[i][j],dp[i-1][j-1]+2) ans=max(ans,dp[i][j]) else: dp[i][j]=max(dp[i-1][j], dp[i][j-1],1)-1 print(ans) ```
output
1
12,658
0
25,317
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,659
0
25,318
Tags: dp, strings Correct Solution: ``` ''' =============================== -- @uthor : Kaleab Asfaw -- Handle : kaleabasfaw2010 -- Bio : High-School Student ===============================''' # Fast IO import sys import os 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") def solve(n, m, a, b): dp = dp = [[0] * (m + 1) for _ in range(n + 1)] maxx = 0 for i in range(1, n+1): for j in range(1, m+1): if a[i-1] == b[j-1]: dp[i][j] = max(dp[i][j], dp[i-1][j-1] + 2) else: dp[i][j] = max(dp[i][j], dp[i-1][j] - 1, dp[i][j-1] - 1) maxx = max(maxx, dp[i][j]) return maxx n, m = list(map(int, input().split())) a = input() b = input() print(solve(n, m, a, b)) ```
output
1
12,659
0
25,319
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,660
0
25,320
Tags: dp, strings Correct Solution: ``` #!/usr/bin/env python import os import sys from io import BytesIO, IOBase import threading from bisect import bisect_right from math import gcd,log from collections import Counter,defaultdict from pprint import pprint def lcs(a,b): ans=0 dp=[[0]*(len(b)+1) for i in range(len(a)+1)] for i in range(1,1+len(a)): for j in range(1,1+len(b)): if a[i-1]==b[j-1]: dp[i][j]=dp[i-1][j-1]+2 dp[i][j]=max(0,dp[i][j],dp[i][j-1]-1,dp[i-1][j]-1) ans=max(ans,dp[i][j]) # pprint(dp) return ans def main(case_no): n,m=map(int,input().split()) a=input() b=input() ans=lcs(a,b) print(ans) 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") # endregion if __name__ == "__main__": for _ in range(1): main(_+1) ```
output
1
12,660
0
25,321
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
instruction
0
12,661
0
25,322
Tags: dp, strings Correct Solution: ``` #include <CodeforcesSolutions.h> #include <ONLINE_JUDGE <solution.cf(contestID = "1447",questionID = "A",method = "GET")>.h> """ Author : thekushalghosh Team : CodeDiggers I prefer Python language over the C++ language :p :D Visit my website : thekushalghosh.github.io """ import sys,math,cmath,time start_time = time.time() ########################################################################## ################# ---- THE ACTUAL CODE STARTS BELOW ---- ################# def solve(): n,m = invr() a = insr() b = insr() dp = [[0] * (m + 1) for i in range(n + 1)] q = 0 for i in range(n): for j in range(m): if a[i] == b[j]: dp[i + 1][j + 1] = max(dp[i + 1][j] - 1,dp[i][j] + 2,dp[i][j + 1] - 1) q = max(q,dp[i + 1][j + 1]) else: dp[i + 1][j + 1] = max(dp[i][j + 1] - 1,dp[i + 1][j] - 1,0) print(q) ################## ---- THE ACTUAL CODE ENDS ABOVE ---- ################## ########################################################################## def main(): global tt if not ONLINE_JUDGE: sys.stdin = open("input.txt","r") sys.stdout = open("output.txt","w") t = 1 for tt in range(1,t + 1): solve() if not ONLINE_JUDGE: print("Time Elapsed :",time.time() - start_time,"seconds") sys.stdout.close() #----------------- USER DEFINED INPUT - OUTPUT FUNCTIONS -----------------# def inp(): return(int(input())) def inlt(): return(list(map(int,input().split()))) def insr(): return(input().strip()) def invr(): return(map(int,input().split())) def prints(a,qw = " "): sys.stdout.write(qw.join(map(str,a)) + "\n") #------------------ USER DEFINED PROGRAMMING FUNCTIONS ------------------# def counter(a): q = [0] * max(a) for i in range(len(a)): q[a[i] - 1] = q[a[i] - 1] + 1 return(q) def counter_elements(a): q = dict() for i in range(len(a)): if a[i] not in q: q[a[i]] = 0 q[a[i]] = q[a[i]] + 1 return(q) def string_counter(a): q = [0] * 26 for i in range(len(a)): q[ord(a[i]) - 97] = q[ord(a[i]) - 97] + 1 return(q) def factorial(n,m = 1000000007): q = 1 for i in range(n): q = (q * (i + 1)) % m return(q) def factors(n): q = [] for i in range(1,int(n ** 0.5) + 1): if n % i == 0: q.append(i); q.append(n // i) return(list(sorted(list(set(q))))) def prime_factors(n): q = [] while n % 2 == 0: q.append(2); n = n // 2 for i in range(3,int(n ** 0.5) + 1,2): while n % i == 0: q.append(i); n = n // i if n > 2: q.append(n) return(list(sorted(q))) def transpose(a): n,m = len(a),len(a[0]) b = [[0] * n for i in range(m)] for i in range(m): for j in range(n): b[i][j] = a[j][i] return(b) def power_two(x): return (x and (not(x & (x - 1)))) def ceil(a, b): return -(-a // b) def seive(n): a = [1] prime = [True for i in range(n + 1)] p = 2 while (p * p <= n): if (prime[p] == True): for i in range(p ** 2,n + 1,p): prime[i] = False p = p + 1 for p in range(2,n + 1): if prime[p]: a.append(p) return(a) def ncr(n,r): return(math.factorial(n) // (math.factorial(n - r) * math.factorial(r))) def npr(n,r): return(math.factorial(n) // math.factorial(n - r)) #-----------------------------------------------------------------------# ONLINE_JUDGE = __debug__ if ONLINE_JUDGE: #import io,os #input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline input = sys.stdin.readline main() ```
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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 strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` n, m = map(int, input().split());a = input();b = input();LR = [0 for _ in range(n+1)];best = 0 for c in b: NR = [0 for _ in range(n+1)] for i in range(1,n+1): back = NR[i-1] - 1;up = LR[i] - 1;diag = LR[i-1] - 2 if c == a[i-1]: diag += 4 NR[i] = max(back, up, diag, 0);best = max(best, NR[i]) LR = NR print(best) ```
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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 strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` import os import sys from io import BytesIO, IOBase import math import itertools as iter from collections import defaultdict as ddic from collections import Counter as Co from collections import deque import threading def increase_stack(): sys.setrecursionlimit(2**32//2-1) threading.stack_size(1 << 27) #sys.setrecursionlimit(10**6) #threading.stack_size(10**8) t = threading.Thread(target=main) t.start() t.join() #? Region Funtions def binary(n): return (bin(n).replace("0b", "")) def decimal(s): return (int(s, 2)) def pow2(n): p = 0 while (n > 1): n //= 2 p += 1 return (p) def primeFactors(n): l=[] while n % 2 == 0: l.append(2) n = n / 2 for i in range(3, int(math.sqrt(n)) + 1, 2): while n % i == 0: l.append(i) n = n / i if n > 2: l.append(int(n)) return (l) def isPrime(n): if (n == 1): return (False) else: root = int(n ** 0.5) root += 1 for i in range(2, root): if (n % i == 0): return (False) return (True) def maxPrimeFactors(n): maxPrime = -1 while n % 2 == 0: maxPrime = 2 n >>= 1 for i in range(3, int(math.sqrt(n)) + 1, 2): while n % i == 0: maxPrime = i n = n / i if n > 2: maxPrime = n return int(maxPrime) def countchar(s,i): c=0 ch=s[i] for i in range(i,len(s)): if(s[i]==ch): c+=1 else: break return(c) def lis(arr): n = len(arr) lis = [1] * n maximum=0 for i in range(1, n): for j in range(0, i): if arr[i] > arr[j] and lis[i] < lis[j] + 1: lis[i] = lis[j] + 1 maximum=max(maximum,lis[i]) return maximum def lcm(arr): a=arr[0]; val=arr[0] for i in range(1,len(arr)): gcd=gcd(a,arr[i]) a=arr[i]; val*=arr[i] return val//gcd #? Region Taking Input def inint(): return int(input()) def inarr(): return list(map(int,input().split())) def invar(): return map(int,input().split()) def instr(): s=input() return list(s) #? 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") #!==================================== Write The Useful Code Here ============================ def solver(): pass #! This is the Main Function def main(): n,m=invar() s1=input() s2=input() ans=0 dp=[[0]*(m+1) for i in range(0,n+1)] #print(dp) for i in range(0,n): for j in range(0,m): if(s1[i]==s2[j]): dp[i+1][j+1]=max(0,dp[i][j]+2) else: dp[i+1][j+1]=max(0,dp[i+1][j]-1,dp[i][j+1]-1) ans=max(ans,dp[i+1][j+1]) print(ans) #? End Region if __name__ == "__main__": #? Incresing Stack Limit #increase_stack() #! Calling Main Function main() ```
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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 strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` n, m = map(int, input().split()) A = input() B = input() dp = [] for i, a in enumerate(A): dp.append([]) for j, b in enumerate(B): if i == 0 and j == 0: if a == b: dp[i].append(2) else: dp[i].append(0) elif i == 0: if a == b: dp[i].append(2) else: dp[i].append(max(0, dp[i][j-1] - 1)) elif j == 0: if a == b: dp[i].append(2) else: dp[i].append(max(0, dp[i-1][j] - 1)) else: if a != b: dp[i].append(max(0, dp[i-1][j]-1, dp[i][j-1]-1)) else: dp[i].append(max(0, dp[i-1][j-1]+2, dp[i-1][j]-1, dp[i][j-1]-1)) maxi = max([max(val) for val in dp]) print(maxi) ```
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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 strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` import pprint n, m = map(int, input().split()) s = input() t = input() ans = 0 X = s Y = t m = len(X) n = len(Y) L = [[0]*(n + 1) for i in range(m + 1)] i = 1 j = 1 while i < m + 1: j = 1 while j < n + 1: v = 0 if X[i-1] == Y[j-1]: v = max(L[i - 1][j - 1] + 2, 2) if L[i][j - 1] > v: v = L[i][j - 1] - 1 if L[i - 1][j] > v: v = L[i - 1][j] - 1 L[i][j] = v if v > ans: ans = v j += 1 i += 1 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. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` import sys from math import gcd,sqrt,ceil,log2 from collections import defaultdict,Counter,deque from bisect import bisect_left,bisect_right import math sys.setrecursionlimit(2*10**5+10) import heapq from itertools import permutations # input=sys.stdin.readline # def print(x): # sys.stdout.write(str(x)+"\n") # sys.stdin = open('input.txt', 'r') # sys.stdout = open('output.txt', 'w') import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 aa='abcdefghijklmnopqrstuvwxyz' 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") # import sys # import io, os # input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline def get_sum(bit,i): s = 0 i+=1 while i>0: s+=bit[i] i-=i&(-i) return s def update(bit,n,i,v): i+=1 while i<=n: bit[i]+=v i+=i&(-i) def modInverse(b,m): g = math.gcd(b, m) if (g != 1): return -1 else: return pow(b, m - 2, m) def primeFactors(n): sa = [] # sa.add(n) while n % 2 == 0: sa.append(2) n = n // 2 for i in range(3,int(math.sqrt(n))+1,2): while n % i== 0: sa.append(i) n = n // i # sa.add(n) if n > 2: sa.append(n) return sa def seive(n): pri = [True]*(n+1) p = 2 while p*p<=n: if pri[p] == True: for i in range(p*p,n+1,p): pri[i] = False p+=1 return pri def check_prim(n): if n<0: return False for i in range(2,int(sqrt(n))+1): if n%i == 0: return False return True def getZarr(string, z): n = len(string) # [L,R] make a window which matches # with prefix of s l, r, k = 0, 0, 0 for i in range(1, n): # if i>R nothing matches so we will calculate. # Z[i] using naive way. if i > r: l, r = i, i # R-L = 0 in starting, so it will start # checking from 0'th index. For example, # for "ababab" and i = 1, the value of R # remains 0 and Z[i] becomes 0. For string # "aaaaaa" and i = 1, Z[i] and R become 5 while r < n and string[r - l] == string[r]: r += 1 z[i] = r - l r -= 1 else: # k = i-L so k corresponds to number which # matches in [L,R] interval. k = i - l # if Z[k] is less than remaining interval # then Z[i] will be equal to Z[k]. # For example, str = "ababab", i = 3, R = 5 # and L = 2 if z[k] < r - i + 1: z[i] = z[k] # For example str = "aaaaaa" and i = 2, # R is 5, L is 0 else: # else start from R and check manually l = i while r < n and string[r - l] == string[r]: r += 1 z[i] = r - l r -= 1 def search(text, pattern): # Create concatenated string "P$T" concat = pattern + "$" + text l = len(concat) z = [0] * l getZarr(concat, z) ha = [] for i in range(l): if z[i] == len(pattern): ha.append(i - len(pattern) - 1) return ha # n,k = map(int,input().split()) # l = list(map(int,input().split())) # # n = int(input()) # l = list(map(int,input().split())) # # hash = defaultdict(list) # la = [] # # for i in range(n): # la.append([l[i],i+1]) # # la.sort(key = lambda x: (x[0],-x[1])) # ans = [] # r = n # flag = 0 # lo = [] # ha = [i for i in range(n,0,-1)] # yo = [] # for a,b in la: # # if a == 1: # ans.append([r,b]) # # hash[(1,1)].append([b,r]) # lo.append((r,b)) # ha.pop(0) # yo.append([r,b]) # r-=1 # # elif a == 2: # # print(yo,lo) # # print(hash[1,1]) # if lo == []: # flag = 1 # break # c,d = lo.pop(0) # yo.pop(0) # if b>=d: # flag = 1 # break # ans.append([c,b]) # yo.append([c,b]) # # # # elif a == 3: # # if yo == []: # flag = 1 # break # c,d = yo.pop(0) # if b>=d: # flag = 1 # break # if ha == []: # flag = 1 # break # # ka = ha.pop(0) # # ans.append([ka,b]) # ans.append([ka,d]) # yo.append([ka,b]) # # if flag: # print(-1) # else: # print(len(ans)) # for a,b in ans: # print(a,b) def mergeIntervals(arr): # Sorting based on the increasing order # of the start intervals arr.sort(key = lambda x: x[0]) # array to hold the merged intervals m = [] s = -10000 max = -100000 for i in range(len(arr)): a = arr[i] if a[0] > max: if i != 0: m.append([s,max]) max = a[1] s = a[0] else: if a[1] >= max: max = a[1] #'max' value gives the last point of # that particular interval # 's' gives the starting point of that interval # 'm' array contains the list of all merged intervals if max != -100000 and [s, max] not in m: m.append([s, max]) return m class SortedList: def __init__(self, iterable=[], _load=200): """Initialize sorted list instance.""" values = sorted(iterable) self._len = _len = len(values) self._load = _load self._lists = _lists = [values[i:i + _load] for i in range(0, _len, _load)] self._list_lens = [len(_list) for _list in _lists] self._mins = [_list[0] for _list in _lists] self._fen_tree = [] self._rebuild = True def _fen_build(self): """Build a fenwick tree instance.""" self._fen_tree[:] = self._list_lens _fen_tree = self._fen_tree for i in range(len(_fen_tree)): if i | i + 1 < len(_fen_tree): _fen_tree[i | i + 1] += _fen_tree[i] self._rebuild = False def _fen_update(self, index, value): """Update `fen_tree[index] += value`.""" if not self._rebuild: _fen_tree = self._fen_tree while index < len(_fen_tree): _fen_tree[index] += value index |= index + 1 def _fen_query(self, end): """Return `sum(_fen_tree[:end])`.""" if self._rebuild: self._fen_build() _fen_tree = self._fen_tree x = 0 while end: x += _fen_tree[end - 1] end &= end - 1 return x def _fen_findkth(self, k): """Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`).""" _list_lens = self._list_lens if k < _list_lens[0]: return 0, k if k >= self._len - _list_lens[-1]: return len(_list_lens) - 1, k + _list_lens[-1] - self._len if self._rebuild: self._fen_build() _fen_tree = self._fen_tree idx = -1 for d in reversed(range(len(_fen_tree).bit_length())): right_idx = idx + (1 << d) if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]: idx = right_idx k -= _fen_tree[idx] return idx + 1, k def _delete(self, pos, idx): """Delete value at the given `(pos, idx)`.""" _lists = self._lists _mins = self._mins _list_lens = self._list_lens self._len -= 1 self._fen_update(pos, -1) del _lists[pos][idx] _list_lens[pos] -= 1 if _list_lens[pos]: _mins[pos] = _lists[pos][0] else: del _lists[pos] del _list_lens[pos] del _mins[pos] self._rebuild = True def _loc_left(self, value): """Return an index pair that corresponds to the first position of `value` in the sorted list.""" if not self._len: return 0, 0 _lists = self._lists _mins = self._mins lo, pos = -1, len(_lists) - 1 while lo + 1 < pos: mi = (lo + pos) >> 1 if value <= _mins[mi]: pos = mi else: lo = mi if pos and value <= _lists[pos - 1][-1]: pos -= 1 _list = _lists[pos] lo, idx = -1, len(_list) while lo + 1 < idx: mi = (lo + idx) >> 1 if value <= _list[mi]: idx = mi else: lo = mi return pos, idx def _loc_right(self, value): """Return an index pair that corresponds to the last position of `value` in the sorted list.""" if not self._len: return 0, 0 _lists = self._lists _mins = self._mins pos, hi = 0, len(_lists) while pos + 1 < hi: mi = (pos + hi) >> 1 if value < _mins[mi]: hi = mi else: pos = mi _list = _lists[pos] lo, idx = -1, len(_list) while lo + 1 < idx: mi = (lo + idx) >> 1 if value < _list[mi]: idx = mi else: lo = mi return pos, idx def add(self, value): """Add `value` to sorted list.""" _load = self._load _lists = self._lists _mins = self._mins _list_lens = self._list_lens self._len += 1 if _lists: pos, idx = self._loc_right(value) self._fen_update(pos, 1) _list = _lists[pos] _list.insert(idx, value) _list_lens[pos] += 1 _mins[pos] = _list[0] if _load + _load < len(_list): _lists.insert(pos + 1, _list[_load:]) _list_lens.insert(pos + 1, len(_list) - _load) _mins.insert(pos + 1, _list[_load]) _list_lens[pos] = _load del _list[_load:] self._rebuild = True else: _lists.append([value]) _mins.append(value) _list_lens.append(1) self._rebuild = True def discard(self, value): """Remove `value` from sorted list if it is a member.""" _lists = self._lists if _lists: pos, idx = self._loc_right(value) if idx and _lists[pos][idx - 1] == value: self._delete(pos, idx - 1) def remove(self, value): """Remove `value` from sorted list; `value` must be a member.""" _len = self._len self.discard(value) if _len == self._len: raise ValueError('{0!r} not in list'.format(value)) def pop(self, index=-1): """Remove and return value at `index` in sorted list.""" pos, idx = self._fen_findkth(self._len + index if index < 0 else index) value = self._lists[pos][idx] self._delete(pos, idx) return value def bisect_left(self, value): """Return the first index to insert `value` in the sorted list.""" pos, idx = self._loc_left(value) return self._fen_query(pos) + idx def bisect_right(self, value): """Return the last index to insert `value` in the sorted list.""" pos, idx = self._loc_right(value) return self._fen_query(pos) + idx def count(self, value): """Return number of occurrences of `value` in the sorted list.""" return self.bisect_right(value) - self.bisect_left(value) def __len__(self): """Return the size of the sorted list.""" return self._len def __getitem__(self, index): """Lookup value at `index` in sorted list.""" pos, idx = self._fen_findkth(self._len + index if index < 0 else index) return self._lists[pos][idx] def __delitem__(self, index): """Remove value at `index` from sorted list.""" pos, idx = self._fen_findkth(self._len + index if index < 0 else index) self._delete(pos, idx) def __contains__(self, value): """Return true if `value` is an element of the sorted list.""" _lists = self._lists if _lists: pos, idx = self._loc_left(value) return idx < len(_lists[pos]) and _lists[pos][idx] == value return False def __iter__(self): """Return an iterator over the sorted list.""" return (value for _list in self._lists for value in _list) def __reversed__(self): """Return a reverse iterator over the sorted list.""" return (value for _list in reversed(self._lists) for value in reversed(_list)) def __repr__(self): """Return string representation of sorted list.""" return 'SortedList({0})'.format(list(self)) def ncr(n, r, p): num = den = 1 for i in range(r): num = (num * (n - i)) % p den = (den * (i + 1)) % p return (num * pow(den, p - 2, p)) % p def sol(n): seti = set() for i in range(1,int(sqrt(n))+1): if n%i == 0: seti.add(n//i) seti.add(i) return seti def lcm(a,b): return (a*b)//gcd(a,b) # # n,p = map(int,input().split()) # # s = input() # # if n <=2: # if n == 1: # pass # if n == 2: # pass # i = n-1 # idx = -1 # while i>=0: # z = ord(s[i])-96 # k = chr(z+1+96) # flag = 1 # if i-1>=0: # if s[i-1]!=k: # flag+=1 # else: # flag+=1 # if i-2>=0: # if s[i-2]!=k: # flag+=1 # else: # flag+=1 # if flag == 2: # idx = i # s[i] = k # break # if idx == -1: # print('NO') # exit() # for i in range(idx+1,n): # if # def moore_voting(l): count1 = 0 count2 = 0 first = 10**18 second = 10**18 n = len(l) for i in range(n): if l[i] == first: count1+=1 elif l[i] == second: count2+=1 elif count1 == 0: count1+=1 first = l[i] elif count2 == 0: count2+=1 second = l[i] else: count1-=1 count2-=1 for i in range(n): if l[i] == first: count1+=1 elif l[i] == second: count2+=1 if count1>n//3: return first if count2>n//3: return second return -1 def find_parent(u,parent): if u!=parent[u]: parent[u] = find_parent(parent[u],parent) return parent[u] def dis_union(n): par = [i for i in range(n+1)] rank = [1]*(n+1) k = int(input()) for i in range(k): a,b = map(int,input().split()) z1,z2 = find_parent(a,par),find_parent(b,par) if z1!=z2: par[z1] = z2 rank[z2]+=rank[z1] def dijkstra(n,tot,hash): hea = [[0,n]] dis = [10**18]*(tot+1) dis[n] = 0 boo = defaultdict(bool) check = defaultdict(int) while hea: a,b = heapq.heappop(hea) if boo[b]: continue boo[b] = True for i,w in hash[b]: if b == 1: c = 0 if (1,i,w) in nodes: c = nodes[(1,i,w)] del nodes[(1,i,w)] if dis[b]+w<dis[i]: dis[i] = dis[b]+w check[i] = c elif dis[b]+w == dis[i] and c == 0: dis[i] = dis[b]+w check[i] = c else: if dis[b]+w<=dis[i]: dis[i] = dis[b]+w check[i] = check[b] heapq.heappush(hea,[dis[i],i]) return check def power(x,y,p): res = 1 x = x%p if x == 0: return 0 while y>0: if (y&1) == 1: res*=x x = x*x y = y>>1 return res n,m = map(int,input().split()) s1 = input() s2 = input() dp = defaultdict(int) maxi = 0 for i in range(n+1): for j in range(m+1): if i == 0 or j == 0: continue if s1[i-1] == s2[j-1]: dp[(i,j)] = max(dp[(i,j)],dp[(i-1,j-1)]+2) else: dp[(i,j)] = max(dp[(i-1,j)],dp[(i,j-1)]) - 1 maxi = max(dp[(i,j)],maxi) print(maxi) ```
instruction
0
12,666
0
25,332
No
output
1
12,666
0
25,333
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` n,m = list(map(int,input().split())) a = input() b = input() l1 = len(a) l2 = len(b) lcs = [[0 for j in range(l2+1)] for i in range(l1+1)] for i in range(1,l1+1): for j in range(1,l2+1): if a[i-1]==b[j-1]: lcs[i][j] = lcs[i-1][j-1]+1 else: lcs[i][j] = max(lcs[i-1][j],lcs[i][j-1]) i,j = l1,l2 ilist = [] jlist = [] while i>0 and j>0: if a[i-1]==b[j-1]: ilist.append(i) jlist.append(j) i-=1 j-=1 else: if lcs[i][j]==lcs[i][j-1]: j-=1 else: i-=1 out = lcs[-1][-1] la,lb = 0,0 if ilist and jlist: la = ilist[0]-ilist[-1]+1 lb = jlist[0]-jlist[-1]+1 print(4*out-la-lb) ```
instruction
0
12,667
0
25,334
No
output
1
12,667
0
25,335
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` """ #If FastIO not needed, use this and don't forget to strip #import sys, math #input = sys.stdin.readline """ import os import sys from io import BytesIO, IOBase import heapq as h from bisect import bisect_left, bisect_right import time from types import GeneratorType BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): import os self.os = os 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 = self.os.read(self._fd, max(self.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 = self.os.read(self._fd, max(self.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: self.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 collections import defaultdict as dd, deque as dq, Counter as dc import math, string #start_time = time.time() def getInts(): return [int(s) for s in input().split()] def getInt(): return int(input()) def getStrs(): return [s for s in input().split()] def getStr(): return input() def listStr(): return list(input()) def getMat(n): return [getInts() for _ in range(n)] MOD = 10**9+7 """ 4*L(C,D) - |C| - |D| 5 7 8 5 3 4 6 2 4 6 7 3 abba babab Substrings can have length 0 to len(S) in each dp = [[0 for j in range(M+1)] for i in range(N+1)] dp[1][0] = dp[0][1] = 0 dp[1][1] = 0 if S[0] != T[0] else 2 """ def solve(): N, M = getInts() S = [0]+listStr() T = [0]+listStr() ans = 0 dp = [[0 for m in range(M+1)] for n in range(N+1)] for i in range(1,N+1): for j in range(1,M+1): dp[i][j] = max(dp[i-1][j]-1,dp[i][j-1]-1) if S[i] == T[j]: dp[i][j] = max(dp[i][j],dp[i-1][j-1]+2) ans = max(ans,dp[i][j]) return ans #for _ in range(getInt()): print(solve()) #print(time.time()-start_time) ```
instruction
0
12,668
0
25,336
No
output
1
12,668
0
25,337
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. You believe that only some part of the essays could have been copied, therefore you're interested in their substrings. Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. If X is a string, |X| denotes its length. A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem). Input The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. The second line contains a string consisting of n lowercase Latin letters — string A. The third line contains a string consisting of m lowercase Latin letters — string B. Output Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. Examples Input 4 5 abba babab Output 5 Input 8 10 bbbbabab bbbabaaaaa Output 12 Input 7 7 uiibwws qhtkxcn Output 0 Note For the first case: abb from the first string and abab from the second string have LCS equal to abb. The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5. Submitted Solution: ``` import sys import math def II(): return int(sys.stdin.readline()) def LI(): return list(map(int, sys.stdin.readline().split())) def MI(): return map(int, sys.stdin.readline().split()) def SI(): return sys.stdin.readline().strip() def FACT(n, mod): s = 1 facts = [1] for i in range(1,n+1): s*=i s%=mod facts.append(s) return facts[n] def C(n, k, mod): return (FACT(n,mod) * pow((FACT(k,mod)*FACT(n-k,mod))%mod,mod-2, mod))%mod n,m = MI() a = list(SI()) b = list(SI()) n1 = len(a) n2 = len(b) ans = 0 dp = [[0 for i in range(n2 + 1)] for i in range(n1 + 1)] dp1 = [[[1,1] for i in range(n2 + 1)] for i in range(n1 + 1)] for i in range(1,n+1): for j in range(1,m+1): if a[i-1] == b[j-1]: dp[i][j] = dp[i-1][j-1]+1 dp1[i][j] = dp1[i-1][j-1] if dp[i][j] == 1: dp1[i][j] = [i,j] x,y = dp1[i][j] ans = max(ans,4*dp[i][j]-(i-x+1)-(j-y+1)) else: if dp[i-1][j]>dp[i][j-1]: dp[i][j] = dp[i-1][j] dp1[i][j] = dp1[i-1][j] elif dp[i][j-1]>dp[i-1][j]: dp[i][j] = dp[i][j-1] dp1[i][j] = dp1[i][j-1] else: x,y = dp1[i][j-1] x2,y2 = dp1[i-1][j] if x2-x+y2-y > 0: dp1[i][j] = dp1[i-1][j] else: dp1[i][j] = dp1[i][j-1] print(ans) ```
instruction
0
12,669
0
25,338
No
output
1
12,669
0
25,339
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,160
0
26,320
"Correct Solution: ``` N = int(input()) *A, = map(int, input().split()) def check(K): st = [] for i, a in enumerate(A): #print(K, i, st, a) while st and a < st[-1][0]: st.pop() u = i > 0 and A[i-1] >= A[i] if not st: st.append([a, u]) continue l = st[-1] if l[0] == a: l[1] += 1 while st and l[1] == K: st.pop(); a -= 1 if a == 0: return 0 if not st: st.append([a, 1]) break l = st[-1] if l[0] == a: l[1] += 1 else: st.append([a, 1]) break #print(l, st) else: st.append([a, u]) #print(st) return 1 ok = 1 for i in range(N-1): if not A[i] < A[i+1]: ok = 0 if ok: print(1) exit(0) left = 1; right = N+1 while left+1 < right: mid = (left + right) // 2 if check(mid): right = mid else: left = mid print(right) ```
output
1
13,160
0
26,321
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,161
0
26,322
"Correct Solution: ``` import sys stdin = sys.stdin sys.setrecursionlimit(10**5) def li(): return map(int, stdin.readline().split()) def li_(): return map(lambda x: int(x)-1, stdin.readline().split()) def lf(): return map(float, stdin.readline().split()) def ls(): return stdin.readline().split() def ns(): return stdin.readline().rstrip() def lc(): return list(ns()) def ni(): return int(stdin.readline()) def nf(): return float(stdin.readline()) def shave(stack:list, nex:int, prv:int): res = prv-nex while res > 0: if res >= stack[-1][1]: _,y = stack.pop() res -= y else: stack[-1][1] -= res res = 0 def normalize(stack: list): if stack[-1][0] == stack[-2][0]: stack[-2][1] += stack[-1][1] stack.pop() def add(stack:list): if stack[-1][1] == 1: stack[-1][0] += 1 else: stack[-1][1] -= 1 stack.append([stack[-1][0]+1, 1]) def kuriagari(stack:list): _, y = stack.pop() add(stack) normalize(stack) stack.append([1,y]) def check(a:list, upto:int): stack = [[0,0]] for i in range(n): if a[i+1] > a[i]: stack.append([1, a[i+1]-a[i]]) normalize(stack) else: shave(stack, a[i+1], a[i]) if stack[-1][0] == upto and stack[-1][1] == a[i+1]: return False elif stack[-1][0] == upto: kuriagari(stack) else: add(stack) normalize(stack) return True def binsearch(a:list): low = 0 high = 10**9+1 while high-low > 1: mid = (high+low) // 2 if check(a, mid): high = mid else: low = mid return high n = ni() a = [0] + list(li()) ans = binsearch(a) print(ans) ```
output
1
13,161
0
26,323
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,162
0
26,324
"Correct Solution: ``` n = int(input()) a = list(map(int, input().split())) ok, ng = n, 0 while ok-ng > 1: x = (ok+ng)//2 #d = defaultdict(int) d = dict() last = 0 valid = True if x == 1: for i in range(n-1): if a[i] >= a[i+1]: valid = False break if valid: ok = x else: ng = x continue for i in range(n-1): dels = [] if a[i] < a[i+1]: last = a[i+1] continue j = a[i+1] for k in d.keys(): if j < k: dels.append(k) while j > 0: if j in d and d[j] == x-1: #d[j] = 0 dels.append(j) j -= 1 else: break if j in d: d[j] += 1 else: d[j] = 1 for k in dels: del d[k] if 0 in d: valid = False break last = j if valid: ok = x else: ng = x print(ok) ```
output
1
13,162
0
26,325
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,163
0
26,326
"Correct Solution: ``` import sys input = sys.stdin.readline N = int(input()) A = [int(x) for x in input().split()] A.append(1) B = [A[0]] B_cnt = [1] for i,(x,y) in enumerate(zip(A[:-1],A[1:])): if x < y and y < A[i+2]: continue if x == y: B_cnt[-1] += 1 else: B.append(y) B_cnt.append(1) def test(x): digit = [0] cnt = [0] for a,a_cnt in zip(B,B_cnt): if digit[-1] < a: digit.append(a) cnt.append(a_cnt) continue if digit[-1] == a: cnt[-1] += a_cnt continue while True: # 繰り上がり処理をしながら左に戻る if digit[-1] <= a: break n = digit.pop() k = cnt.pop() if k <= x: continue if digit[-1] == n-1: cnt[-1] += (k-1)//x else: digit.append(n-1) cnt.append((k-1)//x + 1) if digit[-1] == a: cnt[-1] += a_cnt else: digit.append(a) cnt.append(1+a_cnt) return cnt[1] <= x+1 if all(x<y for x,y in zip(A[:-2],A[1:-1])): print(1) exit() left = 1 # 無理 right = 10 # 可能? while not test(right): left *= 10 right *= 10 right = min(right,N) while right > left + 1: mid = (left+right)//2 if test(mid): right = mid else: left = mid answer = right print(answer) ```
output
1
13,163
0
26,327
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,164
0
26,328
"Correct Solution: ``` N = int(input()) A = [int(a) for a in input().split()] def chk(k): if k == 1: for i in range(1, N): if A[i] <= A[i-1]: return 0 return 1 X = [(0, 0)] def add(x, y): if x <= 0: return 0 if x > X[-1][0]: X.append((x, 0 if x == y else 1)) elif x == X[-1][0]: if X[-1][1] + 1 < k: X[-1] = (X[-1][0], X[-1][1] + 1) else: if add(x-1, y) == 0: return 0 else: while X[-1][0] > x: X.pop() if x > X[-1][0]: X.append((x, 1)) elif x == X[-1][0]: if X[-1][1] + 1 < k: X[-1] = (X[-1][0], X[-1][1] + 1) else: if add(x-1, y) == 0: return 0 if X[-1][0] < y: X.append((y, 0)) return 1 for a in A: if add(a, a) == 0: return 0 return 1 l, r = 0, 1 << 18 while r - l > 1: m = (l + r) // 2 if chk(m): r = m else: l = m print(r) ```
output
1
13,164
0
26,329
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,165
0
26,330
"Correct Solution: ``` def is_possible(x, A): current = {} length = 0 for a in A: if a <= length: if x == 1: return False current = {k: current[k] for k in current if k < a} i = a - 1 if i not in current: current[i] = 0 current[i] += 1 while i in current and current[i] >= x: if i == 0: return False if (i-1) not in current: current[i-1] = 0 current[i-1] += 1 del current[i] i -= 1 length = a return True def main(): N = int(input()) A = list(map(int, input().split())) left = 1 right = N while left < right: center = (left + right) // 2 if is_possible(center, A): right = center else: left = center + 1 print(left) if __name__ == "__main__": main() ```
output
1
13,165
0
26,331
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,166
0
26,332
"Correct Solution: ``` N = int(input()) A_raw = list(map(int, input().split())) flg = 1 prev = 0 A = [] for i in range(N): if A_raw[i] <= prev: flg = 0 prev = A_raw[i] if A_raw[i] <= 50: A.append(A_raw[i]) if flg: print(1) exit() N = len(A) if N <= 1: print(2) exit() ok = N ng = 1 mid = (ok + ng) // 2 while ok - ng > 1: ng_flg = 0 word = [1] * A[0] for i in range(1, N): if A[i] > A[i-1]: word.extend([1] * (A[i] - A[i-1])) else: word_prev = word[:A[i]] k = A[i] - 1 while True: if k == -1: ng_flg = 1 break if word_prev[k] != mid: word_prev[k] += 1 word = word_prev break else: word_prev[k] = 1 k -= 1 if ng_flg == 1: break if not ng_flg: ok = mid else: ng = mid mid = (ok + ng) // 2 print(ok) ```
output
1
13,166
0
26,333
Provide a correct Python 3 solution for this coding contest problem. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2
instruction
0
13,167
0
26,334
"Correct Solution: ``` def solve(aaa): l = 1 r = 200000 while l < r: m = (l + r) // 2 if check(m, aaa): r = m else: l = m + 1 return r def check(d, aaa): if d == 1: return all(a1 < a2 for a1, a2 in zip(aaa, aaa[1:])) l = 0 word = [[0, 0]] for a in aaa: if l >= a: if not carry(d, word, a): return False l = a return True def carry(d, word, i): while word[-1][0] > i: word.pop() while word[-1] == [i, d]: word.pop() i -= 1 if i == 0: return False if word[-1][0] == i: word[-1][1] += 1 else: word.append([i, 2]) return True n = int(input()) aaa = list(map(int, input().split())) print(solve(aaa)) ```
output
1
13,167
0
26,335
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` def main(): import heapq n = int(input()) a = list(map(int, input().split())) for i in range(n-1): if a[i] >= a[i+1]: break else: print(1) return h = [] heapq.heapify(h) kind = 1 length = 0 d = dict() for i in a: if length >= i: while h: hh = -heapq.heappop(h) if hh > i: d.pop(hh) else: heapq.heappush(h, -hh) break for j in range(i, 0, -1): if j not in d: d[j] = 2 heapq.heappush(h, -j) kind = max(kind, 2) while h: hh = -heapq.heappop(h) if hh > j: d.pop(hh) else: heapq.heappush(h, -hh) break break else: if d[j] < kind: d[j] += 1 while h: hh = -heapq.heappop(h) if hh > j: d.pop(hh) else: heapq.heappush(h, -hh) break break else: d[i] += 1 kind += 1 length = i def value(kind): length = 0 d = dict() for i in a: if length >= i: del_list = [] for j in d: if j > i: del_list.append(j) for j in del_list: d.pop(j) for j in range(i, 0, -1): if j not in d: d[j] = 2 break else: if d[j] < kind: d[j] += 1 break else: d.pop(j) else: return False length = i return True def b_search(ok, ng, value): while abs(ok-ng) > 1: mid = (ok+ng)//2 if value(mid): ok = mid else: ng = mid return ok print(b_search(kind, max(1, kind-30), value)) main() ```
instruction
0
13,168
0
26,336
Yes
output
1
13,168
0
26,337
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` import random input() A = [int(_) for _ in input().split()] A = [A[0]] + [j for i, j in zip(A, A[1:]) if i >= j] N = len(A) def cut(array, index): if index < 1: return [] if index <= array[0][0]: return [(index, array[0][1])] for _ in range(len(array)-1, 0, -1): if array[_ - 1][0] < index: return array[:_] + [(index, array[_][1])] def is_possible(K): dp = [(A[0], 0)] for a in A[1:]: if a <= dp[-1][0]: dp = cut(dp, a) else: dp += [(a, 0)] is_added = False for j in range(len(dp) - 1, -1, -1): if dp[j][1] < K - 1: dp = cut(dp, dp[j][0] - 1) + [(dp[j][0], dp[j][1] + 1)] if dp[-1][0] < a: dp += [(a, 0)] is_added = True break if not is_added: return False return True def bis(x, y): if y == x + 1: return y elif is_possible((x + y) // 2): return bis(x, (x + y) // 2) else: return bis((x + y) // 2, y) print(bis(0, N)) ```
instruction
0
13,169
0
26,338
Yes
output
1
13,169
0
26,339
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` import sys input = sys.stdin.readline N = int(input()) A = list(map(int, input().split())) # import random # N = 10**5 # A = [random.randrange(1,10**9+1) for _ in range(N)] # import time def main(): l = 0 r = N while r-l > 1: m = (r+l)//2 ok = True if m == 1: pre = -1 for a in A: if pre >= a: ok = False break pre = a else: dp = {} needreset = 10**15 exception = set() pre = -1 for a in A: ind = a for _ in range(40): # 修正 if needreset >= ind or ind in exception: if not ind in dp: dp[ind] = 0 if pre < a else 1 else: dp[ind] = 0 if pre < a else 1 exception.add(ind) # たす if dp[ind] < m: dp[ind] += 1 break elif ind == 1: ok = False break else: # 繰り上がり dp[ind] = 1 ind -= 1 if not ok: break # 更新 if pre > a: needreset = a exception = set() pre = a if ok: r = m else: l = m print(r) if __name__ == "__main__": #dt = time.time() main() #print(time.time()-dt) ```
instruction
0
13,170
0
26,340
Yes
output
1
13,170
0
26,341
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` import bisect from collections import deque """ def pl(d,k): now = d ind = bisect.bisect_left(dlis,d) while ind > 0: dic[dlis[ind]] += 1 if dic[dlis[ind]] // k == 0: dic[dlis[ind]] = 0 else: break ind -= 1 def able(k): ndep = A[0] for i in range(len(dlis)): dic[dlis[i]] = 0 for i in range(N-1): i += 1 if ndep < A[i]: dic[A[i]] = 0 ndep = A[i] else: ndep = A[i] pl(ndep,k) print (dic,k) if dic[dlis[0]] < k: return True else: return False """ def updiv(a,b): if a % b == 0: return a // b else: return a // b + 1 def able(k): nq = deque([0]) num = deque([A[0]]) for i in range(N-1): i += 1 if A[i] > A[i-1]: if nq[-1] == 0: num[-1] += A[i] - A[i-1] else: nq.append(0) num.append(A[i] - A[i-1]) else: if A[i] < A[i-1]: ds = A[i-1] - A[i] while len(num) > 0 and ds >= num[-1]: nq.pop() ds -= num[-1] num.pop() if len(num) == 0: return False num[-1] -= ds now = 0 while len(nq) > 0 and nq[-1] == k-1: now += num[-1] nq.pop() num.pop() if len(nq) == 0: return False if num[-1] == 1: nq[-1] += 1 else: num[-1] -= 1 nq.append(nq[-1] + 1) num.append(1) if now > 0: nq.append(0) num.append(now) while len(nq) > 1 and nq[-1] == nq[-2]: num[-2] += num[-1] nq.pop() num.pop() #print (k,A[i]) #print (nq) #print (num) return True N = int(input()) A = list(map(int,input().split())) A.append(1) l = 0 r = N while r - l != 1 : m = (l + r) // 2 if able(m): r = m else: l = m print (r) ```
instruction
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13,171
0
26,342
Yes
output
1
13,171
0
26,343
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` from collections import defaultdict from copy import copy n = int(input()) a = list(map(int, input().split())) ok, ng = n, 0 while ok-ng > 1: x = (ok+ng)//2 d = defaultdict(int) last = 0 valid = True if x == 1: for i in range(n-1): if a[i] >= a[i+1]: valid = False break if valid: ok = x else: ng = x continue for i in range(n-1): if a[i] > a[i+1]: if a[i+1] > last: d[a[i+1]] = 1 else: j = a[i+1] while d[j] == x-1 and j > 0: del d[j] j -= 1 d[j] += 1 last = a[i+1] elif a[i] == a[i+1]: j = a[i+1] while d[j] == x-1 and j > 0: del d[j] j -= 1 d[j] += 1 last = a[i+1] e = copy(d) for k in d.keys(): if k > last: del e[k] d = copy(e) #if x < 5: #print(x, last, d) if d[0] > 0: valid = False break if valid: ok = x else: ng = x print(ok) ```
instruction
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No
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13,172
0
26,345
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` N = int(input()) A = list(map(int, input().split())) ans = 0 for i in range(N - 1): if A[i] > A[i + 1]: ans += 1 print(ans) ```
instruction
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0
26,346
No
output
1
13,173
0
26,347
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` def main(): n = int(input()) a = list(map(int, input().split())) for i in range(n-1): if a[i] >= a[i+1]: break else: print(1) return def value(kind): length = 0 d = [] for i in a: if length >= i: while d: j, k = d[-1] if j > i: d.pop() else: break l = len(d)-1 if d: jj, k = d[-1] else: jj, k = -1, -1 for j in range(i, 0, -1): if jj != j: d.append([j, 2]) kind = max(kind, 2) break else: if k < kind: d[l][1] += 1 for jjj in range(l+1, len(d)): d.pop() else: l -= 1 else: return False length = i return True def b_search(ok, ng, value): while abs(ok-ng) > 1: mid = (ok+ng)//2 if value(mid): ok = mid else: ng = mid return ok print(b_search(n, 1, value)) main() ```
instruction
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0
26,348
No
output
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13,174
0
26,349
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left. At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i? Constraints * 1 \leq N \leq 2\times 10^5 * 1 \leq A_i \leq 10^9 * A_i is an integer. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the minimum possible number of different characters contained in the strings. Examples Input 3 3 2 1 Output 2 Input 5 2 3 2 1 2 Output 2 Submitted Solution: ``` N = int(input()) A = [int(i) for i in input().split()] def f(al, X): def g(stack, X): if not any(stack): stack.append(-1) return l = stack.pop() if l >= X: g(stack, X) stack.append(1) else: stack.append(l + 1) st = [] s = 0 for t in al: d = t - s if d > 0: st.extend([1] * d) else: for _ in range(-d): st.pop() g(st, X) if st[0] < 0: return False s = t return True max_N = N min_N = len([i for i in A if i == 1]) b_max_N = 0 b_min_N = 0 while max_N != min_N: nx = (max_N + min_N) // 2 if f(A, nx): max_N = nx else: min_N = nx if b_max_N == max_N and b_min_N == min_N: break b_max_N = max_N b_min_N = min_N print(max_N) ```
instruction
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13,175
0
26,350
No
output
1
13,175
0
26,351
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya owns three strings s , a and b, each of them consists only of first k Latin letters. Let a template be such a string of length k that each of the first k Latin letters appears in it exactly once (thus there are k! distinct templates). Application of template p to the string s is the replacement of each character in string s with p_i, i is the index of this letter in the alphabet. For example, applying template "bdca" to a string "aabccd" yields string "bbdcca". Vasya wants to know if there exists such a template which yields a string lexicographically greater than or equal to string a and lexicographically less than or equal to string b after applying it to s. If there exist multiple suitable templates, print any of them. String a is lexicographically less than string b if there is some i (1 ≤ i ≤ n) that a_i < b_i and for any j (1 ≤ j < i) a_j = b_j. You are required to answer t testcases independently. Input The first line contains a single integer t (1 ≤ t ≤ 10^6) — the number of testcases. In hacks you can only use t = 1. Each of the next t lines contains the description of the testcase in the following form: The first line of the testcase contains a single integer k (1 ≤ k ≤ 26) — the length of the template. The second line of the testcase contains the string s (1 ≤ |s| ≤ 10^6). The third line of the testcase contains the string a. The fourth line of the testcase contains the string b. Strings s, a and b have the same length (|s| = |a| = |b|) and consist only of the first k Latin letters, all letters are lowercase. It is guaranteed that string a is lexicographically less than or equal to string b. It is also guaranteed that the total length of strings over all testcase won't exceed 3 ⋅ 10^6. Output Print the answers to all testcases in the following form: If there exists no suitable template then print "NO" in the first line. Otherwise print "YES" in the first line and the template itself in the second line (k lowercase letters, each of the first k Latin letters should appear exactly once). If there exist multiple suitable templates, print any of them. Example Input 2 4 bbcb aada aada 3 abc bbb bbb Output YES badc NO Submitted Solution: ``` from itertools import permutations alpha = [a for a in 'qwertyuiopasdfghjklzxcvbnm'] alpha.sort() def f(k, s, a, b): for key in permutations(alpha[:k], k): d = {alpha[i]: key[i] for i in range(k)} s = [d[x] for x in s] if a <= ''.join(s) <= b: return key, True return '', False def main(): t = int(input()) res = [] for i in range(t): k = int(input()) s = input() a = input() b = input() key, r = f(k, s, a, b) if r: res.append('YES\n'+''.join(key)) else: res.append('NO') print('\n'.join(res)) if __name__ == '__main__': main() ```
instruction
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13,339
0
26,678
No
output
1
13,339
0
26,679
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya owns three strings s , a and b, each of them consists only of first k Latin letters. Let a template be such a string of length k that each of the first k Latin letters appears in it exactly once (thus there are k! distinct templates). Application of template p to the string s is the replacement of each character in string s with p_i, i is the index of this letter in the alphabet. For example, applying template "bdca" to a string "aabccd" yields string "bbdcca". Vasya wants to know if there exists such a template which yields a string lexicographically greater than or equal to string a and lexicographically less than or equal to string b after applying it to s. If there exist multiple suitable templates, print any of them. String a is lexicographically less than string b if there is some i (1 ≤ i ≤ n) that a_i < b_i and for any j (1 ≤ j < i) a_j = b_j. You are required to answer t testcases independently. Input The first line contains a single integer t (1 ≤ t ≤ 10^6) — the number of testcases. In hacks you can only use t = 1. Each of the next t lines contains the description of the testcase in the following form: The first line of the testcase contains a single integer k (1 ≤ k ≤ 26) — the length of the template. The second line of the testcase contains the string s (1 ≤ |s| ≤ 10^6). The third line of the testcase contains the string a. The fourth line of the testcase contains the string b. Strings s, a and b have the same length (|s| = |a| = |b|) and consist only of the first k Latin letters, all letters are lowercase. It is guaranteed that string a is lexicographically less than or equal to string b. It is also guaranteed that the total length of strings over all testcase won't exceed 3 ⋅ 10^6. Output Print the answers to all testcases in the following form: If there exists no suitable template then print "NO" in the first line. Otherwise print "YES" in the first line and the template itself in the second line (k lowercase letters, each of the first k Latin letters should appear exactly once). If there exist multiple suitable templates, print any of them. Example Input 2 4 bbcb aada aada 3 abc bbb bbb Output YES badc NO Submitted Solution: ``` t = int(input()) list = ["a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z"] for i in range(t): l = int(input()) sample = input() a = input() b = input() # print(sample) # print(a) # print(b) panel = dict(zip(list[:l],[0]*l)) print(panel) for i in range(l): if a[i]==b[i]: panel[a[i]] = sample[i] print(panel) alphas = [] count = 0 for value in panel.values(): if str(value).isalpha(): alphas.append(value) else: count += 1 if count+len(alphas): print("YES") panel = sorted(panel.items(), key=lambda x:x[0]) result = [] for item in panel: result.append(item[1]) a = 0 for i in range(l): if result[i]==0: while(a<26): if list[a] not in result: result[i] = list[a] a += 1 break a += 1 print(result) else: print("NO") ```
instruction
0
13,340
0
26,680
No
output
1
13,340
0
26,681
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya owns three strings s , a and b, each of them consists only of first k Latin letters. Let a template be such a string of length k that each of the first k Latin letters appears in it exactly once (thus there are k! distinct templates). Application of template p to the string s is the replacement of each character in string s with p_i, i is the index of this letter in the alphabet. For example, applying template "bdca" to a string "aabccd" yields string "bbdcca". Vasya wants to know if there exists such a template which yields a string lexicographically greater than or equal to string a and lexicographically less than or equal to string b after applying it to s. If there exist multiple suitable templates, print any of them. String a is lexicographically less than string b if there is some i (1 ≤ i ≤ n) that a_i < b_i and for any j (1 ≤ j < i) a_j = b_j. You are required to answer t testcases independently. Input The first line contains a single integer t (1 ≤ t ≤ 10^6) — the number of testcases. In hacks you can only use t = 1. Each of the next t lines contains the description of the testcase in the following form: The first line of the testcase contains a single integer k (1 ≤ k ≤ 26) — the length of the template. The second line of the testcase contains the string s (1 ≤ |s| ≤ 10^6). The third line of the testcase contains the string a. The fourth line of the testcase contains the string b. Strings s, a and b have the same length (|s| = |a| = |b|) and consist only of the first k Latin letters, all letters are lowercase. It is guaranteed that string a is lexicographically less than or equal to string b. It is also guaranteed that the total length of strings over all testcase won't exceed 3 ⋅ 10^6. Output Print the answers to all testcases in the following form: If there exists no suitable template then print "NO" in the first line. Otherwise print "YES" in the first line and the template itself in the second line (k lowercase letters, each of the first k Latin letters should appear exactly once). If there exist multiple suitable templates, print any of them. Example Input 2 4 bbcb aada aada 3 abc bbb bbb Output YES badc NO Submitted Solution: ``` col = int(input()) sp = {'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} sp1 = {0: 'a', 1: 'b', 2: 'c', 3: 'd', 4: 'e', 5: 'f', 6: 'g', 7: 'h', 8: 'i', 9: 'j', 10: 'k', 11: 'l', 12: 'm', 13: 'n', 14: 'o', 15: 'p', 16: 'q', 17: 'r', 18: 's', 19: 't', 20: 'u', 21: 'v', 22: 'w', 23: 'x', 24: 'y', 25: 'z'} def getdiff(a, b): return abs(sp.get(a) - sp.get(b)) def yorn(a, b, s): flag = False for i in range(len(a)): dif = getdiff(a[i], b[i]) if dif > 1: return (1, i) elif dif == 1: flag = True return (0, flag) def pattern(a, b, s, i, leng): pat = ['a']*leng for j in range(i): pat[sp.get(a[j])] = a[j] pat[sp.get(a[i])] = sp1.get(sp.get(a[i]) + 1) return ''.join(pat) def pattern1(a, b, s, i, leng): pat = list(a) if sp.get(a[i]) + 1 > 26: return 0 pat[sp.get(a[i])] = sp1.get(sp.get(a[i]) + 1) return ''.join(pat) res = '' for i in range(col): leng = int(input()) s = input() a = input() b = input() yes = yorn(a, b, s) if len(set(a)) < len(set(s)): res += "NO\n" #print('NO') elif yes[0]: #print('YES') #print(pattern(a, b, s, yes[1], leng)) res += "YES\n" res += pattern(a, b, s, yes[1], leng) + "\n" else: itog = pattern1(a, b, s, yes[1], leng) if not itog: res += "NO\n" #print('NO') else: #print('YES') #print(itog) res += "YES\n" res += itog + "\n" print(res[:-1]) ''' 1 4 abcd abcd cdef ''' '''sch = 0 for i in 'abcdefghijklmnopqrstuvwxyz': s[i] = sch sch += 1 print(s)''' ```
instruction
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13,341
0
26,682
No
output
1
13,341
0
26,683
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya owns three strings s , a and b, each of them consists only of first k Latin letters. Let a template be such a string of length k that each of the first k Latin letters appears in it exactly once (thus there are k! distinct templates). Application of template p to the string s is the replacement of each character in string s with p_i, i is the index of this letter in the alphabet. For example, applying template "bdca" to a string "aabccd" yields string "bbdcca". Vasya wants to know if there exists such a template which yields a string lexicographically greater than or equal to string a and lexicographically less than or equal to string b after applying it to s. If there exist multiple suitable templates, print any of them. String a is lexicographically less than string b if there is some i (1 ≤ i ≤ n) that a_i < b_i and for any j (1 ≤ j < i) a_j = b_j. You are required to answer t testcases independently. Input The first line contains a single integer t (1 ≤ t ≤ 10^6) — the number of testcases. In hacks you can only use t = 1. Each of the next t lines contains the description of the testcase in the following form: The first line of the testcase contains a single integer k (1 ≤ k ≤ 26) — the length of the template. The second line of the testcase contains the string s (1 ≤ |s| ≤ 10^6). The third line of the testcase contains the string a. The fourth line of the testcase contains the string b. Strings s, a and b have the same length (|s| = |a| = |b|) and consist only of the first k Latin letters, all letters are lowercase. It is guaranteed that string a is lexicographically less than or equal to string b. It is also guaranteed that the total length of strings over all testcase won't exceed 3 ⋅ 10^6. Output Print the answers to all testcases in the following form: If there exists no suitable template then print "NO" in the first line. Otherwise print "YES" in the first line and the template itself in the second line (k lowercase letters, each of the first k Latin letters should appear exactly once). If there exist multiple suitable templates, print any of them. Example Input 2 4 bbcb aada aada 3 abc bbb bbb Output YES badc NO Submitted Solution: ``` print("dddddddddddddddddddddddddddd") print("dddddddddddddddddddddddddddd") ```
instruction
0
13,342
0
26,684
No
output
1
13,342
0
26,685
Provide tags and a correct Python 3 solution for this coding contest problem. This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different. You are given a string s consisting of n lowercase Latin letters. You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s). After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times. The goal is to make the string sorted, i.e. all characters should be in alphabetical order. Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps. Input The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s. The second line of the input contains the string s consisting of exactly n lowercase Latin letters. Output If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line. Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise). Examples Input 9 abacbecfd Output YES 001010101 Input 8 aaabbcbb Output YES 01011011 Input 7 abcdedc Output NO Input 5 abcde Output YES 00000
instruction
0
13,411
0
26,822
Tags: constructive algorithms, dp, graphs, greedy, sortings Correct Solution: ``` def main(): n = int(input()) ss = list(zip(input(), range(0,n))) res = [1]*n max_colour = 1 nextx = [0] * 26 colours_after = [[True]+[False]*26 for _ in range(26)] for i in range(n): ch = ord(ss[i][0]) - ord('a') opos = ss[i][1] nx = nextx[ch] # ss[nx:i + 1] = [ss[i]] + ss[nx:i] col = colours_after[ch].index(False) if col > max_colour: max_colour = col res[opos] = col for c in range(ch): colours_after[c][col] = True for c in range(ch, 26): nextx[c] = min(nextx[c], nx+1) print(max_colour) print(' '.join(map(str, res))) if __name__ == "__main__": main() ```
output
1
13,411
0
26,823
Provide tags and a correct Python 3 solution for this coding contest problem. This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different. You are given a string s consisting of n lowercase Latin letters. You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s). After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times. The goal is to make the string sorted, i.e. all characters should be in alphabetical order. Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps. Input The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s. The second line of the input contains the string s consisting of exactly n lowercase Latin letters. Output If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line. Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise). Examples Input 9 abacbecfd Output YES 001010101 Input 8 aaabbcbb Output YES 01011011 Input 7 abcdedc Output NO Input 5 abcde Output YES 00000
instruction
0
13,412
0
26,824
Tags: constructive algorithms, dp, graphs, greedy, sortings Correct Solution: ``` n = int(input()) s = input() ans = [-1] * n f = True for i in range(n): if ans[i] == -1: ans[i] = 0 for j in range(i + 1, n): if (s[j] < s[i]): if ans[j] == -1: ans[j] = (ans[i] - 1) ** 2 else: now = ans[j] new = (ans[i] - 1) ** 2 if new != now: f = False else: ans[j] = new if not f: print("NO") else: print("YES") for i in range(n): print(ans[i], end='') ```
output
1
13,412
0
26,825
Provide tags and a correct Python 3 solution for this coding contest problem. This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different. You are given a string s consisting of n lowercase Latin letters. You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s). After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times. The goal is to make the string sorted, i.e. all characters should be in alphabetical order. Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps. Input The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s. The second line of the input contains the string s consisting of exactly n lowercase Latin letters. Output If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line. Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise). Examples Input 9 abacbecfd Output YES 001010101 Input 8 aaabbcbb Output YES 01011011 Input 7 abcdedc Output NO Input 5 abcde Output YES 00000
instruction
0
13,413
0
26,826
Tags: constructive algorithms, dp, graphs, greedy, sortings Correct Solution: ``` n=int(input()) s=input() last,last1='a','a' ans='' flag=1 for i in s: if i<last and i<last1: flag=0 break elif i>=last: last=i ans+='0' else: last1=i ans+='1' if flag: print('YES') print(ans) else: print('NO') ```
output
1
13,413
0
26,827
Provide tags and a correct Python 3 solution for this coding contest problem. This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different. You are given a string s consisting of n lowercase Latin letters. You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s). After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times. The goal is to make the string sorted, i.e. all characters should be in alphabetical order. Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps. Input The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s. The second line of the input contains the string s consisting of exactly n lowercase Latin letters. Output If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line. Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise). Examples Input 9 abacbecfd Output YES 001010101 Input 8 aaabbcbb Output YES 01011011 Input 7 abcdedc Output NO Input 5 abcde Output YES 00000
instruction
0
13,414
0
26,828
Tags: constructive algorithms, dp, graphs, greedy, sortings Correct Solution: ``` import sys def main(): n = int(sys.stdin.readline().split()[0]) s = sys.stdin.readline().split()[0] color = [None]*n color[0] = 0 for i in range(n): if color[i] == None: color[i] = 0 for j in range(i+1, n): if ord(s[j]) < ord(s[i]): if color[j] == color[i]: print("NO") return if color[j] == None: color[j] = color[i]^1 print("YES") print(*color, sep = "") main() ```
output
1
13,414
0
26,829
Provide tags and a correct Python 3 solution for this coding contest problem. This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different. You are given a string s consisting of n lowercase Latin letters. You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s). After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times. The goal is to make the string sorted, i.e. all characters should be in alphabetical order. Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps. Input The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s. The second line of the input contains the string s consisting of exactly n lowercase Latin letters. Output If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line. Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise). Examples Input 9 abacbecfd Output YES 001010101 Input 8 aaabbcbb Output YES 01011011 Input 7 abcdedc Output NO Input 5 abcde Output YES 00000
instruction
0
13,415
0
26,830
Tags: constructive algorithms, dp, graphs, greedy, sortings Correct Solution: ``` # ---------------------------iye ha aam zindegi--------------------------------------------- import math import random import heapq, bisect import sys from collections import deque, defaultdict from fractions import Fraction import sys import threading from collections import defaultdict #threading.stack_size(10**8) mod = 10 ** 9 + 7 mod1 = 998244353 # ------------------------------warmup---------------------------- import os import sys from io import BytesIO, IOBase #sys.setrecursionlimit(300000) 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") # -------------------game starts now----------------------------------------------------import math class TreeNode: def __init__(self, k, v): self.key = k self.value = v self.left = None self.right = None self.parent = None self.height = 1 self.num_left = 1 self.num_total = 1 class AvlTree: def __init__(self): self._tree = None def add(self, k, v): if not self._tree: self._tree = TreeNode(k, v) return node = self._add(k, v) if node: self._rebalance(node) def _add(self, k, v): node = self._tree while node: if k < node.key: if node.left: node = node.left else: node.left = TreeNode(k, v) node.left.parent = node return node.left elif node.key < k: if node.right: node = node.right else: node.right = TreeNode(k, v) node.right.parent = node return node.right else: node.value = v return @staticmethod def get_height(x): return x.height if x else 0 @staticmethod def get_num_total(x): return x.num_total if x else 0 def _rebalance(self, node): n = node while n: lh = self.get_height(n.left) rh = self.get_height(n.right) n.height = max(lh, rh) + 1 balance_factor = lh - rh n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right) n.num_left = 1 + self.get_num_total(n.left) if balance_factor > 1: if self.get_height(n.left.left) < self.get_height(n.left.right): self._rotate_left(n.left) self._rotate_right(n) elif balance_factor < -1: if self.get_height(n.right.right) < self.get_height(n.right.left): self._rotate_right(n.right) self._rotate_left(n) else: n = n.parent def _remove_one(self, node): """ Side effect!!! Changes node. Node should have exactly one child """ replacement = node.left or node.right if node.parent: if AvlTree._is_left(node): node.parent.left = replacement else: node.parent.right = replacement replacement.parent = node.parent node.parent = None else: self._tree = replacement replacement.parent = None node.left = None node.right = None node.parent = None self._rebalance(replacement) def _remove_leaf(self, node): if node.parent: if AvlTree._is_left(node): node.parent.left = None else: node.parent.right = None self._rebalance(node.parent) else: self._tree = None node.parent = None node.left = None node.right = None def remove(self, k): node = self._get_node(k) if not node: return if AvlTree._is_leaf(node): self._remove_leaf(node) return if node.left and node.right: nxt = AvlTree._get_next(node) node.key = nxt.key node.value = nxt.value if self._is_leaf(nxt): self._remove_leaf(nxt) else: self._remove_one(nxt) self._rebalance(node) else: self._remove_one(node) def get(self, k): node = self._get_node(k) return node.value if node else -1 def _get_node(self, k): if not self._tree: return None node = self._tree while node: if k < node.key: node = node.left elif node.key < k: node = node.right else: return node return None def get_at(self, pos): x = pos + 1 node = self._tree while node: if x < node.num_left: node = node.left elif node.num_left < x: x -= node.num_left node = node.right else: return (node.key, node.value) raise IndexError("Out of ranges") @staticmethod def _is_left(node): return node.parent.left and node.parent.left == node @staticmethod def _is_leaf(node): return node.left is None and node.right is None def _rotate_right(self, node): if not node.parent: self._tree = node.left node.left.parent = None elif AvlTree._is_left(node): node.parent.left = node.left node.left.parent = node.parent else: node.parent.right = node.left node.left.parent = node.parent bk = node.left.right node.left.right = node node.parent = node.left node.left = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) def _rotate_left(self, node): if not node.parent: self._tree = node.right node.right.parent = None elif AvlTree._is_left(node): node.parent.left = node.right node.right.parent = node.parent else: node.parent.right = node.right node.right.parent = node.parent bk = node.right.left node.right.left = node node.parent = node.right node.right = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) @staticmethod def _get_next(node): if not node.right: return node.parent n = node.right while n.left: n = n.left return n # -----------------------------------------------binary seacrh tree--------------------------------------- class SegmentTree1: def __init__(self, data, default=2**30, func=lambda a, b: min(a , b)): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------game starts now----------------------------------------------------import math class SegmentTree: def __init__(self, data, default=0, func=lambda a, b:a + b): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------------------iye ha chutiya zindegi------------------------------------- class Factorial: def __init__(self, MOD): self.MOD = MOD self.factorials = [1, 1] self.invModulos = [0, 1] self.invFactorial_ = [1, 1] def calc(self, n): if n <= -1: print("Invalid argument to calculate n!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.factorials): return self.factorials[n] nextArr = [0] * (n + 1 - len(self.factorials)) initialI = len(self.factorials) prev = self.factorials[-1] m = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = prev * i % m self.factorials += nextArr return self.factorials[n] def inv(self, n): if n <= -1: print("Invalid argument to calculate n^(-1)") print("n must be non-negative value. But the argument was " + str(n)) exit() p = self.MOD pi = n % p if pi < len(self.invModulos): return self.invModulos[pi] nextArr = [0] * (n + 1 - len(self.invModulos)) initialI = len(self.invModulos) for i in range(initialI, min(p, n + 1)): next = -self.invModulos[p % i] * (p // i) % p self.invModulos.append(next) return self.invModulos[pi] def invFactorial(self, n): if n <= -1: print("Invalid argument to calculate (n^(-1))!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.invFactorial_): return self.invFactorial_[n] self.inv(n) # To make sure already calculated n^-1 nextArr = [0] * (n + 1 - len(self.invFactorial_)) initialI = len(self.invFactorial_) prev = self.invFactorial_[-1] p = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p self.invFactorial_ += nextArr return self.invFactorial_[n] class Combination: def __init__(self, MOD): self.MOD = MOD self.factorial = Factorial(MOD) def ncr(self, n, k): if k < 0 or n < k: return 0 k = min(k, n - k) f = self.factorial return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD # --------------------------------------iye ha combinations ka zindegi--------------------------------- def powm(a, n, m): if a == 1 or n == 0: return 1 if n % 2 == 0: s = powm(a, n // 2, m) return s * s % m else: return a * powm(a, n - 1, m) % m # --------------------------------------iye ha power ka zindegi--------------------------------- def sort_list(list1, list2): zipped_pairs = zip(list2, list1) z = [x for _, x in sorted(zipped_pairs)] return z # --------------------------------------------------product---------------------------------------- def product(l): por = 1 for i in range(len(l)): por *= l[i] return por # --------------------------------------------------binary---------------------------------------- def binarySearchCount(arr, n, key): left = 0 right = n - 1 count = 0 while (left <= right): mid = int((right + left) / 2) # Check if middle element is # less than or equal to key if (arr[mid] < key): count = mid + 1 left = mid + 1 # If key is smaller, ignore right half else: right = mid - 1 return count # --------------------------------------------------binary---------------------------------------- def countdig(n): c = 0 while (n > 0): n //= 10 c += 1 return c def binary(x, length): y = bin(x)[2:] return y if len(y) >= length else "0" * (length - len(y)) + y def countGreater(arr, n, k): l = 0 r = n - 1 # Stores the index of the left most element # from the array which is greater than k leftGreater = n # Finds number of elements greater than k while (l <= r): m = int(l + (r - l) / 2) if (arr[m] > k): leftGreater = m r = m - 1 # If mid element is less than # or equal to k update l else: l = m + 1 # Return the count of elements # greater than k return (n - leftGreater) # --------------------------------------------------binary------------------------------------ class TrieNode: def __init__(self): self.children = [None] * 26 self.isEndOfWord = False class Trie: def __init__(self): self.root = self.getNode() def getNode(self): return TrieNode() def _charToIndex(self, ch): return ord(ch) - ord('a') def insert(self, key): pCrawl = self.root length = len(key) for level in range(length): index = self._charToIndex(key[level]) if not pCrawl.children[index]: pCrawl.children[index] = self.getNode() pCrawl = pCrawl.children[index] pCrawl.isEndOfWord = True def search(self, key): pCrawl = self.root length = len(key) for level in range(length): index = self._charToIndex(key[level]) if not pCrawl.children[index]: return False pCrawl = pCrawl.children[index] return pCrawl != None and pCrawl.isEndOfWord #-----------------------------------------trie--------------------------------- class Node: def __init__(self, data): self.data = data self.count=0 self.left = None # left node for 0 self.right = None # right node for 1 class BinaryTrie: def __init__(self): self.root = Node(0) def insert(self, pre_xor): self.temp = self.root for i in range(31, -1, -1): val = pre_xor & (1 << i) if val: if not self.temp.right: self.temp.right = Node(0) self.temp = self.temp.right self.temp.count+=1 if not val: if not self.temp.left: self.temp.left = Node(0) self.temp = self.temp.left self.temp.count += 1 self.temp.data = pre_xor def query(self, xor): self.temp = self.root for i in range(31, -1, -1): val = xor & (1 << i) if not val: if self.temp.left and self.temp.left.count>0: self.temp = self.temp.left elif self.temp.right: self.temp = self.temp.right else: if self.temp.right and self.temp.right.count>0: self.temp = self.temp.right elif self.temp.left: self.temp = self.temp.left self.temp.count-=1 return xor ^ self.temp.data #-------------------------bin trie------------------------------------------- n=int(input()) d=dict() for i in range(97,124): d[chr(i)]=0 l=input() d[l[0]]+=1 ans=[0]*n ans[0]=d[l[0]] for i in range(1,n): for j in sorted(d.keys(),reverse=True): if j>l[i]: ans[i]=max(ans[i],d[j]+1) else: break d[l[i]]=ans[i] print(max(ans)) print(*ans,sep=" ") ```
output
1
13,415
0
26,831
Provide tags and a correct Python 3 solution for this coding contest problem. This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different. You are given a string s consisting of n lowercase Latin letters. You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s). After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times. The goal is to make the string sorted, i.e. all characters should be in alphabetical order. Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps. Input The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s. The second line of the input contains the string s consisting of exactly n lowercase Latin letters. Output If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line. Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise). Examples Input 9 abacbecfd Output YES 001010101 Input 8 aaabbcbb Output YES 01011011 Input 7 abcdedc Output NO Input 5 abcde Output YES 00000
instruction
0
13,416
0
26,832
Tags: constructive algorithms, dp, graphs, greedy, sortings Correct Solution: ``` #t = int(input()) t=1 while t!=0: t-=1 n = int(input()) s = input() l1, l2 = 'a' , 'a' ans = '' for i in range(n): if s[i]>=l1: l1 = s[i] ans+='0' elif s[i]>=l2: l2 = s[i] ans+='1' else: ans='NO' break if ans=='NO': print(ans) else: print('YES') print(ans) ```
output
1
13,416
0
26,833
Provide tags and a correct Python 3 solution for this coding contest problem. This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different. You are given a string s consisting of n lowercase Latin letters. You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s). After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times. The goal is to make the string sorted, i.e. all characters should be in alphabetical order. Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps. Input The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s. The second line of the input contains the string s consisting of exactly n lowercase Latin letters. Output If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line. Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise). Examples Input 9 abacbecfd Output YES 001010101 Input 8 aaabbcbb Output YES 01011011 Input 7 abcdedc Output NO Input 5 abcde Output YES 00000
instruction
0
13,417
0
26,834
Tags: constructive algorithms, dp, graphs, greedy, sortings Correct Solution: ``` def main(): n = int(input()) s = list(input()) colors = [-1]*n for i in range(len(s)): if colors[i] == -1: colors[i] = 0 for j in range(i+1,n): if s[j] < s[i]: if colors[j] == colors[i]: print('NO') return if colors[j] == -1: if colors[i] == 0: colors[j] = 1 else: colors[j] = 0 print('YES') for i in colors: print(i,end = '') main() ```
output
1
13,417
0
26,835