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Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Tags: implementation, strings
Correct Solution:
```
k = int(input())
s = input()
ans = []
cur = ""
se = set()
for i in range(len(s)):
if s[i] not in se:
if len(cur) > 0:
ans.append(cur)
cur = ""
cur = s[i]
se.add(s[i])
else:
cur += s[i]
if cur:
ans.append(cur)
l = len(ans)
if len(ans) < k:
print("NO")
else:
print("YES")
for i in range(k, len(ans)):
ans[k-1] += ans[i]
print("\n".join(ans[:k]))
```
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Tags: implementation, strings
Correct Solution:
```
# 544A
# O(|q|) time
# O(|q|) space
__author__ = 'artyom'
# SOLUTION
def main():
b = [False] * 26
n = read()
s = read(0)
if n == 1:
return ['YES', s]
tokens = ['YES']
token = ''
i = 1
p = 0
for c in s:
if not b[ord(c) - 97]:
b[ord(c) - 97] = True
if token:
tokens.append(token)
i += 1
if i == n:
break
else:
token = ''
token += c
p += 1
tokens.append(s[p:])
if len(tokens) - 1 < n:
return 'NO'
return tokens
# HELPERS
def read(mode=1, size=None):
# 0: String
# 1: Integer
# 2: List of strings
# 3: List of integers
# 4: Matrix of integers
if mode == 0: return input().strip()
if mode == 1: return int(input().strip())
if mode == 2: return input().strip().split()
if mode == 3: return list(map(int, input().strip().split()))
a = []
for _ in range(size):
a.append(read(3))
return a
def write(s="\n"):
if s is None: s = ''
if isinstance(s, tuple) or isinstance(s, list): s = '\n'.join(map(str, s))
s = str(s)
print(s, end="\n")
write(main())
```
| 2,028
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Tags: implementation, strings
Correct Solution:
```
import sys
import math
import bisect
def solve(s, k):
d = dict()
for i in range(len(s)):
if s[i] not in d:
d[s[i]] = i
A = list(d.values())
#print('s: %s, k: %d, A: %s' % (s, k, A))
if len(A) < k:
return None
B = []
for i in range(k):
if i == k - 1:
B.append(s[A[i]:])
else:
B.append(s[A[i]:A[i+1]])
return B
def main():
k = int(input())
s = input()
ans = solve(s, k)
if ans:
print('YES')
for a in ans:
print(a)
else:
print('NO')
if __name__ == "__main__":
main()
```
| 2,029
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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 a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
n = int(input())
q = input()
if n > len(q):
print("NO")
else:
if n == 1:
print("YES")
print(q)
else:
arr = [0]*len(q)
for x in range(0, len(q)):
arr[x] = q[x]
con = arr[0]
res = []
count = 0
x = 0
used = ["-1"]*len(q)
used[0] = con
usedCount = 0
while count < n-1:
if x + 1 < len(arr) and (arr[x] == arr[x+1] or arr[x+1] in used):
con += arr[x+1]
x += 1
else:
res.append(con)
usedCount += 1
if x + 1 < len(arr):
used[usedCount] = arr[x+1]
con = arr[x+1]
count +=1
x += 1
totalLen = 0
for x in range(0, count):
totalLen += len(res[x])
res.append(q[totalLen:])
for x in res:
if x.isspace() or x == "":
res.remove(x)
res1 = set(res)
length = 0
for each in res1:
length += 1
if res[len(res) - 1] == "-1" or length < n:
print("NO")
else:
print("YES")
for x in res:
print(x)
```
Yes
| 2,030
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
n = int(input())
s = input()
a = []
if len(s) < n:
print ("NO")
else:
for i in s:
if len(a) == n:
break
if i in a:
continue
else:
a.append(i)
l = []
for i in range(len(a)):
if i == len(a)-1:
l.append(s[s.index(a[i]):])
else:
l.append(s[s.index(a[i]):s.index(a[i+1])])
if len(a) == n:
print ("YES")
for i in l:
print (i)
else:
print ("NO")
```
Yes
| 2,031
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
K = int(input())
used = set()
S = input()
indexes = []
ind = 0
while len(indexes) < K and ind < len(S):
if S[ind] not in used:
indexes += [ind]
used.add(S[ind])
ind += 1
if len(indexes) < K:
print("NO")
else:
print("YES")
for i, v in enumerate(indexes):
if i == len(indexes) - 1:
print(S[v:])
else:
print(S[v:indexes[i+1]])
```
Yes
| 2,032
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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 a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
r = lambda : map(int,input().split())
import sys
n = int(input())
s = input()
q = set()
if n>len(set(s)) :
print('NO')
else :
print('YES')
k = 0
ans = []
for i in range(len(s)) :
if k==n : break
if s[i] not in q :
ans.append(i)
q.add(s[i])
k+=1
ans.append(len(s))
for i in range(len(ans)-1) :
print(s[ans[i]:ans[i+1]])
```
Yes
| 2,033
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
n = int(input())
q = input()
if n > len(q):
print("NO")
else:
if n == 1:
print("YES")
print(q)
else:
arr = [0]*len(q)
for x in range(0, len(q)):
arr[x] = q[x]
con = arr[0]
res = ["-1"]*n
count = 0
x = 0
while(count < n-1):
if arr[x] == arr[x+1]:
con += arr[x+1]
x += 1
else:
res[count] = con
con = arr[x+1]
count +=1
x += 1
res[count] = q[3:]
res1 = set(res)
length = 0
for each in res1:
length += 1
if res[len(res) - 1] == "-1" or length < n:
print("NO")
else:
print("YES")
for x in res:
print(x)
```
No
| 2,034
|
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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 a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
from collections import defaultdict
def cutter(a, cuts):
if cuts == 1:
return [a]
comparador = set([a[0]])
aux = a[0]
ans = []
flag = True
for i in range(1, len(a)):
# print(a[i])
if a[i] not in comparador:
ans.append(aux)
aux = a[i]
comparador.union(set([a[i]]))
else:
aux += a[i]
# print(aux)
if len(ans) == cuts - 1 :
ans.append(a[i:])
break
return ans
def isBeautiful(a):
mapa = defaultdict(int)
for i in a:
mapa[i[0]] += 1
if mapa[i[0]] > 1:
return False
return True
def func():
n = int(input())
p = input()
if len(p) < n:
print('NO')
return
lista = cutter(p, n)
# print(lista)
if len(lista) < n:
print('NO')
return
if isBeautiful(lista):
print('YES')
for i in lista:
print(i)
else:
print('NO')
return
func()
```
No
| 2,035
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
N = int(input())
S = input()
found = set()
for i in range(len(S)):
k = S[i]
if(not (k in found)):
found.add(k)
if(len(found)>=N):
print("YES")
ptr1 = 0
count = 0
found.remove(S[ptr1])
for i in range(len(S)):
#print (found)
if(count==N-1):
print(S[ptr1:])
break
if(i>0 and (S[i] in found)):
print(S[ptr1:i])
ptr1=i
count+=1
found.remove(S[ptr1])
else:
print("NO")
```
No
| 2,036
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.
Input
The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.
The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.
Output
If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk.
If there are multiple possible answers, print any of them.
Examples
Input
1
abca
Output
YES
abca
Input
2
aaacas
Output
YES
aaa
cas
Input
4
abc
Output
NO
Note
In the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.
Submitted Solution:
```
# http://codeforces.com/problemset/problem/544/A
def main():
n = int(input())
s = str(input())
if n > len(s):
print('NO')
return
elif n == 1:
print('YES')
print(s)
else:
strings = []
letters = len(set(list(s)))
if letters < n:
print('NO')
return
curr = s[0]
comp = s[0]
used = {s[0]: 1}
cant = 0
for i in range(1, len(s)):
if s[i] == comp:
curr += s[i]
else:
check = used.get(s[i], -1)
if check != -1:
curr += s[i]
if i == len(s) - 1:
strings.append(curr)
break
continue
else:
strings.append(curr)
cant += 1
if cant == n:
strings[-1] = strings[-1] + s[i:]
break
curr = s[i]
comp = s[i]
used[comp] = 1
if i == len(s) - 1:
strings.append(curr)
break
print('YES')
for i in strings:
print(i)
main()
```
No
| 2,037
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
(n, m) = (int(t) for t in input().split())
s = [c for c in input()]
fs = 0
for i in range(1, len(s)):
if s[i] == '.' and s[i - 1] == '.':
fs += 1
out = []
for k in range(m):
t = input().split()
i = int(t[0]) - 1
c = t[1]
if (c == '.') != (s[i] == '.'):
if i - 1 > -1 and s[i - 1] == '.':
fs += 1 if c == '.' else -1
if i + 1 < len(s) and s[i + 1] == '.':
fs += 1 if c == '.' else -1
s[i] = c
out.append(str(fs))
out.append('\n')
print(''.join(out), end='')
```
| 2,038
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
import math,sys,bisect,heapq
from collections import defaultdict,Counter,deque
from itertools import groupby,accumulate
from functools import lru_cache
from heapq import heapify,heappop,heappush
#sys.setrecursionlimit(200000000)
int1 = lambda x: int(x) - 1
#def input(): return sys.stdin.readline().strip()m
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
aj = lambda: list(map(int, input().split()))
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
#MOD = 1000000000 + 7
def Y(c): print(["NO","YES"][c])
def y(c): print(["no","yes"][c])
def Yy(c): print(["No","Yes"][c])
n,m = aj()
s = ['$'] + [*input()] + ['$']
count = 0
for i in range(len(s)-1):
if s[i] == s[i+1] == '.':
count += 1
for i in range(m):
a,b = input().split()
a = int(a)
if s[a] == b == '.':
print(count)
elif s[a] != '.' and b!= '.':
print(count)
elif s[a] == '.':
if s[a-1] == '.':
count -= 1
if s[a+1] == '.':
count -= 1
print(count)
s[a] = b
else:
if s[a-1] == '.':
count += 1
if s[a+1] == '.':
count += 1
print(count)
s[a] = b
```
| 2,039
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
def solve(string, updates):
count = sum(string) - sum([not string[i] and string[i + 1]
for i in range(len(string) - 1)])
for (pos, val) in updates:
if string[pos] != val:
sign = 1 if val else -1
count += sign
count += sign * (string[pos - 1] and string[pos + 1])
count -= sign * (not string[pos - 1] and not string[pos + 1])
string[pos] = val
yield count
def read_input():
from sys import stdin
input_lines = stdin.readline
(n, m) = map(int, input_lines().split())
string = [False] + [c == '.' for c in input_lines()] + [False]
def parse_update(line):
pos, val = line.split()
return int(pos), val == '.'
updates = (parse_update(input_lines()) for _ in range(m))
return string, updates
def main():
string, updates = read_input()
for x in solve(string, updates):
print(x)
main()
```
| 2,040
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
n, m = map(int, input().split())
a = list(input())
res=0
b = []
for i in range(1, n):
if a[i]+a[i-1] =='..':
res += 1
for i in range(m):
g, c = input().split()
p = int(g)-1
if p > 0 and a[p-1] + a[p] == '..':
res -= 1
if p + 1 < n and a[p+1] + a[p] == '..':
res -= 1
a[p] = c
if p > 0 and a[p-1] + a[p] == '..':
res += 1
if p + 1 < n and a[p+1] + a[p] == '..':
res += 1
b.append(str(res))
print(' '.join(b))
```
| 2,041
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
import sys
n, m = map(int, sys.stdin.readline().split())
s = input()
left = 0
right = 0
ans = 0
while True:
left = s.find('.', right)
if left < 0:
break
right = left+1
while right < n and s[right] == '.':
right += 1
if right - left > 1:
ans += right-left-1
l = list(s)
ans_list = []
for i in range(m):
query = list(sys.stdin.readline().split())
xi = int(query[0]) - 1
ci = query[1]
if (ci == '.' and l[xi] == '.') or (ci != '.' and l[xi] != '.'):
pass
elif ci == '.' and l[xi] != '.':
if xi > 0 and l[xi-1] == '.':
ans += 1
if xi < n-1 and l[xi+1] == '.':
ans += 1
elif ci != '.' and l[xi] == '.':
if xi > 0 and l[xi-1] == '.':
ans -= 1
if xi < n-1 and l[xi+1] == '.':
ans -= 1
ans_list.append(ans)
l[xi] = ci
print('\n'.join(map(str, ans_list)))
```
| 2,042
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
n, m = map(int, input().split())
s = [c != '.' for c in input()] + [1]
k = sum(s[i] == s[i + 1] == 0 for i in range(n - 1))
t = [0] * m
for i in range(m):
x, c = input().split()
x, c = int(x) - 1, c != '.'
if not s[x]:
if c: k += s[x - 1] + s[x + 1] - 2
elif not c: k += 2 - s[x - 1] - s[x + 1]
s[x] = c
t[i] = k
print('\n'.join(map(str, t)))
```
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
from sys import stdin
input = stdin.readline
n,m = map(int,input().split())
s = list((0,1)[c == '.'] for c in list(input()))
res = 0
cnt = 0
for k in s:
if k == 1:
cnt += 1
else:
res += max(cnt-1,0)
cnt = 0
res += max(0,cnt-1)
for i in range(m):
x,c = input().split()
x = int(x)
nc = (0,1)[c == '.']
if s[x-1] != nc:
diff = 0
if x < n:
if s[int(x)] == 1: diff += 1
if x > 1:
if s[int(x-2)] == 1: diff += 1
if nc == 1:
res += diff
else:
res -= diff
s[x-1] = nc
print(res)
```
| 2,044
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] | 0
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Tags: constructive algorithms, data structures, implementation
Correct Solution:
```
from sys import stdin,stdout
input = stdin.readline
import operator
from array import array
n,m = map(int,input().split())
def calc():
s = array('B',[0])
s.extend(c == '.' for c in input())
res = sum(map(operator.mul,s[1:],s))
for i in range(m):
x,c = input().split()
x = int(x)
nc = c == '.'
if s[x] != nc:
diff = s[x-1] + s[x+1]
res += (-diff,diff) [nc]
s[x] = nc
yield str(res)
stdout.write('\n'.join(calc()))
```
| 2,045
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
import sys
input = sys.stdin.readline
def segtree(i,a,tree,l,r):
if l==r:
tree[i]=a[l]
return tree[i]
m=(l+r)//2
tree[i]= segtree(2*i+1,a,tree,l,m) + segtree(2*i+2,a,tree,m+1,r)
return tree[i]
def update(i,a,tree,l,r,ind):
if ind<l or ind>r:
return
elif l==r:
tree[i]=a[l]
return
m=(l+r)//2
update(2*i+1,a,tree,l,m,ind)
update(2*i+2,a,tree,m+1,r,ind)
tree[i]=tree[2*i+1]+tree[2*i+2]
n,m=map(int,input().split())
s=list(input())
a=[0]*n
for i in range(1,n):
if s[i]=='.' and s[i-1]=='.':
a[i]=1
i=0
while 2**i<=n:
i=i+1
tree=[0]*(2**(i+1)-1)
segtree(0,a,tree,0,n-1)
for _ in range(m):
i,c=input().split()
i=int(i)-1
if c=='.':
if s[i]!='.':
if i>0:
if s[i-1]=='.':
a[i]=1
update(0,a,tree,0,n-1,i)
if i+1<n:
if s[i+1]=='.' and a[i+1]==0:
a[i+1]=1
update(0,a,tree,0,n-1,i+1)
else:
if s[i]=='.':
a[i]=0
update(0,a,tree,0,n-1,i)
if i+1<n and a[i+1]==1:
a[i+1]=0
update(0,a,tree,0,n-1,i+1)
s[i]=c
sys.stdout.write(str(tree[0]) + "\n")
```
Yes
| 2,046
|
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
import sys
def count(s):
sm = 0
ln = 0
i = 0
while i < len(s):
cnt = 0
while i < len(s) and s[i] == '.':
cnt += 1
i += 1
if cnt > 1:
sm += cnt
ln += 1
i += 1
return sm - ln
n, m = map(int, sys.stdin.readline().split())
string = ['#'] + list(input()) + ['#']
ans = count(string)
arans = [0 for i in range(m)]
for _ in range(m):
i, s = sys.stdin.readline().split()
i = int(i)
if s == '.':
if string[i] == s:
sys.stdout.write(str(ans)+'\n')
continue
string[i] = s
if string[i + 1] == '.': ans += 1
if string[i - 1] == '.': ans += 1
else:
if '.' != string[i]:
sys.stdout.write(str(ans)+'\n')
continue
string[i] = s
if string[i + 1] == '.': ans -= 1
if string[i - 1] == '.': ans -= 1
sys.stdout.write(str(ans)+'\n')
```
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.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
n, m = map(int, input().split())
s = [True] + [c != '.' for c in input()] + [True]
ans = sum(s[i] == s[i + 1] == 0 for i in range(1, n + 1))
out = [0] * m
for i in range(m):
pos, c = input().split()
pos, c = int(pos), c != '.'
if not s[pos]:
if c: ans -= 2 - (s[pos - 1] + s[pos + 1])
else:
if not c: ans += 2 - (s[pos - 1] + s[pos + 1])
s[pos] = c
out[i] = ans
print('\n'.join(map(str, out)))
import time, sys
sys.stderr.write('{0:.3f} ms\n'.format(time.clock() * 1000));
# by Andrey Kim
```
Yes
| 2,048
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
n, m = map(int, input().split())
s = [c != '.' for c in input()] + [1]
f = sum(s[i] == 0 and s[i + 1] != 1 for i in range(n))
t = [0] * m
for i in range(m):
x, c = input().split()
x, c = int(x) - 1, c != '.'
d = s[x - 1] + s[x + 1] - 2
f += (c - s[x]) * d
s[x], t[i] = c, f
print('\n'.join(map(str, t)))
```
Yes
| 2,049
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
n, m = [int(x) for x in input().split()]
s = [x for x in input()]
ans = 0
c = 0
for i in range(len(s)):
if s[i] == '.':
c += 1
else:
if c > 1:
ans += c - 1
c = 0
if c != 0:
ans += c - 1
for i in range(m):
n, sym = [x for x in input().split()]
if sym == ".":
if int(n) != len(s) and s[int(n)] == '.':
ans += 1
if int(n) != 1 and s[int(n) - 2] == '.':
ans += 1
else:
if s[int(n) - 1] == '.':
if int(n) != len(s) and s[int(n)] == '.':
ans -= 1
if int(n) != 1 and s[int(n) - 2] == '.':
ans -= 1
s[int(n) - 1] = sym
print(ans)
```
No
| 2,050
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
# -*- coding: utf-8 -*-
# Baqir Khan
# Software Engineer (Backend)
n, m = map(int, input().split())
s = list(str(input()))
ans = 0
for i in range(n - 1):
if s[i] == "." and s[i + 1] == ".":
ans += 1
while m:
m -= 1
inp = input().split()
index = int(inp[0]) - 1
char = inp[1]
if char == ".":
if index != 0 and index != n - 1 and s[index + 1] == "." and s[index - 1] == ".":
ans += 2
elif (index != 0 and s[index - 1] == ".") or (index != n - 1 and s[index + 1] == "."):
ans += 1
elif s[index] == ".":
if index != 0 and index != n - 1 and s[index + 1] == "." and s[index - 1] == ".":
ans -= 2
elif (index != 0 and s[index - 1] == ".") or (index != n - 1 and s[index + 1] == "."):
ans -= 1
s[index] = char
print(ans)
```
No
| 2,051
|
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
import sys,os,io
import math,bisect,operator
inf,mod = float('inf'),10**9+7
# sys.setrecursionlimit(10 ** 6)
from itertools import groupby,accumulate
from heapq import heapify,heappop,heappush
from collections import deque,Counter,defaultdict
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
Neo = lambda : list(map(int,input().split()))
# test, = Neo()
n,m = Neo()
s = ['*']+list(input())+['*']
t = 0
for i,j in zip(s,s[1:]):
if i+j == '..':
t += 1
for i in range(m):
ind,c = input().split()
ind = int(ind)
if c == '.':
if s[ind] != '.':
if s[ind-1]+s[ind+1] == '..':
t += 2
s[ind] = c
elif s[ind-1] == '.' or s[ind+1] == '.':
t += 1
s[ind] = c
else:
if s[ind-1]+s[ind]+s[ind+1] == '...':
t -= 2
s[ind] = c
elif s[ind-1]+s[ind] == '..' or s[ind]+s[ind+1] == '..':
t -= 1
s[ind] = c
else:
s[ind] = c
print(t)
```
No
| 2,052
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string s contains no two consecutive periods, then nothing happens.
Let's define f(s) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process m queries, the i-th results in that the character at position xi (1 ≤ xi ≤ n) of string s is assigned value ci. After each operation you have to calculate and output the value of f(s).
Help Daniel to process all queries.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 300 000) the length of the string and the number of queries.
The second line contains string s, consisting of n lowercase English letters and period signs.
The following m lines contain the descriptions of queries. The i-th line contains integer xi and ci (1 ≤ xi ≤ n, ci — a lowercas English letter or a period sign), describing the query of assigning symbol ci to position xi.
Output
Print m numbers, one per line, the i-th of these numbers must be equal to the value of f(s) after performing the i-th assignment.
Examples
Input
10 3
.b..bz....
1 h
3 c
9 f
Output
4
3
1
Input
4 4
.cc.
2 .
3 .
2 a
1 a
Output
1
3
1
1
Note
Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
* after the first query f(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")
* after the second query f(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")
* after the third query f(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
* after the first query: f(..c.) = 1 ("[..]c." → ".c.")
* after the second query: f(....) = 3 ("[..].." → "[..]." → "[..]" → ".")
* after the third query: f(.a..) = 1 (".a[..]" → ".a.")
* after the fourth query: f(aa..) = 1 ("aa[..]" → "aa.")
Submitted Solution:
```
from sys import stdin, stdout
input = stdin.readline
n, m = map(int, input().split())
s = list(input())
f = 0
ans = []
for i in range(1,n):
if s[i] == s[i-1] and s[i] == '.':
f+= 1
for i in range(m):
x, ch = input().split()
x = int(x) - 1
if s[x] != ch:
if ch == '.':
if x > 0 and s[x-1] == '.':
f += 1
if x < n - 1 and s[x+1] == '.':
f += 1
else:
if x > 0 and s[x-1] == '.':
f -= 1
if x < n - 1 and s[x+1] == '.':
f -= 1
s[x] = ch
ans.append(f)
stdout.write("\n".join(map(str,ans)))
```
No
| 2,053
|
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|
Provide a correct Python 3 solution for this coding contest problem.
You are a treasure hunter traveling around the world. Finally, you’ve got an ancient text indicating the place where the treasure was hidden. The ancient text looks like a meaningless string of characters at first glance. Actually, the secret place is embedded as the longest repeated subsequence of the text.
Well, then, what is the longest repeated subsequence of a string? First, you split the given string S into two parts F and R. Then, you take the longest common subsequence L of F and R (longest string L that is a subsequence of both F and R). Since there are many possible ways to split S into two parts, there are many possible L's. The longest repeated subsequence is the longest one among them. For example, the longest repeated subsequence of “ABCABCABAB” is “ABAB”, which is obtained when you split “ABCABCABAB” into “ABCABC” and “ABAB”.
Now your task is clear. Please find the longest repeated subsequence and get the hidden treasure!
Input
The input consists of multiple data sets. Each data set comes with a single line that contains one string of up to 300 capital letters. It is guaranteed that there is at least one repeated subsequence in each string.
The end of input is indicated by a line that contains “#END”. This line should not be processed.
Output
For each data set, print the longest repeated subsequence on a line. If there are multiple longest subsequence, print any one of them.
Examples
Input
ABCABCABAB
ZZZZZZZZZZZZ
#END
Output
ABAB
ZZZZZZ
Input
ABCABCABAB
ZZZZZZZZZZZZ
END
Output
ABAB
ZZZZZZ
"Correct Solution:
```
def lcs(x, y, pre_lcs, pre_lcs_len):
pm = dict((zip('ABCDEFGHIJKLMNOPQRSTUVWXYZ', [0] * 26)))
for c in pm:
for i, xc in enumerate(x):
if c == xc:
pm[c] |= (1 << i)
V = (1 << len(x)) - 1
rec = []
for yc in y:
V = ((V + (V & pm[yc])) | (V & ~pm[yc]))
rec.append(bin(V)[-len(x):])
lcs_len = bin(V)[-len(x):].count('0')
if lcs_len > pre_lcs_len:
rx = x[::-1]
lcs = ''
idx = 0
for v, yc in zip(rec[::-1], reversed(y)):
idx = v.find('0', idx)
if yc == rx[idx]:
lcs += yc
if len(lcs) == lcs_len:
return (lcs[::-1], lcs_len)
idx += 1
else:
return (pre_lcs, pre_lcs_len)
from sys import stdin
def solve():
file_input = stdin
ans_out = []
for s in file_input:
s = s.rstrip()
if s[0] == '#':
break
s_len = len(s)
sep = s_len // 2
ans, ans_len = lcs(s[:sep], s[sep:], '', 0)
while sep > ans_len:
ans, ans_len = lcs(s[:-sep], s[-sep:], ans, ans_len)
sep -= 1
ans, ans_len = lcs(s[:sep], s[sep:], ans, ans_len)
ans_out.append(ans)
print(*ans_out, sep='\n')
solve()
```
| 2,417
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a treasure hunter traveling around the world. Finally, you’ve got an ancient text indicating the place where the treasure was hidden. The ancient text looks like a meaningless string of characters at first glance. Actually, the secret place is embedded as the longest repeated subsequence of the text.
Well, then, what is the longest repeated subsequence of a string? First, you split the given string S into two parts F and R. Then, you take the longest common subsequence L of F and R (longest string L that is a subsequence of both F and R). Since there are many possible ways to split S into two parts, there are many possible L's. The longest repeated subsequence is the longest one among them. For example, the longest repeated subsequence of “ABCABCABAB” is “ABAB”, which is obtained when you split “ABCABCABAB” into “ABCABC” and “ABAB”.
Now your task is clear. Please find the longest repeated subsequence and get the hidden treasure!
Input
The input consists of multiple data sets. Each data set comes with a single line that contains one string of up to 300 capital letters. It is guaranteed that there is at least one repeated subsequence in each string.
The end of input is indicated by a line that contains “#END”. This line should not be processed.
Output
For each data set, print the longest repeated subsequence on a line. If there are multiple longest subsequence, print any one of them.
Examples
Input
ABCABCABAB
ZZZZZZZZZZZZ
#END
Output
ABAB
ZZZZZZ
Input
ABCABCABAB
ZZZZZZZZZZZZ
END
Output
ABAB
ZZZZZZ
Submitted Solution:
```
def lcs(x, y):
rec = []
idx = []
for c in y:
s = 0
for i, k in enumerate(idx):
t = x.find(c, s) + 1
if t < 1:
break
if t < k:
idx[i] = t
s = k
else:
t = x.find(c, s) + 1
if t:
idx.append(t)
rec.append(idx.copy())
lcs = ''
pos = len(idx) - 1
for line, yc in zip(rec[::-1], y[::-1]):
i = line[pos] - 1
xc = x[i]
if xc == yc:
lcs += xc
if pos == 0:
return lcs[::-1]
pos -= 1
def solve():
import sys
file_input = sys.stdin
for s in file_input:
s = s.rstrip()
if s == '#END':
break
sep = len(s) // 2
ans = lcs(s[:sep], s[sep:])
ans_len = len(ans)
while sep > len(ans):
sep -= 1
a1 = lcs(s[:sep], s[sep:])
a2 = lcs(s[:-sep], s[-sep:])
if ans_len < len(a1):
ans = a1
ans_len = len(ans)
if ans_len < len(a2):
ans = a2
ans_len = len(ans)
print(ans)
solve()
```
No
| 2,418
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a treasure hunter traveling around the world. Finally, you’ve got an ancient text indicating the place where the treasure was hidden. The ancient text looks like a meaningless string of characters at first glance. Actually, the secret place is embedded as the longest repeated subsequence of the text.
Well, then, what is the longest repeated subsequence of a string? First, you split the given string S into two parts F and R. Then, you take the longest common subsequence L of F and R (longest string L that is a subsequence of both F and R). Since there are many possible ways to split S into two parts, there are many possible L's. The longest repeated subsequence is the longest one among them. For example, the longest repeated subsequence of “ABCABCABAB” is “ABAB”, which is obtained when you split “ABCABCABAB” into “ABCABC” and “ABAB”.
Now your task is clear. Please find the longest repeated subsequence and get the hidden treasure!
Input
The input consists of multiple data sets. Each data set comes with a single line that contains one string of up to 300 capital letters. It is guaranteed that there is at least one repeated subsequence in each string.
The end of input is indicated by a line that contains “#END”. This line should not be processed.
Output
For each data set, print the longest repeated subsequence on a line. If there are multiple longest subsequence, print any one of them.
Examples
Input
ABCABCABAB
ZZZZZZZZZZZZ
#END
Output
ABAB
ZZZZZZ
Input
ABCABCABAB
ZZZZZZZZZZZZ
END
Output
ABAB
ZZZZZZ
Submitted Solution:
```
def lcs(x, y, pre_lcs, pre_lcs_len):
rec = []
idx = []
for c in y:
s = 0
for i, k in enumerate(idx):
t = x.find(c, s) + 1
if t < 1:
break
if t < k:
idx[i] = t
s = k
else:
t = x.find(c, s) + 1
if t:
idx.append(t)
rec.append(idx.copy())
lcs_len = len(idx)
if lcs_len > pre_lcs_len:
lcs = ''
pos = len(idx) - 1
for line, yc in zip(rec[::-1], y[::-1]):
i = line[pos] - 1
xc = x[i]
if xc == yc:
lcs += xc
if pos == 0:
return (lcs[::-1], lcs_len)
pos -= 1
else:
return (pre_lcs, pre_lcs_len)
def solve():
import sys
#file_input = sys.stdin
file_input = open('2090_in', 'r')#
ans_out = []
for s in file_input:
s = s.rstrip()
if s == '#END':
break
s_len = len(s)
sep = s_len // 2
ans, ans_len = lcs(s[:sep], s[sep:], '', 0)
while sep > ans_len:
ans, ans_len = lcs(s[:-sep], s[-sep:], ans, ans_len)
sep -= 1
ans, ans_len = lcs(s[:sep], s[sep:], ans, ans_len)
print(ans)
solve()
```
No
| 2,419
|
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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 a treasure hunter traveling around the world. Finally, you’ve got an ancient text indicating the place where the treasure was hidden. The ancient text looks like a meaningless string of characters at first glance. Actually, the secret place is embedded as the longest repeated subsequence of the text.
Well, then, what is the longest repeated subsequence of a string? First, you split the given string S into two parts F and R. Then, you take the longest common subsequence L of F and R (longest string L that is a subsequence of both F and R). Since there are many possible ways to split S into two parts, there are many possible L's. The longest repeated subsequence is the longest one among them. For example, the longest repeated subsequence of “ABCABCABAB” is “ABAB”, which is obtained when you split “ABCABCABAB” into “ABCABC” and “ABAB”.
Now your task is clear. Please find the longest repeated subsequence and get the hidden treasure!
Input
The input consists of multiple data sets. Each data set comes with a single line that contains one string of up to 300 capital letters. It is guaranteed that there is at least one repeated subsequence in each string.
The end of input is indicated by a line that contains “#END”. This line should not be processed.
Output
For each data set, print the longest repeated subsequence on a line. If there are multiple longest subsequence, print any one of them.
Examples
Input
ABCABCABAB
ZZZZZZZZZZZZ
#END
Output
ABAB
ZZZZZZ
Input
ABCABCABAB
ZZZZZZZZZZZZ
END
Output
ABAB
ZZZZZZ
Submitted Solution:
```
def lcs(x, y, pre_lcs, pre_lcs_len):
rec = []
idx = []
for c in y:
s = 0
for i, k in enumerate(idx):
t = x.find(c, s) + 1
if t < 1:
break
if t < k:
idx[i] = t
s = k
else:
t = x.find(c, s) + 1
if t:
idx.append(t)
rec.append(idx.copy())
lcs_len = len(idx)
if lcs_len > pre_lcs_len:
lcs = ''
pos = len(idx) - 1
for line, yc in zip(rec[::-1], y[::-1]):
i = line[pos] - 1
xc = x[i]
if xc == yc:
lcs += xc
if pos == 0:
return (lcs[::-1], lcs_len)
pos -= 1
else:
return (pre_lcs, pre_lcs_len)
def lrs(s):
s = s.rstrip()
s_len = len(s)
sep = s_len // 2
ans, ans_len = lcs(s[:sep], s[sep:], '', 0)
while sep > ans_len:
ans, ans_len = lcs(s[:-sep], s[-sep:], ans, ans_len)
sep -= 1
ans, ans_len = lcs(s[:sep], s[sep:], ans, ans_len)
return ans
import sys
input_lines = sys.stdin.readlines()
for line in input_lines[:-1]:
print(lrs(line))
```
No
| 2,420
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are a treasure hunter traveling around the world. Finally, you’ve got an ancient text indicating the place where the treasure was hidden. The ancient text looks like a meaningless string of characters at first glance. Actually, the secret place is embedded as the longest repeated subsequence of the text.
Well, then, what is the longest repeated subsequence of a string? First, you split the given string S into two parts F and R. Then, you take the longest common subsequence L of F and R (longest string L that is a subsequence of both F and R). Since there are many possible ways to split S into two parts, there are many possible L's. The longest repeated subsequence is the longest one among them. For example, the longest repeated subsequence of “ABCABCABAB” is “ABAB”, which is obtained when you split “ABCABCABAB” into “ABCABC” and “ABAB”.
Now your task is clear. Please find the longest repeated subsequence and get the hidden treasure!
Input
The input consists of multiple data sets. Each data set comes with a single line that contains one string of up to 300 capital letters. It is guaranteed that there is at least one repeated subsequence in each string.
The end of input is indicated by a line that contains “#END”. This line should not be processed.
Output
For each data set, print the longest repeated subsequence on a line. If there are multiple longest subsequence, print any one of them.
Examples
Input
ABCABCABAB
ZZZZZZZZZZZZ
#END
Output
ABAB
ZZZZZZ
Input
ABCABCABAB
ZZZZZZZZZZZZ
END
Output
ABAB
ZZZZZZ
Submitted Solution:
```
def lcs(x, y, pre_lcs, pre_lcs_len):
rec = []
idx = []
for c in y:
s = 0
for i, k in enumerate(idx):
t = x.find(c, s) + 1
if t < 1:
break
if t < k:
idx[i] = t
s = k
else:
t = x.find(c, s) + 1
if t:
idx.append(t)
rec.append(idx.copy())
lcs_len = len(idx)
if lcs_len > pre_lcs_len:
lcs = ''
pos = len(idx) - 1
for line, yc in zip(rec[::-1], y[::-1]):
i = line[pos] - 1
xc = x[i]
if xc == yc:
lcs += xc
if pos == 0:
return (lcs[::-1], lcs_len)
pos -= 1
else:
return (pre_lcs, pre_lcs_len)
def solve():
import sys
file_input = sys.stdin
ans_out = []
for s in file_input:
s = s.rstrip()
if s == '#END':
break
s_len = len(s)
sep = s_len // 2
ans, ans_len = lcs(s[:sep], s[sep:], '', 0)
while sep > ans_len:
ans, ans_len = lcs(s[:-sep], s[-sep:], ans, ans_len)
sep -= 1
ans, ans_len = lcs(s[:sep], s[sep:], ans, ans_len)
print(ans)
solve()
```
No
| 2,421
|
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|
Provide a correct Python 3 solution for this coding contest problem.
Problem
Taro has N character strings, each of which is L in length. Taro loves palindromes, so I want to make palindromes as long as possible by selecting some of the N character strings and arranging them in any order.
Find the longest palindrome that Taro can make. If there are more than one, output the smallest one in lexicographical order. If you can't make a palindrome no matter how you choose and arrange them, output a blank line.
Constraints
The input satisfies the following conditions.
* 1 ≤ N ≤ 1000
* 1 ≤ L ≤ 30
* s_i is a character string consisting of lowercase letters.
Input
The input is given in the following format.
N L
s1
s2
..
..
..
sN
The number N of strings and the length L of strings are given on the first line. From the second line that follows, N & plus; The character string s_i that Taro has is given to the first line.
Output
Output the longest palindrome with the smallest dictionary order. If you cannot make a palindrome, output a blank line.
Examples
Input
4 2
oi
io
rr
rr
Output
iorrrroi
Input
5 1
a
b
c
a
c
Output
acbca
Input
3 3
uki
uku
uke
Output
uku
"Correct Solution:
```
from functools import cmp_to_key
n, l = map(int, input().split())
ss = {}
for i in range(n):
s = input()
ss[s] = ss.get(s, 0) + 1
ans = ""
ma = ""
for s in sorted(ss):
if s[::-1] == s:
ans += s * (ss[s]//2)
ss[s] -= 2*(ss[s]//2)
if ss[s] > 0 and len(ma) < len(s):
ma = s
else:
rev = s[::-1]
if rev in ss:
cnt = min(ss[s], ss[rev])
ans += s * cnt
ss[s] -= cnt
ss[rev] -= cnt
print(ans + ma + ans[::-1])
```
| 2,433
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's denote (yet again) the sequence of Fibonacci strings:
F(0) = 0, F(1) = 1, F(i) = F(i - 2) + F(i - 1), where the plus sign denotes the concatenation of two strings.
Let's denote the lexicographically sorted sequence of suffixes of string F(i) as A(F(i)). For example, F(4) is 01101, and A(F(4)) is the following sequence: 01, 01101, 1, 101, 1101. Elements in this sequence are numbered from 1.
Your task is to print m first characters of k-th element of A(F(n)). If there are less than m characters in this suffix, then output the whole suffix.
Input
The only line of the input contains three numbers n, k and m (1 ≤ n, m ≤ 200, 1 ≤ k ≤ 10^{18}) denoting the index of the Fibonacci string you have to consider, the index of the element of A(F(n)) and the number of characters you have to output, respectively.
It is guaranteed that k does not exceed the length of F(n).
Output
Output m first characters of k-th element of A(F(n)), or the whole element if its length is less than m.
Examples
Input
4 5 3
Output
110
Input
4 3 3
Output
1
Submitted Solution:
```
import sys
def test(n,k,m):
res1 = f2(f1(n))
r = res1[k-1][:m]
print(r)
return r
def f1(n):
strHash = {0:"0",1:"1",2:"01",3:"101"}
for i in range(3,n+1) :
strHash[i] = strHash[i-2] + strHash[i -1]
#print(strHash)
#print(strHash[n])
return(strHash[n])
def f2(str):
lenq = len(str)
print("this is {} ".format(str))
result = []
i = 0;
while(i < lenq ):
result.append(str[i:])
i+=1
print(sorted(result))
return sorted(result)
#return result.sort()
if __name__ == '__main__':
str_list = sys.stdin.readline().strip("\n").split(" ")
number_list = [int(str(i)) for i in str_list]
a = number_list[0]
b = number_list[1]
c = number_list[2]
print(test(a,b,c))
```
No
| 2,483
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's denote (yet again) the sequence of Fibonacci strings:
F(0) = 0, F(1) = 1, F(i) = F(i - 2) + F(i - 1), where the plus sign denotes the concatenation of two strings.
Let's denote the lexicographically sorted sequence of suffixes of string F(i) as A(F(i)). For example, F(4) is 01101, and A(F(4)) is the following sequence: 01, 01101, 1, 101, 1101. Elements in this sequence are numbered from 1.
Your task is to print m first characters of k-th element of A(F(n)). If there are less than m characters in this suffix, then output the whole suffix.
Input
The only line of the input contains three numbers n, k and m (1 ≤ n, m ≤ 200, 1 ≤ k ≤ 10^{18}) denoting the index of the Fibonacci string you have to consider, the index of the element of A(F(n)) and the number of characters you have to output, respectively.
It is guaranteed that k does not exceed the length of F(n).
Output
Output m first characters of k-th element of A(F(n)), or the whole element if its length is less than m.
Examples
Input
4 5 3
Output
110
Input
4 3 3
Output
1
Submitted Solution:
```
import itertools
def fib(i):
if(i==0):
return '0'
elif i==1:
return '1'
else:
return fib(i-2)+fib(i-1)
n,k,m=list(map(int,input().split()))
ans=fib(n)
ans=ans[::-1]
ans=list(ans)
mainl=list(itertools.accumulate(ans,lambda x,y : x+y))
mainl2=[]
mainl2=[i[::-1] for i in mainl]
mainl2.sort(key=len)
mainl2.sort(key=lambda x:int(x[0]))
s=mainl2[k-1]
print(s[:m])
```
No
| 2,484
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's denote (yet again) the sequence of Fibonacci strings:
F(0) = 0, F(1) = 1, F(i) = F(i - 2) + F(i - 1), where the plus sign denotes the concatenation of two strings.
Let's denote the lexicographically sorted sequence of suffixes of string F(i) as A(F(i)). For example, F(4) is 01101, and A(F(4)) is the following sequence: 01, 01101, 1, 101, 1101. Elements in this sequence are numbered from 1.
Your task is to print m first characters of k-th element of A(F(n)). If there are less than m characters in this suffix, then output the whole suffix.
Input
The only line of the input contains three numbers n, k and m (1 ≤ n, m ≤ 200, 1 ≤ k ≤ 10^{18}) denoting the index of the Fibonacci string you have to consider, the index of the element of A(F(n)) and the number of characters you have to output, respectively.
It is guaranteed that k does not exceed the length of F(n).
Output
Output m first characters of k-th element of A(F(n)), or the whole element if its length is less than m.
Examples
Input
4 5 3
Output
110
Input
4 3 3
Output
1
Submitted Solution:
```
n,m,k=map(int,input().split())
prev=1
next=1
l=[]
while(len(l)<n+1):
temp=next
next=next+prev
prev=temp
l.append(next)
b=bin(l[-1])
b=b[2:]
if(m>len(b)):
m1=m-len(b)
b=m1*'0'+b
else:
b='0'+b
#print(b)
l1=[]
for i in range(0,len(b)):
l1.append(b[i:])
l1.sort()
#print(l1)
s=l1[m-1]
#print(s)
if(len(s)>k):
print(s[:k])
else:
print(s)
```
No
| 2,485
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's denote (yet again) the sequence of Fibonacci strings:
F(0) = 0, F(1) = 1, F(i) = F(i - 2) + F(i - 1), where the plus sign denotes the concatenation of two strings.
Let's denote the lexicographically sorted sequence of suffixes of string F(i) as A(F(i)). For example, F(4) is 01101, and A(F(4)) is the following sequence: 01, 01101, 1, 101, 1101. Elements in this sequence are numbered from 1.
Your task is to print m first characters of k-th element of A(F(n)). If there are less than m characters in this suffix, then output the whole suffix.
Input
The only line of the input contains three numbers n, k and m (1 ≤ n, m ≤ 200, 1 ≤ k ≤ 10^{18}) denoting the index of the Fibonacci string you have to consider, the index of the element of A(F(n)) and the number of characters you have to output, respectively.
It is guaranteed that k does not exceed the length of F(n).
Output
Output m first characters of k-th element of A(F(n)), or the whole element if its length is less than m.
Examples
Input
4 5 3
Output
110
Input
4 3 3
Output
1
Submitted Solution:
```
import itertools
def fib(i):
if(i==0):
return '0'
elif i==1:
return '1'
else:
return fib(i-2)+fib(i-1)
n,k,m=list(map(int,input().split()))
ans=fib(n)
ans=ans[::-1]
ans=list(ans)
mainl=list(itertools.accumulate(ans,lambda x,y : x+y))
mainl2=[]
for i in mainl:
mainl2.append(i[::-1])
mainl2.sort(key=len)
mainl2.sort(key=lambda x:int(x[0]))
s=mainl2[k-1]
print(s[:m])
```
No
| 2,486
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
from sys import stdin
uu=0
n=int(stdin.readline().strip())
s1=stdin.readline().strip()
s=list(map(int,stdin.readline().strip().split()))
dp=[-1 for i in range(n+1)]
def sol1(x):
if dp[x]!=-1:
return dp[x]
if x==0:
return 0
ans=0
for i in range(x):
ans=max(ans,s[i]+sol1(x-i-1))
dp[x]=ans
for i in range(n):
sol1(i+1)
dp[0]=0
s2=[]
x=1
for i in range(1,len(s)):
if s1[i]!=s1[i-1]:
s2.append(x)
x=1
else:
x+=1
s2.append(x)
dp1=[[[-1 for i in range(n+1)]for j in range(n+1)] for k in range(n+1)]
n=len(s2)
s=s2.copy()
def sol(l,r,k):
if l==r:
return dp[s[l]+k]
if l>r:
return 0
if dp1[l][r][k]!=-1:
return dp1[l][r][k]
ans=0
for i in range(l,r+1,2):
if i!=l:
ans=max(ans,sol(l+1,i-1,0)+sol(i,r,s[l]+k))
else:
ans=max(ans,sol(i+1,r,0)+dp[s[l]+k])
dp1[l][r][k]=ans
return ans
print(sol(0,len(s)-1,0))
```
| 2,487
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
# returns answer to the subproblem with interval range [start, end],
# but with a total of "extra" additional stuff on the end
# that must be deleted last.
memo = {}
def f(dat, rewards, start, end, extra):
curr = (start, end, extra)
if curr in memo:
return memo[curr]
if start > end:
return 0
if start == end:
memo[curr] = rewards[dat[start] + extra]
return memo[curr]
# test all possible "cut points".
# "cut" is the earliest index to die in the same deletion as "end".
out = 0
for cut in range(end, start-1, -2):
if cut == end:
# in this case, we're deleting the last interval right away.
out_curr = rewards[dat[cut] + extra]
out_curr += f(dat, rewards, start, cut-1, 0)
else:
# split into 2 pieces:
# 1) slots [start, cut] plus [end + extra]
# 2) slots [cut+1, end-1] (with no extra, this needs to get deleted first).
out_curr = f(dat, rewards, start, cut, extra + dat[end])
out_curr += f(dat, rewards, cut+1, end-1, 0)
out = max(out, out_curr)
memo[curr] = out
return memo[curr]
def solve(dat_str, rewards_orig):
# break into intervals.
dat = []
pos = 0
while pos < len(dat_str):
end = pos
while end < len(dat_str) and dat_str[pos] == dat_str[end]:
end += 1
dat.append(end - pos)
pos = end
# compute the highest-value way to remove a run of size k.
# (google translated from C++ thinking)
rewards = [0, rewards_orig[0]]
for k in range(2, len(rewards_orig) + 1):
# print(
# "{}: {}".format(
# k,
# [
# rewards[k-j] + rewards_orig[j-1]
# for j in range(1, k+1)
# ]
# )
# )
rewards.append(
max(
rewards[k-j] + rewards_orig[j-1]
for j in range(1, k+1)
)
)
# print("dat: {}".format(dat))
# print("rewards: {}".format(rewards))
return f(dat, rewards, 0, len(dat)-1, 0)
# get the integer
int_dummy = input()
# get the string
dat_str = input().strip()
# get the array
rewards_input = input().strip().split()
rewards_ints = [int(x) for x in rewards_input]
# print(dat_str)
# print(rewards_ints)
print(
solve(
dat_str,
rewards_ints,
)
)
# dat_test = "10101"
# rewards_test = [3, 10, 15, 15, 15]
# print(solve(dat_test, rewards_test))
```
| 2,488
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
n = int(input())
s = input()
a = [int(x) for x in input().split()]
dp = [[[False for i in range(101)] for j in range(101)] for k in range(101)]
def f(i, j, k):
if not dp[i][j][k]:
if i == j:
dp[i][j][k] = 0
else:
dp[i][j][k] = f(i+1, j, 0) + a[k]
for m in range(i+1, j):
if s[i] == s[m]:
dp[i][j][k] = max(dp[i][j][k], f(i+1, m, 0) + f(m, j, k+1))
return dp[i][j][k]
answer = f(0, n, 0)
print(answer)
```
| 2,489
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
n = int(input())
s = input().strip()
a = [0] + list(map(int, input().split()))
MX = 105
dp = [0] * (MX ** 3)
def f(i, j, k):
if i == j: return 0
idx = i * MX * MX + j * MX + k
if not dp[idx]:
dp[idx] = f(i + 1, j, 1) + a[k]
for m in range(i + 1, j):
if s[i] == s[m]:
dp[idx] = max(dp[idx], f(i + 1, m, 1) + f(m, j, k + 1))
return dp[idx]
print(f(0, n, 1))
```
| 2,490
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
n = int(input())
s = input()
ai = [0] + list(map(int,input().split()))
ar = [ai[i] for i in range(n+1)]
for i in range(1,n):
num = 0
for j in range(0,(i+1) // 2 + 1):
ar[i] = max(ar[i],ar[j] + ar[i-j])
ar2 = []
num = 1
for i in range(1,n):
if s[i] == s[i-1]:
num += 1
else:
ar2 += [num]
num = 1
ar2 += [num]
n2 = len(ar2)
ar = ar
ar3 = [[-1] * (n2 + 5) for i in range(n2+5)]
ar4 = [[[-1] * (102) for i in range(102)] for i in range(102)]
num5 = 0
def fun(i, n3, num3):
if i > n3 - 1:
return 0
ans = 0
num = num3
num2 = 0
for j in range(i,n3,2):
num += ar2[j]
if ar3[j+1][n3] == -1:
ar3[j+1][n3] = fun(j+1,n3,0)
ans = max(ans, ar3[j+1][n3] + ar[num] + num2)
for z in range(j+3,n3,2):
if ar3[j+1][z+1] == -1:
ar3[j+1][z+1] = fun(j+1,z+1,0)
if ar4[z+1][n3][num] == -1:
ar4[z+1][n3][num] = fun(z+1,n3,num)
ans = max(ans, ar3[j+1][z+1] + ar4[z+1][n3][num] + num2)
if j < n3 - 1:
num2 += ar[ar2[j+1]]
return ans
print(fun(0, n2, 0))
```
| 2,491
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
# 545 ms
from functools import lru_cache
n = int(input())
s = input()
A = [0] + list(map(int, input().split()))
dp = [0] * (n + 1)
for i in range(1, n + 1):
dp[i] = max(dp[j] + A[i - j] for j in range(0, i))
@lru_cache(None)
def score(s):
length = len(s)
if length == 0:
return 0
ans = 0
start = 0
i = 1
while i < length and s[i] == s[start]:
i += 1
ans = dp[i] + score(s[i:])
for j in range(i, length):
if s[j] == s[start]:
ans = max(ans, score(s[i:j]) + score(s[:i] + s[j:]))
return ans
print(score(s))
```
| 2,492
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
import sys
from math import *
from fractions import gcd
readints=lambda:map(int, input().strip('\n').split())
n=int(input())
s=input()
a=list(readints())
a=[0]+a #1-index
cache={}
def solve(i,j,k):
if i>j: return 0
if i==j: return a[k]
if (i,j,k) in cache: return cache[(i,j,k)]
best=a[k]+solve(i+1,j,1)
for x in range(i+1,j+1):
if s[i]==s[x]:
best=max(best,solve(i+1,x-1,1)+solve(x,j,k+1))
#print(i,j,best)
cache[(i,j,k)]=best
return best
ans=solve(0,n-1,1)
print(ans)
```
| 2,493
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Tags: dp
Correct Solution:
```
from functools import lru_cache
n = int(input())
s = input()
A = [0] + list(map(int, input().split()))
dp = [0] * (n + 1)
for i in range(1, n + 1):
dp[i] = max(dp[j] + A[i - j] for j in range(0, i))
res = {}
@lru_cache(None)
def score(s):
length = len(s)
if length == 0:
return 0
ans = 0
start = 0
i = 1
while i < length and s[i] == s[start]:
i += 1
ans = dp[i] + score(s[i:])
for j in range(i, length):
if s[j] == s[start]:
ans = max(ans, score(s[i:j]) + score(s[:i] + s[j:]))
return ans
print(score(s))
```
| 2,494
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
from sys import stdin
n=int(stdin.readline().strip())
s1=stdin.readline().strip()
s=list(map(int,stdin.readline().strip().split()))
dp=[-1 for i in range(n+1)]
def sol1(x):
if dp[x]!=-1:
return dp[x]
if x==0:
return 0
ans=0
for i in range(x):
ans=max(ans,s[i]+sol1(x-i-1))
dp[x]=ans
for i in range(n):
sol1(i+1)
dp[0]=0
s2=[]
x=1
for i in range(1,len(s)):
if s1[i]!=s1[i-1]:
s2.append(x)
x=1
else:
x+=1
s2.append(x)
dp1=[[[-1 for i in range(n+1)]for j in range(n+1)] for k in range(n+1)]
n=len(s2)
s=s2.copy()
def sol(l,r,k):
if l==r:
return dp[s[l]+k]
if l>r:
return 0
if dp1[l][r][k]!=-1:
return dp1[l][r][k]
ans=0
for i in range(l,r+1,2):
if i!=l:
ans=max(ans,sol(l+1,i-1,0)+sol(i,r,s[l]+k))
else:
ans=max(ans,sol(i+1,r,0)+dp[s[l]+k])
dp1[l][r][k]=ans
return ans
print(sol(0,len(s)-1,0))
```
Yes
| 2,495
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline
n = int(input())
s = input()
a = list(map(int, input().split()))
N = len(a)
dp = [[[-1] * N for i in range(N)] for j in range(N)]
def calc(l, r, k):
if dp[l][r][k] != -1:
return dp[l][r][k]
if l == r:
return a[k]
tmp = 0
for i in range(l, r):
tmp = max(tmp, calc(l, i, 0) + calc(i + 1, r, k))
if s[i] == s[r]:
tmp = max(tmp, calc(i + 1, r - 1, 0) + calc(l, i, k + 1))
dp[l][r][k] = tmp
return tmp
print(calc(0, n - 1, 0))
```
Yes
| 2,496
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
n = int(input())
s = input()
A = [0] + list(map(int, input().split()))
dp = [0] * (n + 1)
for i in range(1, n + 1):
dp[i] = max(dp[j] + A[i - j] for j in range(0, i))
res = {}
def score(s):
length = len(s)
if length == 0:
return 0
if s not in res.keys():
ans = 0
start = 0
i = 1
while i < length and s[i] == s[start]:
i += 1
ans = dp[i] + score(s[i:])
for j in range(i, length):
if s[j] == s[start]:
ans = max(ans, score(s[i:j]) + score(s[:i] + s[j:]))
res[s] = ans
return res[s]
print(score(s))
```
Yes
| 2,497
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
n = int(input())
s = input().strip()
a = [0] + list(map(int, input().split()))
MX = 105
dp = [0] * (MX ** 3)
idx = lambda i, j, k: i * MX * MX + j * MX + k
for i in range(n + 1):
for k in range(1, n + 1):
dp[idx(i, i, k)] = 0
for gap in range(1, n + 1):
for i in range(n):
j = i + gap
if j > n: break
for k in range(1, n + 1):
cur = idx(i, j, k)
dp[cur] = dp[idx(i + 1, j, 1)] + a[k]
for m in range(i + 1, j):
if s[i] == s[m]:
dp[cur] = max(dp[cur], dp[idx(i + 1, m, 1)] + dp[idx(m, j, k + 1)])
print(dp[idx(0, n, 1)])
```
Yes
| 2,498
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
# returns answer to the subproblem with first N intervals,
# but with last interval extended by 'extra'.
memo = {}
def f(dat, rewards, N, extra):
curr = (N, extra)
if curr in memo:
return memo[curr]
if N == -1:
memo[curr] = rewards[extra]
# print(
# "for {} {}, return {}.".format(
# N,
# extra,
# memo[curr],
# )
# )
return memo[curr]
if N == 0:
memo[curr] = rewards[dat[0] + extra]
# print(
# "for {} {}, return {}.".format(
# N,
# extra,
# memo[curr],
# )
# )
return memo[curr]
##### Ben, you're in charge of stopping me as soon as you realize what I'm doing + can explain why it doesn't work.
### deal
##### I always start by coding stuff fast with bugs everywhere. I think the current version contains my full idea but probably has off by ones?
# method 1: discard interval N-1 first.
#i think it looks right. Thinking this is n*n?
### I agree N^2. N^3 would make more sense for limit 100 though... for N^2 I'd expect bound like 2e3 or something
### yeah I feel mostly convinced. I'm bad at python though.
#haha that's beautiful. all the errors
## what is?
method1 = rewards[ dat[N-1] ] + f(dat, rewards, N-2, extra + dat[N])
# method 2: discard interval N first.
method2 = rewards[ dat[N] + extra ] + f(dat, rewards, N-1, 0)
if method1 >= method2:
memo[curr] = method1
# print("better to discard N-1 first from {} {}, score is {}".format(N, extra, memo[curr]))
# print(
# "contributions were {} + {}".format(
# rewards[ dat[N-1] ],
# f(dat, rewards, N-2, extra + dat[N]),
# )
# )
else:
memo[curr] = method2
# print("better to discard N first from {} {}, score is {}".format(N, extra, memo[curr]))
# print(
# "contributions were {} + {}".format(
# rewards[ dat[N] + extra ],
# f(dat, rewards, N-1, 0),
# )
# )
return memo[curr]
def solve(dat_str, rewards_orig):
# break into intervals.
dat = []
pos = 0
while pos < len(dat_str):
end = pos
while end < len(dat_str) and dat_str[pos] == dat_str[end]:
end += 1
dat.append(end - pos)
pos = end
# compute the highest-value way to remove a run of size k.
# (google translated from C++ thinking)
rewards = [0, rewards_orig[0]]
for k in range(2, len(rewards_orig)):
# print(
# "{}: {}".format(
# k,
# [
# rewards[k-j] + rewards_orig[j-1]
# for j in range(1, k+1)
# ]
# )
# )
rewards.append(
max(
rewards[k-j] + rewards_orig[j-1]
for j in range(1, k+1)
)
)
# print("dat: {}".format(dat))
# print("rewards: {}".format(rewards))
return f(dat, rewards, len(dat)-1, 0)
# get the integer
int_dummy = input()
# get the string
dat_str = input().strip()
# get the array
rewards_input = input().strip().split()
rewards_ints = [int(x) for x in rewards_input]
# print(dat_str)
# print(rewards_ints)
print(
solve(
dat_str,
rewards_ints,
)
)
# dat_test = "1101001"
# rewards_test = [3, 4, 9, 100, 1, 2, 3]
# print(solve(dat_test, rewards_test))
```
No
| 2,499
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
def rlist(): return list(map(int, input().split()))
def rdi(): return int(input())
def f(q, p):
if q == p:
if string[q] == '0':
return [(1, 0), (0, dp[0])]
else:
return [(0, dp[0]), (1, 0)]
ll = q
rr = p
while ll < rr and (string[ll] == string[q] or string[rr] == string[p]):
if string[ll] == string[q]:
ll += 1
if string[rr] == string[p]:
rr -= 1
if ll > rr and string[q] == string[p]:
if string[q] == '0':
return [(q - p + 1, 0), (0, dp[q - p])]
else:
return [(0, dp[q - p]), (q - p + 1, 0)]
elif ll > rr:
if string[q] == 0:
return [(ll - q, dp[p - rr - 1]), (p - rr, dp[ll - q - 1])]
else:
return [(p - rr, dp[ll - q - 1]), (ll - q, dp[p - rr - 1])]
else:
dp_ans = f(ll, rr)
if string[q] == string[p] == '0':
return [(ll - q + p - rr + dp_ans[0][0], dp_ans[0][1]), (dp_ans[1][0], dp_ans[1][1] + dp[ll - q - 1] + dp[p - rr - 1])]
elif string[q] == string[p] == '1':
return [(dp_ans[0][0], dp_ans[0][1] + dp[ll - q - 1] + dp[p - rr - 1]), (ll - q + p - rr + dp_ans[1][0], dp_ans[1][1])]
elif string[q] == '0':
return [(ll - q + dp_ans[0][0], dp_ans[0][1] + dp[p - rr - 1]), (p - rr + dp_ans[1][0], dp_ans[1][1] + dp[ll - q - 1])]
else:
return [(p - rr + dp_ans[0][0], dp_ans[0][1] + dp[ll - q - 1]), (ll - q + dp_ans[1][0], dp_ans[1][1] + dp[p - rr - 1])]
n = rdi()
string = input()
line = rlist()
dp = [0] * (n + 1)
for i in range(n):
for j in range(0, i + 1):
dp[i] = max(dp[i], dp[i - j - 1] + line[j])
ans = f(0, n - 1)
print(max(dp[ans[0][0] - 1] + ans[0][1], dp[ans[1][0] - 1] + ans[1][1]))
```
No
| 2,500
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
n = int(input())
s = input()
ai = list(map(int,input().split()))
ar = [ai[i] for i in range(n)]
for i in range(1,n):
num = 0
for j in range(1,(i+1) // 2 + 1):
num += ar[j-1] + ar[i-j]
ar[i] = max(num,ar[i])
ar2 = []
num = 1
for i in range(1,n):
if s[i] == s[i-1]:
num += 1
else:
ar2 += [num]
num = 1
ar2 += [num]
n2 = len(ar2)
ar = [0] + ar
ar3 = [[-1] * (n2 + 5) for i in range(n2+5)]
ar4 = [[[-1] * (102) for i in range(102)] for i in range(102)]
num5 = 0
def fun(i, n3, num3):
if i > n3 - 1:
return 0
ans = 0
num = num3
num2 = 0
for j in range(i,n3,2):
num += ar2[j]
if ar3[j+1][n3] == -1:
ar3[j+1][n3] = fun(j+1,n3,0)
ans = max(ans, ar3[j+1][n3] + ar[num] + num2)
for z in range(j+3,n3,2):
if ar3[j+1][z+1] == -1:
ar3[j+1][z+1] = fun(j+1,z+1,0)
if ar4[z+1][n3][num] == -1:
ar4[z+1][n3][num] = fun(z+1,n3,num)
ans = max(ans, ar3[j+1][z+1] + ar4[z+1][n3][num] + num2)
if j < n3 - 1:
num2 += ar[ar2[j+1]]
return ans
print(fun(0, n2, 0))
```
No
| 2,501
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a string s of length n consisting only of digits 0 and 1. Also he has an array a of length n.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets a_x points for erasing substring of length x.
Vasya wants to maximize his total points, so help him with this!
Input
The first line contains one integer n (1 ≤ n ≤ 100) — the length of string s.
The second line contains string s, consisting only of digits 0 and 1.
The third line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of points for erasing the substring of length i.
Output
Print one integer — the maximum total points Vasya can get.
Examples
Input
7
1101001
3 4 9 100 1 2 3
Output
109
Input
5
10101
3 10 15 15 15
Output
23
Note
In the first example the optimal sequence of erasings is: 1101001 → 111001 → 11101 → 1111 → ∅.
In the second example the optimal sequence of erasings is: 10101 → 1001 → 11 → ∅.
Submitted Solution:
```
# I'm ashamed for trying this
import time
import sys
start = time.perf_counter()
n = int(input())
st = input() + '$'
A = [int(x) for x in input().split()]
DP = {}
DP[0] = 0
for s in range(1,n+1):
DP[s] = max(DP[i]+A[s-i-1] for i in range(s))
lc = None
count = 0
L = []
for c in st:
if c != lc:
if lc:
L.append(count)
count = 0
count += 1
lc = c
best = 0
def f(state,score=0):
global best
ones = sum(state[::2])
zeros = sum(state[1::2])
if score + DP[ones] + DP[zeros] <= best:
if time.perf_counter() - start > 1.75:
print(best)
sys.exit()
#print('abort')
return
if not state:
if best < score:
best = score
#print(score)
return
for i in range(len(state)):
if i == 0:
nstate = state[1:]
elif i == len(state)-1:
nstate = state[:-1]
else:
nstate = state[:i-1] + [state[i-1]+state[i+1]] + state[i+2:]
f(nstate, score + DP[state[i]])
f(L)
print(best)
```
No
| 2,502
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
from os import path;import sys,time
mod = int(1e9 + 7)
from math import ceil, floor,gcd,log,log2 ,factorial,sqrt
from collections import defaultdict ,Counter , OrderedDict , deque;from itertools import combinations,permutations
from string import ascii_lowercase ,ascii_uppercase
from bisect import *;from functools import reduce;from operator import mul;maxx = float('inf')
I = lambda :int(sys.stdin.buffer.readline())
lint = lambda :[int(x) for x in sys.stdin.buffer.readline().split()]
S = lambda: sys.stdin.readline().strip('\n')
grid = lambda r :[lint() for i in range(r)]
localsys = 0
start_time = time.time()
#left shift --- num*(2**k) --(k - shift)
nCr = lambda n, r: reduce(mul, range(n - r + 1, n + 1), 1) // factorial(r)
def ceill(n,x):
return (n+x -1 )//x
T =0
def solve():
n , m , k = lint()
parent = [i for i in range(n)]
rank =[0]*n
def fs(a):
if parent[a] == a:
return a
parent[a] = fs(parent[a])
return parent[a]
def union(x ,y):
a ,b= fs(x) , fs(y)
if parent[a] != parent[b]:
if rank[a] < rank[b]:
parent[a] = b
elif rank[a] == rank[b]:
rank[a]+=1
parent[b] =a
else:
parent[b] = a
for i in range(n - k +1):
l ,h = i , i+k -1
while l < h :
union(l, h) #every possible pair
l+=1;h-=1
for i in range(n):
fs(i)
print(pow(m, len(set(parent)) , mod))
def run():
if (path.exists('input.txt')):
sys.stdin=open('input.txt','r')
sys.stdout=open('output.txt','w')
run()
T = I() if T else 1
for _ in range(T):
solve()
if localsys:
print("\n\nTime Elased :",time.time() - start_time,"seconds")
```
| 2,670
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
import math
p = [i for i in range(2005)]
def find(x):
if p[x] != x:
p[x] = find(p[x])
return p[x]
def merge(x, y):
r1, r2 = find(x), find(y)
if r1 == r2:
return
p[r1] = r2
def pow(a,b,p):
res = 1
while(b > 0):
if b%2 == 1:
res = (res*a)%p
a = (a*a)%p
b = int(b/2)
return res
n,m,k = list(map(int,input().strip().split()))
mod = 10 ** 9 + 7
for i in range(n):
p[i] = i
for i in range(n - k + 1):
for j in range(k):
if i + j > k + i - j - 1:
break
merge(i + j, k + i - j - 1)
ans = 1
for i in range(n):
if p[i] == i:
ans *= m
ans %= mod
print(ans)
```
| 2,671
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
n,m,k=map(int,input().split())
ans=1
if(k==1 or k>n):
for i in range(n):
ans*=m
ans=ans%1000000007
print(ans)
elif(n==k):
for i in range((n+1)//2):
ans*=m
ans=ans%1000000007
print(ans)
elif(k%2==0):
print(m)
else:
print(m*m)
```
| 2,672
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
import sys
from math import *
from fractions import gcd
readints=lambda:map(int, input().strip('\n').split())
n,m,k=readints()
mod = 10**9 + 7
if k==1 or k>n:
# m^n
res = 1
for _ in range(n):
res *= m
res %= mod
print(res%mod)
elif k==n:
e = (n+1)//2
res = 1
for _ in range(e):
res *= m
res %= mod
print(res%mod)
elif k%2==0:
print(m%mod)
else:
res = m*m
res %= mod
print(res)
```
| 2,673
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
n, m, k = map(int, input().split())
if k == 1 or k > n:
print(pow(m, n, 10**9 + 7))
elif k == n:
print(pow(m, (n+1)//2, 10**9 + 7))
else:
print(pow(m, k%2 + 1, 10**9 + 7))
```
| 2,674
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
n,m,k = map(int,input().split())
mod = 10**9 + 7
if k == 1 or k>n:
print(pow(m,n,mod))
elif k == n:
print(pow(m,(n+1)//2,mod))
elif k%2== 0:
print(m%mod)
else:
print(pow(m,2,mod))
```
| 2,675
|
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] | 0
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
n, m, k = map(int, input().split())
mod = 10 ** 9 + 7
if k == 1 or k > n:
print(pow(m, n, mod))
elif k == n:
print(pow(m, (n + 1) // 2, mod))
else:
print(pow(m, k % 2 + 1, mod))
# Made By Mostafa_Khaled
```
| 2,676
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Tags: combinatorics, dfs and similar, graphs, math
Correct Solution:
```
mod = 1000000007
n,m,k = map(int,input().split())
if k==1 or n<k:
print(pow(m,n,mod))
elif k==n:
print(pow(m,(n+1)//2,mod))
elif k%2!=0:
print((m*m)%mod)
else:
print(m)
```
| 2,677
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
import math
def pow(a,b,p):
res = 1
while(b > 0):
if b%2 == 1:
res = (res*a)%p
a = (a*a)%p
b = int(b/2)
return res
n,m,k = list(map(int,input().strip().split()))
p = 10 ** 9 + 7
if k > n or k == 1:
print(pow(m, n, p))
elif k == n:
print(pow(m, math.ceil(k/2), p))
elif n == 1:
print(m)
elif k % 2 == 0:
print(m)
else:
print(pow(m,2,p))
```
Yes
| 2,678
|
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
import sys,os,io
import math
if(os.path.exists('input.txt')):
sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w")
else:
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
mod = 1000000007
def power(x, y, p) :
res = 1
x = x % p
if (x == 0) :
return 0
while (y > 0) :
if ((y & 1) == 1) :
res = (res * x) % p
y = y >> 1 # y = y/2
x = (x * x) % p
return res
n,m,k = [int(i) for i in input().split()]
parent = [int(i) for i in range(n)]
k-=1
prev = -1
for i in range(n):
j = i
while(j<=i+(k-1)//2):
#print(parent)
x = i+k-(j-i)
if (x>=n):
break
#print(j,x)
J = j
pa = parent[x]
pb = parent[j]
if (pa<pb):
x,j = j,x
pa = parent[x]
pb = parent[j]
#print("pa,pb",pa,pb)
while(parent[pa]!=pa):
pa = parent[pa]
while(parent[pb]!=pb):
pb = parent[pb]
if (pa!=pb):
parent[pa]=pb
j = J+1
cnt = 0
for i in range(n):
if parent[i]==i:
cnt+=1
#print(cnt,m)
print(power(m,cnt,mod))
# for i in range(n):
# if (i%k==0):
# prev = i
# for j in range(i+k,n,k):
# x = j
# #print("fuck",i,x)
# pa = parent[x]
# pb = parent[i]
# while(parent[pa]!=pa):
# pa = parent[pa]
# while(parent[pb]!=pb):
# pb = parent[pb]
# if (pa!=pb):
# parent[pa]=pb
# x = prev+k-i%k
# if (x>=n):
# break
# #print("fuck",i,x)
# pa = parent[x]
# pb = parent[i]
# while(parent[pa]!=pa):
# pa = parent[pa]
# while(parent[pb]!=pb):
# pb = parent[pb]
# if (pa!=pb):
# parent[pa]=pb
# #print(parent)
# #print(len(set(parent)))
```
Yes
| 2,679
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
from os import path;import sys,time
mod = int(1e9 + 7)
from math import ceil, floor,gcd,log,log2 ,factorial,sqrt
from collections import defaultdict ,Counter , OrderedDict , deque;from itertools import combinations,permutations
# from string import ascii_lowercase ,ascii_uppercase
from bisect import *;from functools import reduce;from operator import mul;maxx = float('inf')
I = lambda :int(sys.stdin.buffer.readline())
lint = lambda :[int(x) for x in sys.stdin.buffer.readline().split()]
S = lambda: sys.stdin.readline().strip('\n')
grid = lambda r :[lint() for i in range(r)]
localsys = 0
start_time = time.time()
#left shift --- num*(2**k) --(k - shift)
nCr = lambda n, r: reduce(mul, range(n - r + 1, n + 1), 1) // factorial(r)
def ceill(n,x):
return (n+x -1 )//x
T =0
def solve():
n , m , k = lint()
if k > n or k < 2:
return print((m **n)%mod)
elif n == k :
return print( (m ** ((n+1)//2))%mod)
print(m*m) if k % 2 else print(m)
def run():
if (path.exists('input.txt')):
sys.stdin=open('input.txt','r')
sys.stdout=open('output.txt','w')
run()
T = I() if T else 1
for _ in range(T):
solve()
if localsys:
print("\n\nTime Elased :",time.time() - start_time,"seconds")
```
Yes
| 2,680
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
from sys import stdin,stdout
def find(a):
if par[a]==a:
return a
else:
par[a]=find(par[a])
return par[a]
def union(a,b):
a,b=find(a),find(b)
if a!=b:
if rank[a]>rank[b]:
par[b]=a
elif rank[b]>rank[a]:
par[a]=b
else:
par[a]=b
rank[b]+=1
n,m,k=stdin.readline().strip().split(' ')
n,m,k=int(n),int(m),int(k)
par=[i for i in range(n)]
rank=[0 for i in range(n)]
for i in range(n-k+1):
l=i;u=i+k-1
while l<u:
#print(l,u)
union(l,u)
l+=1;u-=1
for i in range(n):
find(i)
us=len(set(par))
#print(par)
print(pow(m,us,1000000007))
```
Yes
| 2,681
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
import sys
from math import *
from fractions import gcd
readints=lambda:map(int, input().strip('\n').split())
n,m,k=readints()
mod = 10**9 + 7
if k==1:
# m^n
res = 1
for _ in range(n):
res *= m
res %= mod
print(res)
elif k%2==0:
print(m%mod)
else:
res = m*(m-1)
res %= mod
print(res)
```
No
| 2,682
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
n,m,k = map(int,input().split())
mod = 10**9 + 7
if k%2== 0:
if k%2 == 0:
print(m%mod)
else:
print(pow(m,k-1,mod))
```
No
| 2,683
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
n,k,m=map(int,input().split())
ans=1
if(k==1):
for i in range(n):
ans*=m
ans=ans%1000000007
print(ans)
elif(k%2==0):
print(m)
else:
print(m*m)
```
No
| 2,684
|
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!
Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.
Input
The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).
Output
Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).
Examples
Input
1 1 1
Output
1
Input
5 2 4
Output
2
Note
In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").
In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
Submitted Solution:
```
n,m,k=map(eval,input().split())
r = 0
if k>n or k == 1:
r = m**n
elif k == n:
r = m**((n+1)/2)
elif k%2 == 0:
r = m
else:
r = m*m
print (int(r%(10**9+7)))
```
No
| 2,685
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
s = input()
n = len(s)
ans = 0
lb = -1
for i in range(n - 3):
if s[i:i + 4] == 'bear':
left = i-lb
right = n - 3 - i
ans += left * right
lb = i
print(ans)
```
| 2,795
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
s=input()
ans=0
w='bear'
cnt=s.count(w)
for i in range(cnt):
ans+=(s.index(w)+1)*(len(s)-(s.index(w)+3))
s=s[s.index(w)+1:]
print(ans)
```
| 2,796
|
[
0.2420654296875,
0.296630859375,
0.2705078125,
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
#B. Bear and Strings
s = input()
ans = 0
for i in range(len(s)) :
part = s [i : ]
if 'bear' in part :
ans += len(part) - (part.index('bear') + 3 )
print(ans)
```
| 2,797
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
def solution():
s = input()
l = s.split('bear')
if len(l) == 1:
return 0
ans = 0
sums = []
_sum = 0
for i in range(len(l)-1):
_sum += len(l[i])
if i>=1:
_sum +=4
sums.append(_sum)
for i in range(len(l)-1):
if i==0:
ans+=(sums[i]+1)*(len(s)-sums[i]-4+1)
else:
ans+=(sums[i]-sums[i-1])*(len(s)-sums[i]-4+1)
return ans
print(solution())
```
| 2,798
|
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0.477783203125,
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] | 0
|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
z=list(map(str,input()))
x=['b','e','a','r']
a=0
ans=0
for i in range(len(z)-3):
a+=1
if z[i:i+4]==x:
ans+=(a*(len(z)-(i+4))+a)
a=0
print(ans)
```
| 2,799
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
s,ans=input(),0
for i in range(len(s)):
f=s.find("bear",i)
if f!=-1:
ans+=len(s)-f-3
print(ans)
```
| 2,800
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
from math import ceil
s=input();n=len(s);ans=0
last_idx=-1
for i in range(n-3):
if s[i:i+4]=='bear':
if i==0:ans+=(n-1)-(i+3)+1;last_idx=i
else:
k=i-last_idx-1
k1=(n-1)-(i+3)+1
ans+=k*k1
ans+=k1
last_idx=i
print(ans)
```
| 2,801
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
The bear has a string s = s1s2... s|s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = sisi + 1... sj contains at least one string "bear" as a substring.
String x(i, j) contains string "bear", if there is such index k (i ≤ k ≤ j - 3), that sk = b, sk + 1 = e, sk + 2 = a, sk + 3 = r.
Help the bear cope with the given problem.
Input
The first line contains a non-empty string s (1 ≤ |s| ≤ 5000). It is guaranteed that the string only consists of lowercase English letters.
Output
Print a single number — the answer to the problem.
Examples
Input
bearbtear
Output
6
Input
bearaabearc
Output
20
Note
In the first sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9).
In the second sample, the following pairs (i, j) match: (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 10), (2, 11), (3, 10), (3, 11), (4, 10), (4, 11), (5, 10), (5, 11), (6, 10), (6, 11), (7, 10), (7, 11).
Tags: brute force, greedy, implementation, math, strings
Correct Solution:
```
s=input()
if(len(s)<=3):
print(0)
else:
n=len(s)
ans=0
A=0
for i in range(3,n):
if(s[i-3]+s[i-2]+s[i-1]+s[i]=='bear'):
ans+=((i-3)-A+1)*(n-i)
A=i-2
print(ans)
```
| 2,802
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string S of length n with each character being one of the first m lowercase English letters.
Calculate how many different strings T of length n composed from the first m lowercase English letters exist such that the length of LCS (longest common subsequence) between S and T is n - 1.
Recall that LCS of two strings S and T is the longest string C such that C both in S and T as a subsequence.
Input
The first line contains two numbers n and m denoting the length of string S and number of first English lowercase characters forming the character set for strings (1 ≤ n ≤ 100 000, 2 ≤ m ≤ 26).
The second line contains string S.
Output
Print the only line containing the answer.
Examples
Input
3 3
aaa
Output
6
Input
3 3
aab
Output
11
Input
1 2
a
Output
1
Input
10 9
abacadefgh
Output
789
Note
For the first sample, the 6 possible strings T are: aab, aac, aba, aca, baa, caa.
For the second sample, the 11 possible strings T are: aaa, aac, aba, abb, abc, aca, acb, baa, bab, caa, cab.
For the third sample, the only possible string T is b.
Tags: dp, greedy
Correct Solution:
```
n, m = map(int, input().split())
s = input()
p = c = 0
for i in range(1, n):
if s[i] == s[i - 1]:
c += n * (m - 1)
p = i
elif s[i] != s[i - 2]:
p = i - 1
c += i - p
ans = n * n * (m - 1) - c
print(ans)
```
| 2,901
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a string S of length n with each character being one of the first m lowercase English letters.
Calculate how many different strings T of length n composed from the first m lowercase English letters exist such that the length of LCS (longest common subsequence) between S and T is n - 1.
Recall that LCS of two strings S and T is the longest string C such that C both in S and T as a subsequence.
Input
The first line contains two numbers n and m denoting the length of string S and number of first English lowercase characters forming the character set for strings (1 ≤ n ≤ 100 000, 2 ≤ m ≤ 26).
The second line contains string S.
Output
Print the only line containing the answer.
Examples
Input
3 3
aaa
Output
6
Input
3 3
aab
Output
11
Input
1 2
a
Output
1
Input
10 9
abacadefgh
Output
789
Note
For the first sample, the 6 possible strings T are: aab, aac, aba, aca, baa, caa.
For the second sample, the 11 possible strings T are: aaa, aac, aba, abb, abc, aca, acb, baa, bab, caa, cab.
For the third sample, the only possible string T is b.
Tags: dp, greedy
Correct Solution:
```
def main():
n, m = map(int, input().split())
s = input()
k = sum(s[i] != s[i - 1] for i in range(1, n)) + 1
x = i = 0
while i < n - 1:
if s[i] != s[i + 1]:
j = i
while i + 2 < n and s[i] == s[i + 2]:
i += 1
j = (i - j) + 2
x += j * (j - 1) // 2
i += 1
ans = k * (m * n - n) - x
print(ans)
main()
```
| 2,902
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length n with each character being one of the first m lowercase English letters.
Calculate how many different strings T of length n composed from the first m lowercase English letters exist such that the length of LCS (longest common subsequence) between S and T is n - 1.
Recall that LCS of two strings S and T is the longest string C such that C both in S and T as a subsequence.
Input
The first line contains two numbers n and m denoting the length of string S and number of first English lowercase characters forming the character set for strings (1 ≤ n ≤ 100 000, 2 ≤ m ≤ 26).
The second line contains string S.
Output
Print the only line containing the answer.
Examples
Input
3 3
aaa
Output
6
Input
3 3
aab
Output
11
Input
1 2
a
Output
1
Input
10 9
abacadefgh
Output
789
Note
For the first sample, the 6 possible strings T are: aab, aac, aba, aca, baa, caa.
For the second sample, the 11 possible strings T are: aaa, aac, aba, abb, abc, aca, acb, baa, bab, caa, cab.
For the third sample, the only possible string T is b.
Submitted Solution:
```
n,m=map(int,input().split())
s=input()
v=0
c=s[0]
j=1
t=[]
front=0
p='#'
for i in range(1,len(s)):
x=s[i]
if c==x:
j+=1
else:
if p==x and j==1:
v-=1
else:p=c
c=x
t+=[j]
j=1
front+=1
t+=[j]
v+=len(t)*((n-1)*m+(m-1)-(n-1))
v-=front
coll=n-1-front
print(v)
```
No
| 2,903
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
In the beginning of the new year Keivan decided to reverse his name. He doesn't like palindromes, so he changed Naviek to Navick.
He is too selfish, so for a given n he wants to obtain a string of n characters, each of which is either 'a', 'b' or 'c', with no palindromes of length 3 appearing in the string as a substring. For example, the strings "abc" and "abca" suit him, while the string "aba" doesn't. He also want the number of letters 'c' in his string to be as little as possible.
Input
The first line contains single integer n (1 ≤ n ≤ 2·105) — the length of the string.
Output
Print the string that satisfies all the constraints.
If there are multiple answers, print any of them.
Examples
Input
2
Output
aa
Input
3
Output
bba
Note
A palindrome is a sequence of characters which reads the same backward and forward.
Tags: constructive algorithms
Correct Solution:
```
import sys
multistring = (2 * (10 ** 5)) // 4 + 1
s = "aabb" * multistring
n = int(input())
print(s[0:n])
```
| 3,004
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
In the beginning of the new year Keivan decided to reverse his name. He doesn't like palindromes, so he changed Naviek to Navick.
He is too selfish, so for a given n he wants to obtain a string of n characters, each of which is either 'a', 'b' or 'c', with no palindromes of length 3 appearing in the string as a substring. For example, the strings "abc" and "abca" suit him, while the string "aba" doesn't. He also want the number of letters 'c' in his string to be as little as possible.
Input
The first line contains single integer n (1 ≤ n ≤ 2·105) — the length of the string.
Output
Print the string that satisfies all the constraints.
If there are multiple answers, print any of them.
Examples
Input
2
Output
aa
Input
3
Output
bba
Note
A palindrome is a sequence of characters which reads the same backward and forward.
Tags: constructive algorithms
Correct Solution:
```
l = int(input())
s = 'bbaa' *( (l+1)//2)
print (s[:l])
```
| 3,005
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
def main():
n, x, y = map(int, input().split())
s = input()
p = ''
t = []
for c in s:
if c != p:
t.append(c)
p = c
k = 0
for c in t:
if c == '0':
k += 1
if k == 0:
print(0)
elif k == 1:
print (y)
else:
if x < y:
print(x * (k - 1) + y)
else:
print(k * y)
main()
```
| 3,076
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
def main():
n, x, y = map(int, input().split())
s, zo, a = input(), [0, 0], ' '
for b in s:
if a != b:
zo[b == '1'] += 1
a = b
z, o = zo
if s[0] == '1':
o -= 1
if s[-1] == '1':
o -= 1
if o < 0:
o = 0
print(min(z * y, o * x + y))
if __name__ == '__main__':
main()
```
| 3,077
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Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n, x, y = list(map(int, input().split()))
s = ""
len_s = 0
a = input()
for i in range(n):
if len_s == 0:
s += a[i]
len_s += 1
elif a[i] != s[len_s - 1]:
s += a[i]
len_s += 1
sm = 0
if x < y:
if len(s) > 3:
sm += x * ((len(s) - 2)//2)
else:
if len(s) > 3:
sm += y * ((len(s) - 2)//2)
sm += y
if len(s) != 1 and s[0] == '0' and s[len(s) - 1] == '0':
if y < x:
sm += y
else:
sm += x
if s == '1':
sm = 0
print(sm)
```
| 3,078
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n, x, y = list(map(int,input().strip().split(' ')))
s = input()
groups = 0
if s[0] == '0':
groups += 1
for b in range(1,n):
if s[b] == '0' and s[b-1] == '1':
groups += 1
if groups == 0:
print(0)
else:
print((groups - 1) * min(x,y) + y)
```
| 3,079
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n,x,y = map(int,input().split())
s = input()
c=0
for i in range(0,len(s)-1):
if s[i]=='0' and s[i+1]=='1': c+=1
if(s[len(s)-1])=='0': c+=1
if c==0: print(0)
else: print((c-1)*min(x,y)+y)
```
| 3,080
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n, x, y = map(int, input().split())
u = list(map(int, input()))
d0 = 0
k0 = 0
for i in range(n):
if k0 == 1 and u[i] == 1:
d0 += 1
k0 = 0
elif u[i] == 0:
k0 = 1
if k0 == 1:
d0 += 1
if d0 == 0:
p = 0
else:
p = (d0 - 1) * min(x, y) + y
print(p)
```
| 3,081
|
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n , x , y = map(int , input().split())
s = input()
c = 0
for i in range(len(s)-1):
if s[i] == '0' and s[i+1] == '1' :
c += 1
if s[len(s)-1] == '0' :
c += 1
if c == 0 :
print(0)
else :
print((c-1)*min(x , y) + y )
```
| 3,082
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|
Provide tags and a correct Python 3 solution for this coding contest problem.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Tags: brute force, greedy, implementation, math
Correct Solution:
```
n, reverse, change = map(int, input().split())
a = input()
g = list(filter(lambda x: x, a.split('1')))
nGroups = len(g)
print(0 if not nGroups else min((nGroups - 1) * reverse + change, nGroups * change))
```
| 3,083
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
n, x, y = tuple(map(int, input().split()))
str = input()
num = 0
i = 0
while i < len(str):
if str[i] == '0':
j = i + 1
num += 1
while j < len(str) and str[j] == '0':
j += 1
i = j
i += 1
if n*'1' == str:
print(0)
else:
if x <= y:
print((num-1)*x+y)
else:
print(num*y)
```
Yes
| 3,084
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
n,x,y = map(int,input().split())
s = input()
count = 0
if(s[0] == '1'):
tp = -1
else:
tp = 0
count = 1
for i in range(1,n):
if s[i] == '0':
if tp == -1:
tp = 0
count += 1
else:
if tp == 0:
tp = -1
if x >= y:
print(count*y)
else:
if count >= 2:
print((count -1)*x + y)
elif count == 1 :
print(y)
else:
print(0)
```
Yes
| 3,085
|
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
n, x, y = (int (i) for i in input ().split())
s = input ()
on = False
c = 0
for e in s:
if (e == '0' and not on):
on = True
c += 1
elif (e == '1'):
on = False
print (max(0, min((c-1)*x + y, c*y)))
```
Yes
| 3,086
|
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
n, x, y = [int(i) for i in input().split()]
s = [int(i) for i in input()]
lis = []
ind = -1
flag0 = flag1 = 0
for i in range(n):
if s[i] == 0 and flag0 == 0:
ind = i
flag0 = 1
flag1 = 0
else:
if s[i] == 1 and flag1 == 0:
if ind != -1:
lis.append(ind)
flag1 = 1
flag0 = 0
if flag1 == 0 and flag0 == 1:
if ind != -1:
lis.append(ind)
x1 = len(lis)
if x1 == 0:
print(0)
else:
ans = (x1 - 1) * (min(x, y)) + y
print(ans)
```
Yes
| 3,087
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
print(50)
```
No
| 3,088
|
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|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
"""
Code of Ayush Tiwari
Codeforces: servermonk
Codechef: ayush572000
"""
# import sys
# input = sys.stdin.buffer.readline
def solution():
n,x,y=map(int,input().split())
s=input()
flag=0
cnt=0
for i in range(0,n-1):
if s[i]=='0' and s[i+1]=='1':
cnt+=1
if s[i]=='1' and s[i+1]=='0':
cnt+=1
if '0' in s and cnt==0:
cnt=1
# print(cnt)
if cnt==0:
print(0)
else:
if x<y:
print((cnt-1)*x+y)
else:
print((cnt)*y)
solution()
```
No
| 3,089
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
n,x,y=map(int,input().split())
A=list(input())
c=0
cur=A[0]
for i in A:
if i!=cur:
c+=1
cur=i
if x*(c-1)+y<=y*c:
print(x*(c-1)+y)
else:
print(y*c)
```
No
| 3,090
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] | 0
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You've got a string a_1, a_2, ..., a_n, consisting of zeros and ones.
Let's call a sequence of consecutive elements a_i, a_{i + 1}, …, a_j (1≤ i≤ j≤ n) a substring of string a.
You can apply the following operations any number of times:
* Choose some substring of string a (for example, you can choose entire string) and reverse it, paying x coins for it (for example, «0101101» → «0111001»);
* Choose some substring of string a (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying y coins for it (for example, «0101101» → «0110001»).
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.
What is the minimum number of coins you need to spend to get a string consisting only of ones?
Input
The first line of input contains integers n, x and y (1 ≤ n ≤ 300 000, 0 ≤ x, y ≤ 10^9) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).
The second line contains the string a of length n, consisting of zeros and ones.
Output
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print 0, if you do not need to perform any operations.
Examples
Input
5 1 10
01000
Output
11
Input
5 10 1
01000
Output
2
Input
7 2 3
1111111
Output
0
Note
In the first sample, at first you need to reverse substring [1 ... 2], and then you need to invert substring [2 ... 5].
Then the string was changed as follows:
«01000» → «10000» → «11111».
The total cost of operations is 1 + 10 = 11.
In the second sample, at first you need to invert substring [1 ... 1], and then you need to invert substring [3 ... 5].
Then the string was changed as follows:
«01000» → «11000» → «11111».
The overall cost is 1 + 1 = 2.
In the third example, string already consists only of ones, so the answer is 0.
Submitted Solution:
```
a,b,c=map(int,input().split())
n=list(input())
n=n[::-1]
l=0
w=0
p=min(b,c)
i=0
while n[i]=="0":
i+=1
w=1
if i==a:
break
while i<a:
if n[i]=="0":
w+=1
l+=p
while n[i]=="0":
i+=1
if i==a:
break
else:
if n[i]=="1":
while n[i]=="1":
i+=1
if i==a:
break
#print(l,i)
l+=c
print(l)
```
No
| 3,091
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] | 0
|
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.
Input
The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).
Output
Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.
Examples
Input
2 2 1
Output
1100
Input
3 3 3
Output
101100
Input
5 3 6
Output
01010100
Note
All possible answers for the first example:
* 1100;
* 0011.
All possible answers for the second example:
* 110100;
* 101100;
* 110010;
* 100110;
* 011001;
* 001101;
* 010011;
* 001011.
Tags: constructive algorithms
Correct Solution:
```
def binary_string(a, b, x):
s1 = '01'
s2 = '10'
if x % 2 == 0 and a > b:
return s1 * (x // 2) + '1' * (b - x // 2) + '0' * (a - x // 2)
elif x % 2 == 0 and a <= b:
return s2 * (x // 2) + '0' * (a - x // 2) + '1' * (b - x // 2)
elif x % 2 != 0 and a > b:
return s1 * (x // 2) + '0' * (a - x // 2) + '1' * (b - x // 2)
elif x % 2 != 0 and a <= b:
return s2 * (x // 2) + '1' * (b - x // 2) + '0' * (a - x // 2)
A, B, X = [int(j) for j in input().split()]
print(binary_string(A, B, X))
```
| 3,327
|
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] | 0
|
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.
Input
The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).
Output
Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.
Examples
Input
2 2 1
Output
1100
Input
3 3 3
Output
101100
Input
5 3 6
Output
01010100
Note
All possible answers for the first example:
* 1100;
* 0011.
All possible answers for the second example:
* 110100;
* 101100;
* 110010;
* 100110;
* 011001;
* 001101;
* 010011;
* 001011.
Tags: constructive algorithms
Correct Solution:
```
a,b,x = map(int,input().split(' '))
if b>a:
if x%2!=0:
s = '10'*(x-x//2)
s = '1'*(b-(x//2)-1)+s+'0'*(a-(x//2)-1)
else:
s = '10'*((x-1)-(x-1)//2)
s = s+'0'*(a-(x//2))+'1'*(b-(x//2))
else:
if x%2!=0:
s = '01'*(x-x//2)
s = '0'*(a-(x//2)-1)+s+'1'*(b-(x//2)-1)
else:
s = '01'*((x-1)-(x-1)//2)
s = s+'1'*(b-(x//2))+'0'*(a-(x//2))
print(s)
```
| 3,328
|
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