message stringlengths 2 15.4k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 45 107k | cluster float64 21 21 | __index_level_0__ int64 90 214k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular (shortly, RBS) if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are RBS and ")(" and "(()" are not.
We can see that each opening bracket in RBS is paired with some closing bracket, and, using this fact, we can define nesting depth of the RBS as maximum number of bracket pairs, such that the 2-nd pair lies inside the 1-st one, the 3-rd one — inside the 2-nd one and so on. For example, nesting depth of "" is 0, "()()()" is 1 and "()((())())" is 3.
Now, you are given RBS s of even length n. You should color each bracket of s into one of two colors: red or blue. Bracket sequence r, consisting only of red brackets, should be RBS, and bracket sequence, consisting only of blue brackets b, should be RBS. Any of them can be empty. You are not allowed to reorder characters in s, r or b. No brackets can be left uncolored.
Among all possible variants you should choose one that minimizes maximum of r's and b's nesting depth. If there are multiple solutions you can print any of them.
Input
The first line contains an even integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of RBS s.
The second line contains regular bracket sequence s (|s| = n, s_i ∈ \{"(", ")"\}).
Output
Print single string t of length n consisting of "0"-s and "1"-s. If t_i is equal to 0 then character s_i belongs to RBS r, otherwise s_i belongs to b.
Examples
Input
2
()
Output
11
Input
4
(())
Output
0101
Input
10
((()())())
Output
0110001111
Note
In the first example one of optimal solutions is s = "\color{blue}{()}". r is empty and b = "()". The answer is max(0, 1) = 1.
In the second example it's optimal to make s = "\color{red}{(}\color{blue}{(}\color{red}{)}\color{blue}{)}". r = b = "()" and the answer is 1.
In the third example we can make s = "\color{red}{(}\color{blue}{((}\color{red}{)()}\color{blue}{)())}". r = "()()" and b = "(()())" and the answer is 2.
Submitted Solution:
```
def color(rbs, bin):
opened = 0
for i in range(len(rbs)):
if rbs[i]==')' and opened%2 == 1:
bin[i] = '1'
opened -= 1
elif rbs[i]=='(' and opened%2 == 0:
bin[i] = '1'
opened += 1
elif rbs[i]=='(':
opened += 1
elif rbs[i]==')':
opened -= 1
n = int(input())
bin = ['0']*n
rbs = input()
color(rbs, bin)
print(''.join(bin))
``` | instruction | 0 | 56,451 | 21 | 112,902 |
Yes | output | 1 | 56,451 | 21 | 112,903 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular (shortly, RBS) if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are RBS and ")(" and "(()" are not.
We can see that each opening bracket in RBS is paired with some closing bracket, and, using this fact, we can define nesting depth of the RBS as maximum number of bracket pairs, such that the 2-nd pair lies inside the 1-st one, the 3-rd one — inside the 2-nd one and so on. For example, nesting depth of "" is 0, "()()()" is 1 and "()((())())" is 3.
Now, you are given RBS s of even length n. You should color each bracket of s into one of two colors: red or blue. Bracket sequence r, consisting only of red brackets, should be RBS, and bracket sequence, consisting only of blue brackets b, should be RBS. Any of them can be empty. You are not allowed to reorder characters in s, r or b. No brackets can be left uncolored.
Among all possible variants you should choose one that minimizes maximum of r's and b's nesting depth. If there are multiple solutions you can print any of them.
Input
The first line contains an even integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of RBS s.
The second line contains regular bracket sequence s (|s| = n, s_i ∈ \{"(", ")"\}).
Output
Print single string t of length n consisting of "0"-s and "1"-s. If t_i is equal to 0 then character s_i belongs to RBS r, otherwise s_i belongs to b.
Examples
Input
2
()
Output
11
Input
4
(())
Output
0101
Input
10
((()())())
Output
0110001111
Note
In the first example one of optimal solutions is s = "\color{blue}{()}". r is empty and b = "()". The answer is max(0, 1) = 1.
In the second example it's optimal to make s = "\color{red}{(}\color{blue}{(}\color{red}{)}\color{blue}{)}". r = b = "()" and the answer is 1.
In the third example we can make s = "\color{red}{(}\color{blue}{((}\color{red}{)()}\color{blue}{)())}". r = "()()" and b = "(()())" and the answer is 2.
Submitted Solution:
```
#Bhargey Mehta (Sophomore)
#DA-IICT, Gandhinagar
import sys, math, queue
#sys.stdin = open("input.txt", "r")
MOD = 10**9+7
n = int(input())
s = input()
col = [None for i in range(n)]
s0 = 0
s1 = 0
for i in range(n):
if s[i] == '(':
if s0 == 0:
s0 += 1
col[i] = '0'
elif s1 == 0:
s1 += 1
col[i] = '1'
elif s0 < s1:
s0 += 1
col[i] = '0'
else:
s1 += 1
col[i] = '1'
else:
if s0 != 0:
s0 -= 1
col[i] = '0'
else:
s1 -= 1
col[i] = '1'
print(''.join(col))
``` | instruction | 0 | 56,452 | 21 | 112,904 |
Yes | output | 1 | 56,452 | 21 | 112,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular (shortly, RBS) if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are RBS and ")(" and "(()" are not.
We can see that each opening bracket in RBS is paired with some closing bracket, and, using this fact, we can define nesting depth of the RBS as maximum number of bracket pairs, such that the 2-nd pair lies inside the 1-st one, the 3-rd one — inside the 2-nd one and so on. For example, nesting depth of "" is 0, "()()()" is 1 and "()((())())" is 3.
Now, you are given RBS s of even length n. You should color each bracket of s into one of two colors: red or blue. Bracket sequence r, consisting only of red brackets, should be RBS, and bracket sequence, consisting only of blue brackets b, should be RBS. Any of them can be empty. You are not allowed to reorder characters in s, r or b. No brackets can be left uncolored.
Among all possible variants you should choose one that minimizes maximum of r's and b's nesting depth. If there are multiple solutions you can print any of them.
Input
The first line contains an even integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of RBS s.
The second line contains regular bracket sequence s (|s| = n, s_i ∈ \{"(", ")"\}).
Output
Print single string t of length n consisting of "0"-s and "1"-s. If t_i is equal to 0 then character s_i belongs to RBS r, otherwise s_i belongs to b.
Examples
Input
2
()
Output
11
Input
4
(())
Output
0101
Input
10
((()())())
Output
0110001111
Note
In the first example one of optimal solutions is s = "\color{blue}{()}". r is empty and b = "()". The answer is max(0, 1) = 1.
In the second example it's optimal to make s = "\color{red}{(}\color{blue}{(}\color{red}{)}\color{blue}{)}". r = b = "()" and the answer is 1.
In the third example we can make s = "\color{red}{(}\color{blue}{((}\color{red}{)()}\color{blue}{)())}". r = "()()" and b = "(()())" and the answer is 2.
Submitted Solution:
```
n = int(input().split()[0])
s = list(map(str, input()))
res = ""
blue = 0
red = 0
for el in s:
if el == "(":
if red > blue:
blue += 1
res += "1"
else:
red += 1
res += "0"
elif el == ")":
if red > blue:
red -= 1
res += "0"
else:
blue -= 1
res += "1"
print(res)
``` | instruction | 0 | 56,453 | 21 | 112,906 |
Yes | output | 1 | 56,453 | 21 | 112,907 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular (shortly, RBS) if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are RBS and ")(" and "(()" are not.
We can see that each opening bracket in RBS is paired with some closing bracket, and, using this fact, we can define nesting depth of the RBS as maximum number of bracket pairs, such that the 2-nd pair lies inside the 1-st one, the 3-rd one — inside the 2-nd one and so on. For example, nesting depth of "" is 0, "()()()" is 1 and "()((())())" is 3.
Now, you are given RBS s of even length n. You should color each bracket of s into one of two colors: red or blue. Bracket sequence r, consisting only of red brackets, should be RBS, and bracket sequence, consisting only of blue brackets b, should be RBS. Any of them can be empty. You are not allowed to reorder characters in s, r or b. No brackets can be left uncolored.
Among all possible variants you should choose one that minimizes maximum of r's and b's nesting depth. If there are multiple solutions you can print any of them.
Input
The first line contains an even integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of RBS s.
The second line contains regular bracket sequence s (|s| = n, s_i ∈ \{"(", ")"\}).
Output
Print single string t of length n consisting of "0"-s and "1"-s. If t_i is equal to 0 then character s_i belongs to RBS r, otherwise s_i belongs to b.
Examples
Input
2
()
Output
11
Input
4
(())
Output
0101
Input
10
((()())())
Output
0110001111
Note
In the first example one of optimal solutions is s = "\color{blue}{()}". r is empty and b = "()". The answer is max(0, 1) = 1.
In the second example it's optimal to make s = "\color{red}{(}\color{blue}{(}\color{red}{)}\color{blue}{)}". r = b = "()" and the answer is 1.
In the third example we can make s = "\color{red}{(}\color{blue}{((}\color{red}{)()}\color{blue}{)())}". r = "()()" and b = "(()())" and the answer is 2.
Submitted Solution:
```
n=int(input())
s=input()
c=0
o=0
l=[]
for i in range(n):
if s[i]=='(':
o+=1
else:
c+=1
x=o-c
l.append(x)
ans=[1]
for i in range(n-1):
if l[i]%2:
ans.append(1)
else:
ans.append(0)
print(*ans,sep='')
``` | instruction | 0 | 56,454 | 21 | 112,908 |
No | output | 1 | 56,454 | 21 | 112,909 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular (shortly, RBS) if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are RBS and ")(" and "(()" are not.
We can see that each opening bracket in RBS is paired with some closing bracket, and, using this fact, we can define nesting depth of the RBS as maximum number of bracket pairs, such that the 2-nd pair lies inside the 1-st one, the 3-rd one — inside the 2-nd one and so on. For example, nesting depth of "" is 0, "()()()" is 1 and "()((())())" is 3.
Now, you are given RBS s of even length n. You should color each bracket of s into one of two colors: red or blue. Bracket sequence r, consisting only of red brackets, should be RBS, and bracket sequence, consisting only of blue brackets b, should be RBS. Any of them can be empty. You are not allowed to reorder characters in s, r or b. No brackets can be left uncolored.
Among all possible variants you should choose one that minimizes maximum of r's and b's nesting depth. If there are multiple solutions you can print any of them.
Input
The first line contains an even integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of RBS s.
The second line contains regular bracket sequence s (|s| = n, s_i ∈ \{"(", ")"\}).
Output
Print single string t of length n consisting of "0"-s and "1"-s. If t_i is equal to 0 then character s_i belongs to RBS r, otherwise s_i belongs to b.
Examples
Input
2
()
Output
11
Input
4
(())
Output
0101
Input
10
((()())())
Output
0110001111
Note
In the first example one of optimal solutions is s = "\color{blue}{()}". r is empty and b = "()". The answer is max(0, 1) = 1.
In the second example it's optimal to make s = "\color{red}{(}\color{blue}{(}\color{red}{)}\color{blue}{)}". r = b = "()" and the answer is 1.
In the third example we can make s = "\color{red}{(}\color{blue}{((}\color{red}{)()}\color{blue}{)())}". r = "()()" and b = "(()())" and the answer is 2.
Submitted Solution:
```
n = int(input())
s = input()
r=0
b=0
l = []
for i in s:
if i == '(':
if r>b:
l.append(1)
b+=1
else:
l.append(0)
r+=1
else:
if r<b:
l.append(1)
b-=1
else:
l.append(0)
r-=1
print(*l)
``` | instruction | 0 | 56,455 | 21 | 112,910 |
No | output | 1 | 56,455 | 21 | 112,911 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular (shortly, RBS) if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are RBS and ")(" and "(()" are not.
We can see that each opening bracket in RBS is paired with some closing bracket, and, using this fact, we can define nesting depth of the RBS as maximum number of bracket pairs, such that the 2-nd pair lies inside the 1-st one, the 3-rd one — inside the 2-nd one and so on. For example, nesting depth of "" is 0, "()()()" is 1 and "()((())())" is 3.
Now, you are given RBS s of even length n. You should color each bracket of s into one of two colors: red or blue. Bracket sequence r, consisting only of red brackets, should be RBS, and bracket sequence, consisting only of blue brackets b, should be RBS. Any of them can be empty. You are not allowed to reorder characters in s, r or b. No brackets can be left uncolored.
Among all possible variants you should choose one that minimizes maximum of r's and b's nesting depth. If there are multiple solutions you can print any of them.
Input
The first line contains an even integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of RBS s.
The second line contains regular bracket sequence s (|s| = n, s_i ∈ \{"(", ")"\}).
Output
Print single string t of length n consisting of "0"-s and "1"-s. If t_i is equal to 0 then character s_i belongs to RBS r, otherwise s_i belongs to b.
Examples
Input
2
()
Output
11
Input
4
(())
Output
0101
Input
10
((()())())
Output
0110001111
Note
In the first example one of optimal solutions is s = "\color{blue}{()}". r is empty and b = "()". The answer is max(0, 1) = 1.
In the second example it's optimal to make s = "\color{red}{(}\color{blue}{(}\color{red}{)}\color{blue}{)}". r = b = "()" and the answer is 1.
In the third example we can make s = "\color{red}{(}\color{blue}{((}\color{red}{)()}\color{blue}{)())}". r = "()()" and b = "(()())" and the answer is 2.
Submitted Solution:
```
n = int(input())
s = input()
count = 0
prof = 0
for i in range(n):
if s[i] == "(":
count += 1
prof = max(prof,count)
else:
count -= 1
nred = prof // 2
ans = [1 for i in range(n)]
count = 0
idx = -1
point = 0
while point < nred:
idx += 1
if s[idx] == "(":
count += 1
point = max(point,count)
else:
count -= 1
ans[idx] -= 1
while count != 0:
if s[idx] == ")" and s[idx-1] == ")":
count -= 1
ans[idx] -= 1
elif s[idx] == ")" and ans[idx - i] == 0:
count -= 1
ans[idx] -= 1
idx += 1
print(''.join(map(str, ans)))
``` | instruction | 0 | 56,456 | 21 | 112,912 |
No | output | 1 | 56,456 | 21 | 112,913 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A string is called bracket sequence if it does not contain any characters other than "(" and ")". A bracket sequence is called regular (shortly, RBS) if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, "", "(())" and "()()" are RBS and ")(" and "(()" are not.
We can see that each opening bracket in RBS is paired with some closing bracket, and, using this fact, we can define nesting depth of the RBS as maximum number of bracket pairs, such that the 2-nd pair lies inside the 1-st one, the 3-rd one — inside the 2-nd one and so on. For example, nesting depth of "" is 0, "()()()" is 1 and "()((())())" is 3.
Now, you are given RBS s of even length n. You should color each bracket of s into one of two colors: red or blue. Bracket sequence r, consisting only of red brackets, should be RBS, and bracket sequence, consisting only of blue brackets b, should be RBS. Any of them can be empty. You are not allowed to reorder characters in s, r or b. No brackets can be left uncolored.
Among all possible variants you should choose one that minimizes maximum of r's and b's nesting depth. If there are multiple solutions you can print any of them.
Input
The first line contains an even integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of RBS s.
The second line contains regular bracket sequence s (|s| = n, s_i ∈ \{"(", ")"\}).
Output
Print single string t of length n consisting of "0"-s and "1"-s. If t_i is equal to 0 then character s_i belongs to RBS r, otherwise s_i belongs to b.
Examples
Input
2
()
Output
11
Input
4
(())
Output
0101
Input
10
((()())())
Output
0110001111
Note
In the first example one of optimal solutions is s = "\color{blue}{()}". r is empty and b = "()". The answer is max(0, 1) = 1.
In the second example it's optimal to make s = "\color{red}{(}\color{blue}{(}\color{red}{)}\color{blue}{)}". r = b = "()" and the answer is 1.
In the third example we can make s = "\color{red}{(}\color{blue}{((}\color{red}{)()}\color{blue}{)())}". r = "()()" and b = "(()())" and the answer is 2.
Submitted Solution:
```
def color(rbs, bin):
is_opened = False
for i in range(len(rbs)):
if rbs[i]==')' and is_opened:
bin[i] = '1'
is_opened = False
elif rbs[i]=='(' and not is_opened:
bin[i] = '1'
is_opened = True
n = int(input())
bin = ['0']*n
rbs = input()
color(rbs, bin)
print(''.join(bin))
``` | instruction | 0 | 56,457 | 21 | 112,914 |
No | output | 1 | 56,457 | 21 | 112,915 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,163 | 21 | 116,326 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
s=input()
size = len(s)
i = 0
j = size-1
ans = []
while(i<j):
while(i<size and s[i]==')'):
i+=1
while(j>=0 and s[j]=='('):
j-=1
if(i<size and j>=0 and i<j):
ans.append(i+1)
ans.append(j+1)
i+=1
j-=1
if(len(ans)==0):
print(0)
else:
print(1)
print(len(ans))
ans = sorted(ans)
for x in ans:
print(x,end=' ')
print()
``` | output | 1 | 58,163 | 21 | 116,327 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,164 | 21 | 116,328 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
s = input()
st = set()
left = 0
right = len(s) - 1
while True:
while left < right and s[left] != '(':
left += 1
while left < right and s[right] != ')':
right -= 1
if left >= right:
break
else:
st.add(left)
st.add(right)
left += 1
right -= 1
if len(st) > 0:
print(1)
print(len(st))
for v in sorted(st):
print(v + 1, end=" ")
else:
print(0)
``` | output | 1 | 58,164 | 21 | 116,329 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,165 | 21 | 116,330 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
"""def power(x, y):
res = 1
x=x
while (y > 0):
if ((y & 1) == 1) :
res = (res * x)
y = y >> 1
x = (x * x)
return res"""
"""def fact(n):
if(n==0):
return 1
if(n==1):
return 1
return fact(n-1)+fact(n-2)"""
#import collections
import math
#t=int(input())
#for _ in range(t):
#s=input()
#n,k=map(int,input().split())
#x2,y2=map(int,input().split())
s=list(input().strip())
#m,k=map(int,input().split())
#s=input()
l=[]
i=0
j=len(s)-1
while(i<j):
if(s[i]=="("):
if(s[j]==")"):
l.append(i+1)
l.append(j+1)
i+=1
j-=1
continue
else:
j-=1
else:
i+=1
l.sort()
if(len(l)==0):
print("0")
else:
print("1")
print(len(l))
print(*l)
``` | output | 1 | 58,165 | 21 | 116,331 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,166 | 21 | 116,332 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
s = input()
i = 0
j = len(s)
r = []
while i != j:
ii = 0
jj = 0
while i < len(s) and i != j:
if s[i] != '(':
i += 1
else:
ii = i+1
i += 1
break
while j > 0 and i != j:
if s[j-1] != ')':
j -= 1
else:
jj = j
j -= 1
break
if ii>0 and jj>0:
r.append(ii)
r.append(jj)
if len(r)>0:
print(1)
print(len(r))
print(*sorted(r))
else:
print(0)
``` | output | 1 | 58,166 | 21 | 116,333 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,167 | 21 | 116,334 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
"""
NTC here
"""
import sys
inp = sys.stdin.readline
def input(): return inp().strip()
flush = sys.stdout.flush
# import threading
# sys.setrecursionlimit(10**6)
# threading.stack_size(2**25)
def iin(): return int(input())
def lin(): return list(map(int, input().split()))
# range = xrange
# input = raw_input
def main():
s = list(input())
n = len(s)
c1, c2 = [] , []
for j, i in enumerate(s):
if i=='(':
c1.append(j+1)
else:
c2.append(j+1)
ans = [0,[]]
ch = 1
for i in c1:
ch1 = 0
x = i
ch2 = []
for j in c2:
if j>x:
ch2.append(j)
ch1+=1
# print(ch1, ch2, ans)
x = min(ch, ch1)
if x>ans[0]:
ans[0]=x
ans[1]=c1[:x]+ch2[-x:]
ch+=1
# print(c1, c2)
if ans[0]==0:
print(0)
else:
print(1)
print(len(ans[1]))
print(*sorted(ans[1]))
main()
# threading.Thread(target=main).start()
``` | output | 1 | 58,167 | 21 | 116,335 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,168 | 21 | 116,336 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
s = input()
i = 0
j = len(s) - 1
ans = []
cnt = 0
while i < j:
while i < j and s[i] == ')':
i += 1
while i < j and s[j] == '(':
j -= 1
if s[i] == '(' and s[j] == ')':
cnt += 2
ans.append(i+1)
ans.append(j+1)
i += 1
j -= 1
ans.sort()
if cnt > 0:
print(1)
print(cnt)
for x in ans:
print(x, end=' ')
print()
``` | output | 1 | 58,168 | 21 | 116,337 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,169 | 21 | 116,338 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
from os import path
import sys
# mod = int(1e9 + 7)
# import re # can use multiple splits
# from math import ceil, floor,gcd
from collections import defaultdict , Counter
# from bisect import bisect_left, bisect_right
#popping from the end is less taxing,since you don't have to shift any elements
maxx = float('inf')
if (path.exists('input.txt')):
#------------------Sublime--------------------------------------#
sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
I = lambda :int(sys.stdin.buffer.readline())
tup= lambda : map(int , sys.stdin.buffer.readline().split())
lint = lambda :[int(x) for x in sys.stdin.buffer.readline().split()]
S = lambda: sys.stdin.readline().replace('\n', '').strip()
# def grid(r, c): return [lint() for i in range(r)]
# def debug(*args, c=6): print('\033[3{}m'.format(c), *args, '\033[0m', file=sys.stderr)
stpr = lambda x : sys.stdout.write(f'{x}' + '\n')
star = lambda x: print(' '.join(map(str, x)))
else:
#------------------PYPY FAst I/o--------------------------------#
I = lambda :int(sys.stdin.buffer.readline())
tup= lambda : map(int , sys.stdin.buffer.readline().split())
lint = lambda :[int(x) for x in sys.stdin.buffer.readline().split()]
S = lambda: sys.stdin.readline().replace('\n', '').strip()
# def grid(r, c): return [lint() for i in range(r)]
stpr = lambda x : sys.stdout.write(f'{x}' + '\n')
star = lambda x: print(' '.join(map(str, x)))
s = S()
o , c = [] , []
m1 , m2 = - 1, - 1
c1 ,c2 = 0 , 0
for i in range(len(s)):
if s[i] == '(':
f = 1
if f :
c2 =0
c1+=1
m1 =max(m1 ,c1)
o.append(i+1)
else:
f =0
c.append(i+1)
if f ==0:
c1=0
c2+=1
m2 = max(m2 ,c2)
ans1 =[]
ans2 =[]
while o and c :
a, b = o.pop(0), c.pop()
if a < b:
ans1.append(a)
ans2.append(b)
else:break
a = len(ans1)*2
if a == 0:
print(a)
exit()
print(1 , a , sep='\n')
print(*ans1, *sorted(ans2))
``` | output | 1 | 58,169 | 21 | 116,339 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations. | instruction | 0 | 58,170 | 21 | 116,340 |
Tags: constructive algorithms, greedy, strings, two pointers
Correct Solution:
```
s = input()
solved = False
n = len(s)
i1, i2 = 0, n - 1
c = 0
finished = False
ind = []
while True:
try:
_i1 = s.index("(", i1, i2 + 1)
_i2 = s.rindex(")", i1, i2 + 1)
except ValueError:
break
if _i1 < _i2:
ind.append(_i1 + 1)
ind.append(_i2 + 1)
c += 1
i1 = _i1 + 1
i2 = _i2 - 1
else:
break
if len(ind) == 0:
print(0)
else:
print(1)
print(len(ind))
print(*sorted(ind))
``` | output | 1 | 58,170 | 21 | 116,341 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
s=input()
i=0
l=[]
l2=[]
j=len(s)-1
while i<j :
if s[i]=="(" :
if s[j]==")" :
l.append(i+1)
l2.insert(0,j+1)
i+=1
j-=1
else :
j-=1
else :
i+=1
l+=l2
if not l :
print(0)
else :
print(1)
print(len(l))
for i in l :
print(i,end=" ")
``` | instruction | 0 | 58,171 | 21 | 116,342 |
Yes | output | 1 | 58,171 | 21 | 116,343 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
s=input()
starting=[]
ending=[]
for i in range(len(s)):
if(s[i]=='('):
starting.append(i)
else:
ending.append(i)
start=0
c=0
co=0
end=-1
removed=[]
if(len(ending)==0 or len(starting)==0):
print(0)
else:
while(starting[start]<ending[end]):
removed.append(starting[start])
removed.append(ending[end])
start+=1
end-=1
co+=1
c=1
if(abs(end)>len(ending) or start>len(starting)-1):
break
print(c)
removed.sort()
if(c==0):
pass
else:
print(2*co)
for i in removed:
print(i+1,end=" ")
``` | instruction | 0 | 58,172 | 21 | 116,344 |
Yes | output | 1 | 58,172 | 21 | 116,345 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
s = input()
i = 0
j = len(s)-1
res = []
while i < j:
if s[i] == '(' and s[j] == ')':
res.append(i+1)
res.append(j+1)
i += 1
j -= 1
if s[i] == ')':
i += 1
if s[j] == '(':
j -= 1
res.sort()
if len(res):
print(1)
print(len(res))
print(' '.join([str(x) for x in res]))
else:
print(0)
``` | instruction | 0 | 58,173 | 21 | 116,346 |
Yes | output | 1 | 58,173 | 21 | 116,347 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
stringa = input()
n = len(stringa)
left = [n for i in range(len(stringa))]
j = 0
for i in range(len(stringa)):
if(stringa[i] == '('):
left[j] = i
j += 1
right = [-1 for i in range(len(stringa))]
j = 0
for i in range(len(stringa)-1,-1,-1):
if(stringa[i] == ')'):
right[j] = i
j += 1
ans = -1
for i in range(n):
if(left[i] < right[i]):
ans = i
if(ans == -1):
print(0)
else:
lista = []
print(1)
for i in range(ans+1):
lista.append(left[i]+1)
for i in range(ans,-1,-1):
lista.append(right[i]+1)
print(len(lista))
print(*lista)
``` | instruction | 0 | 58,174 | 21 | 116,348 |
Yes | output | 1 | 58,174 | 21 | 116,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
import sys
input = sys.stdin.readline
def main():
S = input().strip()
ans = []
l = 0
r = len(S) - 1
while True:
while l <= len(S) - 1 and S[l] != "(":
l += 1
if l == len(S):
break
while r >= 0 and S[r] != ")":
r -= 1
if r == 0:
break
if r <= l:
break
else:
ans.append(l + 1)
ans.append(r + 1)
l += 1
r -= 1
if len(ans) == 0:
print(0)
return
if len(ans) == len(S):
ans.pop()
ans.pop()
return
print(1)
print(len(ans))
ans.sort()
print(*ans)
if __name__ == '__main__':
main()
``` | instruction | 0 | 58,175 | 21 | 116,350 |
No | output | 1 | 58,175 | 21 | 116,351 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
s = input()
l = list(s)
res = []
out = []
for i,item in enumerate(l):
if item =='(':
res.append(i+1)
flag = 0
for i in range(len(s)-1,-1,-1):
if l[i] == '(':
if flag:
break
else:
del res[-1]
if l[i] == ')':
if(res and res[-1]-1 < i):
out.append(i+1)
out.append(res[-1])
del res[-1]
flag = 1
if out:
print(1)
print(len(out))
print(*sorted(out),sep=' ')
else:
print(0)
``` | instruction | 0 | 58,176 | 21 | 116,352 |
No | output | 1 | 58,176 | 21 | 116,353 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
s = input()
l,c,b=[],0,len(s)
for i in range(len(s)):
a = s[:b].rfind(')')
if s[i]=='(' and a>-1 and a>i:
c +=1
l.append(i+1)
l.append(a+1)
b=a
print(c*2)
l.sort()
for i in l:
print(i,end=' ')
``` | instruction | 0 | 58,177 | 21 | 116,354 |
No | output | 1 | 58,177 | 21 | 116,355 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
Submitted Solution:
```
x=input();n=len(x)
r=x.count(')')
a=[]
p=0
for i in range(n):
if x[i]=='(':
p+=1
a.append(i+1)
else:r-=1
if p==r!=0:
for t in range(i+1,n):
if x[t]==')':
a.append(t+1)
break
if p>r:exit(print(0))
print(1,'\n',p*2,sep='');print(*a)
``` | instruction | 0 | 58,178 | 21 | 116,356 |
No | output | 1 | 58,178 | 21 | 116,357 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,266 | 21 | 118,532 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
from collections import deque, defaultdict
s = input()
mp = defaultdict(int)
stack = deque([-1])
_max = 0
for i,c in enumerate(s):
if c == '(':
stack.append(i)
else:
last = stack.pop()
if len(stack) == 0:
stack.append(i)
else:
curr = i - stack[-1]
if curr > _max:
_max = curr
mp[curr] += 1
if _max == 0:
print(0, 1)
else:
print(_max, mp[_max])
``` | output | 1 | 59,266 | 21 | 118,533 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,267 | 21 | 118,534 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
RI = lambda : [int(x) for x in input().split()]
rw = lambda : [input().strip()]
s=list(input().strip())
stack=[]
index_stack=-1
stack.append(-1)
index_stack+=1
maxo=0
c=0
for i in range(len(s)):
if(s[i]=='('):
stack.append(i)
index_stack+=1
else:
stack.pop()
index_stack-=1
if(len(stack)!=0):
length_temp=i-stack[index_stack]
if(length_temp>maxo):
maxo=length_temp
c=1
elif(length_temp==maxo):
c+=1
else:
stack.append(i)
index_stack+=1
if(c!=0):
print(maxo,end=" ")
print(c)
else:
print("0 1")
``` | output | 1 | 59,267 | 21 | 118,535 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,268 | 21 | 118,536 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
s = input()
d = [-1] * len(s)
e = [-1] * len(s)
stack = []
for i, c in enumerate(s):
if(c == "("):
stack.append(i)
elif(stack):
f = stack.pop()
d[i] = f
e[i] = f
if(e[f - 1] != -1):
e[i] = e[f - 1]
best = 0
count = 0
for i in range(len(s)):
if(e[i] != -1):
if(best < i - e[i] + 1):
best = i - e[i] + 1
count = 0
if(best == i - e[i] + 1):
count += 1
if(best == 0):
print("0 1")
else:
print(best, count)
``` | output | 1 | 59,268 | 21 | 118,537 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,269 | 21 | 118,538 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
t = input()
a = [0] * (len(t) + 1)
m = n = k = 0
for i in range(len(t)):
j = t[i]
if j == '(':
k += 1
if k > 0:
a[k] = i
else:
k -= 1
if k < 0:
k = 0
a[k] = i + 1
w = 0
elif k == 0:
w = i - a[k] + 1
else:
w = i - a[k]
if w > m:
m = w
n = 1
elif w == m:
n += 1
# print(a[:10])
if m == 0:
n = 1
print(m, n)
``` | output | 1 | 59,269 | 21 | 118,539 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,270 | 21 | 118,540 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
def solve(s):
l=[]
length=ref=0
count=1
pos=-1
for i in range(len(s)):
if s[i]=="(":
l.append(i)
elif l:
l.pop()
ref=i-l[-1] if l else i-pos
if ref>length:
length=ref
count=1
elif ref==length:
count+=1
else:
pos=i
print(length,count)
s=input()
solve(s)
``` | output | 1 | 59,270 | 21 | 118,541 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,271 | 21 | 118,542 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
from collections import *
s=input()
score=0
stack=[]
al=defaultdict(int)
val=0
temp=[]
saver=defaultdict(list)
saver[0].append(0)
for i in range(len(s)):
if(s[i]==')'):
if(score==0):
stack=[]
val=0
saver=defaultdict(list)
saver[0].append(i+1)
else:
stack.pop()
score-=1
al[i-(saver[score][-1])+1]+=1
else:
stack.append('(')
score+=1
saver[score].append(i+1)
temp.append(val)
if(len(al)):
print(max(al),al[max(al)])
else:
print(0,1)
``` | output | 1 | 59,271 | 21 | 118,543 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,272 | 21 | 118,544 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
inp,kol,max_len,pos=input(),1,0,[-1];
for i in range(len(inp)):
if(inp[i]=='('):
pos.append(i);
elif(len(pos)>1):
pos.pop();
x=i-pos[-1];
if(max_len<x): max_len,kol=x,1;
elif(max_len==x): kol+=1;
else:
pos[0]=i;
print(max_len,kol);
#the problem requires you to find the longest real bracket sequence and the number ofsuch other sequences that might exist WITH THE SAME MAXIMUM LENGHT.the lenght of the no of brackes bn any two points is the difference bn the last index and the one before the 1st index.
``` | output | 1 | 59,272 | 21 | 118,545 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1 | instruction | 0 | 59,273 | 21 | 118,546 |
Tags: constructive algorithms, data structures, dp, greedy, sortings, strings
Correct Solution:
```
if __name__ == "__main__":
tmp = str(input())
local_start = None
local_max = 0
how_many = 1
lst = [-1]
for i in range(len(tmp)):
if tmp[i]=="(":
lst.append(i)
elif len(lst)>1:
x = lst.pop()
qq = i -lst[-1]
if qq==local_max:
how_many+=1
elif qq>=local_max:
local_max=qq
how_many=1
else:
lst[0]=i
print(local_max,how_many)
``` | output | 1 | 59,273 | 21 | 118,547 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
from collections import Counter as cr
st=input()
s=[]
ans=[0,0]
for i in st:
if i=='(':
ans.append(0)
s.append(i)
else:
if len(s)!=0:
x=ans.pop()
ans.append(x+2)
s.pop()
x=ans.pop()
y=ans.pop()
ans.append(x+y)
else:
ans.append(0)
m=cr(ans)
c=max(ans)
if c==0:
print("0 1")
else:
print(c,m[c])
# (()())()(())()()())())()((()(()(())()()())((()(())()(()()()()))()(())()(((()())()(()((())()(())(()))
``` | instruction | 0 | 59,274 | 21 | 118,548 |
Yes | output | 1 | 59,274 | 21 | 118,549 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
ins, maxlen, count, stack=input(), 0, 1, [-1]
for i,c in enumerate(ins):
if c=='(':
stack.append(i)
elif len(stack)>1:
stack.pop()
x=i-stack[-1]
if maxlen<x:
maxlen, count = x, 1
elif maxlen==x:
count+=1
else:
stack[0]=i
print(maxlen,count)
``` | instruction | 0 | 59,275 | 21 | 118,550 |
Yes | output | 1 | 59,275 | 21 | 118,551 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
s=input()
stack,c,l,ll=[-1],1,0,0
for i in range(len(s)):
if s[i]=="(":
stack.append(i)
else:
stack.pop()
if stack:
k=stack[-1]
if i-stack[-1]>ll:
ll=i-stack[-1]
c=1
elif i-stack[-1]==ll:
c+=1
else:
stack.append(i)
print(ll,c)
``` | instruction | 0 | 59,276 | 21 | 118,552 |
Yes | output | 1 | 59,276 | 21 | 118,553 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
"""
Codeforces
5C - Longest Regular Bracket Sequence
http://codeforces.com/contest/5/problem/C
Héctor González Belver
../07/2018
"""
import sys
def main():
pattern = sys.stdin.readline().strip()
max_length = 0
substring_counter = 1
##longest substring!! --> stack ==> O(n)
#-->the first element: index before the beginning of the next valid substring
#-->store indexes of previous starting brackets
stack = [-1]
for i, c in enumerate(pattern):
if c == '(':
stack.append(i)
else:
stack.pop()
if stack:
if i - stack[-1] > max_length:
max_length = i - stack[-1]
substring_counter = 1
elif i - stack[-1] == max_length:
substring_counter += 1
else:
stack.append(i)
sys.stdout.write(str(max_length) + ' ' + str(substring_counter) + '\n')
if __name__ == '__main__':
main()
``` | instruction | 0 | 59,277 | 21 | 118,554 |
Yes | output | 1 | 59,277 | 21 | 118,555 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
s = input()
n = len(s)
dp = []
stack = []
for i in range(n):
if s[i]=="(":
if len(stack)==0:
dp.append(1)
stack.append(1)
continue
dp.append(stack[-1]+1)
stack.append(stack[-1]+1)
else:
if len(stack)==0:
continue
dp.append(stack[-1])
stack.pop()
if not stack:
print (n,1)
exit()
maxx = 0
count = 1
d = {}
for i in range(len(dp)):
if dp[i] not in d:
d[dp[i]] = i
else:
diff = i - d[dp[i]] + 1
del d[dp[i]]
if diff>maxx:
maxx = diff
count = 1
elif diff==maxx:
count += 1
# print (*dp)
print (maxx,count)
``` | instruction | 0 | 59,278 | 21 | 118,556 |
No | output | 1 | 59,278 | 21 | 118,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
st = input()
a = 0
b = 0
l = 0
cnt = 0
for i in st:
if i=='(':
cnt+=1
else:
cnt-=1
l+=1
if cnt==0 and l>0:
if l>a:
a=l
b=1
elif l==a:
b+=1
elif cnt<0:
cnt=0
l=0
if not b:
b=1
print(str(a)," "+str(b))
``` | instruction | 0 | 59,279 | 21 | 118,558 |
No | output | 1 | 59,279 | 21 | 118,559 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
s=input()
c=0
m=0
a=[]
j=[]
for i in range(len(s)):
if(s[i] == '('):
j.append(i)
a.append('(')
elif(s[i] == ')' and len(a) > 0):
a.pop()
if(len(a) == 0 and len(j) > 0):
m=max(m,i-j[0]+1)
j=[]
c+=1
if(not(m==0 and c==0)):
print(m,c)
else:
print(0,1)
``` | instruction | 0 | 59,280 | 21 | 118,560 |
No | output | 1 | 59,280 | 21 | 118,561 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is yet another problem dealing with regular bracket sequences.
We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
Input
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.
Output
Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".
Examples
Input
)((())))(()())
Output
6 2
Input
))(
Output
0 1
Submitted Solution:
```
string = input()
stack = ["("]
c = []
res = "("
init = string.find("(")+1
exit = len(string)
contingency = 0
for i in range(init, exit):
if string[i] == "(" and i >= init:
stack.append("(")
res += "("
elif string[i] == ")" and len(stack) != 0:
stack.pop()
res += ")"
contingency += 1
if len(stack) == 0:
if i == exit - 1:
c.append(len(res))
elif string[i + 1] == "(":
pass
else:
c.append(len(res))
res = ""
contingency = 0
if len(c) == 0:
print(contingency) if contingency else print(0, 1)
else:
c.sort(reverse=True)
x = c.count(c[0])
print(c[0], x)
``` | instruction | 0 | 59,281 | 21 | 118,562 |
No | output | 1 | 59,281 | 21 | 118,563 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example. | instruction | 0 | 63,981 | 21 | 127,962 |
Tags: dp, strings
Correct Solution:
```
MOD=10**9+7
n=int(input())
s=[c=='(' for c in input()]
m=len(s)
z=[[0,0]]
for v in s:
a=z[-1][v]
z[-1][v]=len(z)
z.append(z[a][:])
z[m][0]=z[m][1]=m
dp=[[0 for _ in range(m+1)] for _ in range(n+1)]
dp[0][0]=1
for _ in range(2*n):
ndp=[[0 for _ in range(m+1)] for _ in range(n+1)]
for i in range(n+1):
for j in range(m+1):
if dp[i][j]<1:continue
if i>0:ndp[i-1][z[j][0]]=(ndp[i-1][z[j][0]]+dp[i][j])%MOD
if i<n:ndp[i+1][z[j][1]]=(ndp[i+1][z[j][1]]+dp[i][j])%MOD
dp=ndp
print(dp[0][m])
``` | output | 1 | 63,981 | 21 | 127,963 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example. | instruction | 0 | 63,982 | 21 | 127,964 |
Tags: dp, strings
Correct Solution:
```
MOD=10**9+7
n=int(input())
s=[c=='(' for c in input()]
m=len(s)
z=[[0,0]]
for v in s:
a=z[-1][v]
z[-1][v]=len(z)
z.append(z[a][:])
z[m][0]=z[m][1]=m
dp=[[0 for _ in range(m+1)] for _ in range(n+1)]
dp[0][0]=1
for _ in range(2*n):
ndp=[[0 for _ in range(m+1)] for _ in range(n+1)]
for i in range(n+1):
for j in range(m+1):
if i>0:ndp[i-1][z[j][0]]=(ndp[i-1][z[j][0]]+dp[i][j])%MOD
if i<n:ndp[i+1][z[j][1]]=(ndp[i+1][z[j][1]]+dp[i][j])%MOD
dp=ndp
print(dp[0][m])
``` | output | 1 | 63,982 | 21 | 127,965 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example. | instruction | 0 | 63,983 | 21 | 127,966 |
Tags: dp, strings
Correct Solution:
```
M=10**9+7
n=int(input())
s=[c=='(' for c in input()]
m=len(s)
z=[[0,0]]
for v in s:
a=z[-1][v]
z[-1][v]=len(z)
z+=[z[a][:]]
z[m]=[m,m]
dp=[[0]*(m+1) for _ in range(n+1)]
dp[0][0]=1
for _ in range(2*n):
ndp=[[0]*(m+1) for _ in range(n+1)]
for i in range(n+1):
for j in range(m+1):
if i>0:ndp[i-1][z[j][0]]=(ndp[i-1][z[j][0]]+dp[i][j])%M
if i<n:ndp[i+1][z[j][1]]=(ndp[i+1][z[j][1]]+dp[i][j])%M
dp=ndp
print(dp[0][m])
``` | output | 1 | 63,983 | 21 | 127,967 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example. | instruction | 0 | 63,984 | 21 | 127,968 |
Tags: dp, strings
Correct Solution:
```
def add(a,b):
if a+b>=mod:
return (a+b)%mod
return a+b
n=int(input())*2
s=input()
d=[[0,0] for i in range(len(s)+1)]
aux=''
for i in range(len(s)):
if s[i]=='(':
d[i][1]=i+1
x=aux+')'
for j in range(1,i+2):
if x[j::] ==s[0:len(x)-j]:
d[i][0]=len(x[j::])
break
else:
d[i][0]=i+1
x=aux+'('
for j in range(1,i+2):
if x[j::] ==s[0:len(x)-j]:
d[i][1]=len(x[j::])
break
aux+=s[i]
d[len(s)][1]=len(s)
d[len(s)][0]=len(s)
dp=[[[0 for i in range(len(s)+1)] for j in range(n//2+1)] for k in range(n+1)]
dp[0][0][0]=1
mod=10**9+7
for i in range(n):
for j in range(1,(n//2)+1):
for k in range(len(s)+1):
dp[i+1][j-1][d[k][0]]=add(dp[i][j][k],dp[i+1][j-1][d[k][0]])
for j in range(n//2):
for k in range(len(s)+1):
dp[i+1][j+1][d[k][1]]=add(dp[i][j][k],dp[i+1][j+1][d[k][1]])
print(dp[n][0][len(s)]%mod)
``` | output | 1 | 63,984 | 21 | 127,969 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example. | instruction | 0 | 63,985 | 21 | 127,970 |
Tags: dp, strings
Correct Solution:
```
def add(a,b):
if a+b>=mod:
return (a+b)%mod
return a+b
n=int(input())*2
s=input()
d=[[0,0] for i in range(len(s)+1)]
aux=''
for i in range(len(s)):
if s[i]=='(':
d[i][1]=i+1
x=aux+')'
for j in range(1,i+2):
if x[j::] ==s[0:len(x)-j]:
d[i][0]=len(x[j::])
break
else:
d[i][0]=i+1
x=aux+'('
for j in range(1,i+2):
if x[j::] ==s[0:len(x)-j]:
d[i][1]=len(x[j::])
break
aux+=s[i]
d[len(s)][1]=len(s)
d[len(s)][0]=len(s)
dp=[[[0 for i in range(len(s)+1)] for j in range(n//2+1)] for k in range(n+1)]
dp[0][0][0]=1
mod=10**9+7
for i in range(n):
for j in range(1,(n//2)+1):
for k in range(len(s)+1):
dp[i+1][j-1][d[k][0]]=(dp[i][j][k]+dp[i+1][j-1][d[k][0]])%mod
for j in range(n//2):
for k in range(len(s)+1):
dp[i+1][j+1][d[k][1]]=(dp[i][j][k]+dp[i+1][j+1][d[k][1]])%mod
print(dp[n][0][len(s)]%mod)
``` | output | 1 | 63,985 | 21 | 127,971 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example.
Submitted Solution:
```
#
import collections, atexit, math, sys
from functools import cmp_to_key
#key=cmp_to_key(lambda x,y: 1 if x not in y else -1 )
sys.setrecursionlimit(1000000)
def getIntList():
return list(map(int, input().split()))
import bisect
try :
#raise ModuleNotFoundError
import numpy
def dprint(*args, **kwargs):
print(*args, **kwargs, file=sys.stderr)
dprint('debug mode')
except ModuleNotFoundError:
def dprint(*args, **kwargs):
pass
def memo(func):
cache={}
def wrap(*args):
if args not in cache:
cache[args]=func(*args)
return cache[args]
return wrap
@memo
def comb (n,k):
if k==0: return 1
if n==k: return 1
return comb(n-1,k-1) + comb(n-1,k)
inId = 0
outId = 0
if inId>0:
dprint('use input', inId)
sys.stdin = open('input'+ str(inId) + '.txt', 'r') #标准输出重定向至文件
if outId>0:
dprint('use output', outId)
sys.stdout = open('stdout'+ str(outId) + '.txt', 'w') #标准输出重定向至文件
atexit.register(lambda :sys.stdout.close()) #idle 中不会执行 atexit
N, = getIntList()
s = input()
nl = 0
t = 0
for x in s:
if x ==')':
t+=1
else:
t-=1
nl = max(nl,t)
s1 = s[::-1]
nr = 0
t = 0
for x in s1:
if x =='(':
t+=1
else:
t-=1
nr = max(nr,t)
maxdp = 2*N - len(s)
dp = [ [0 for x in range(maxdp+2)] for y in range(maxdp+2) ]
dp[0][0] = 1
base = 1000000007
for i in range(0, maxdp+1) :
for j in range(0,maxdp+1):
dp[i+1][j+1] += dp[i][j]
dp[i+1][j+1] %= base
if j>0:
dp[i+1][j-1] += dp[i][j]
dp[i+1][j-1] %= base
res = 0
for i in range(maxdp+1):
for p in range(maxdp+1):
if p<nl: continue
p1 = p+t
if p1 < nr : continue
if p1>maxdp: continue
dprint(i,p,maxdp-i,p1)
res +=dp[i][p] * dp[maxdp-i][p1]
res %= base
print(res)
``` | instruction | 0 | 63,986 | 21 | 127,972 |
No | output | 1 | 63,986 | 21 | 127,973 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example.
Submitted Solution:
```
# Returns count of minimum reversals
# for making expr balanced. Returns -1
# if
def countMinReversals(expr):
lenn = len(expr)
# length of expression must be even
# to make it balanced by using reversals.
if (lenn % 2) :
return -1
# After this loop, stack contains
# unbalanced part of expression,
# i.e., expression of the form "...."
s = []
for i in range(lenn):
if (expr[i] =='' and len(s)):
if (s[0] == '') :
s.pop(0)
else:
s.insert(0, expr[i])
else:
s.insert(0, expr[i])
# Length of the reduced expression
# red_len = (m+n)
red_len = len(s)
# count opening brackets at the
# end of stack
n = 0
while (len(s)and s[0] == '') :
s.pop(0)
n += 1
# return ceil(m/2) + ceil(n/2) which
# is actually equal to (m+n)/2 + n%2
# when m+n is even.
return (red_len // 2 + n % 2)
# Driver Code
if __name__ == '__main__':
expr = "}}{{"
print(countMinReversals(expr.strip()))
``` | instruction | 0 | 63,987 | 21 | 127,974 |
No | output | 1 | 63,987 | 21 | 127,975 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example.
Submitted Solution:
```
n=int(input())*2
s=input()
t=s.count('(')-s.count(')')
ans=0
mod=1000000007
dp=[[0 for i in range(n+1)] for j in range(n+1)]
dp1=[[0 for i in range(n+1)] for j in range(n+1)]
dp[0][0]=1
for i in range(n-1):
for j in range(n-1):
dp[i+1][j+1]=dp[i][j]+dp[i+1][j+1]
for j in range(1,n):
dp[i+1][j-1]=dp[i][j]+dp[i+1][j-1]
for i in range(n-len(s)+1):
for j in range(n):
if dp[i][j]!=0 and j+t>-1 and j+t<n:
dp1[i+len(s)][j+t]+=dp[i][j]
for i in range(n):
for j in range(n-1):
dp1[i+1][j+1]=dp1[i][j]+dp1[i+1][j+1]
for j in range(1,n):
dp1[i+1][j-1]=dp1[i][j]+dp1[i+1][j-1]
print(dp1[-1][0]%mod)
``` | instruction | 0 | 63,988 | 21 | 127,976 |
No | output | 1 | 63,988 | 21 | 127,977 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a bracket sequence s (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.
Your problem is to calculate the number of regular bracket sequences of length 2n containing the given bracket sequence s as a substring (consecutive sequence of characters) modulo 10^9+7 (1000000007).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 100) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to 2n).
The second line of the input contains one string s (1 ≤ |s| ≤ 200) — the string s that should be a substring in each of the resulting regular bracket sequences (|s| is the length of s).
Output
Print only one integer — the number of regular bracket sequences containing the given bracket sequence s as a substring. Since this number can be huge, print it modulo 10^9+7 (1000000007).
Examples
Input
5
()))()
Output
5
Input
3
(()
Output
4
Input
2
(((
Output
0
Note
All regular bracket sequences satisfying the conditions above for the first example:
* "(((()))())";
* "((()()))()";
* "((()))()()";
* "(()(()))()";
* "()((()))()".
All regular bracket sequences satisfying the conditions above for the second example:
* "((()))";
* "(()())";
* "(())()";
* "()(())".
And there is no regular bracket sequences of length 4 containing "(((" as a substring in the third example.
Submitted Solution:
```
vl = 0
mn = 0
mod = 1000000007
n = int(input())
s = input()
for x in s:
if(x == '('):
vl += 1
else:
vl -=1
mn = min(mn, vl)
dp = [[[-1, -1] for i in range(205)] for j in range(205)]
def calc(i, sm, f):
if(sm < 0):
return 0
if(i == n * 2):
if(sm == 0 and f == 1):
return 1
else:
return 0
if(i >= n * 2):
return 0
if(dp[i][sm][f] != -1):
return dp[i][sm][f]
ans = 0
if(f == 0):
if(sm + mn >= 0):
ans = (ans + calc(i + len(s), sm + vl, 1)) % mod
if(sm >= 1):
ans = (ans + calc(i + 1, sm - 1, f)) % mod
ans = (ans + calc(i + 1, sm + 1, f)) % mod
dp[i][sm][f] = ans
return ans
print(calc(0, 0, 0))
``` | instruction | 0 | 63,989 | 21 | 127,978 |
No | output | 1 | 63,989 | 21 | 127,979 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja has a bracket sequence s1, s2, ..., sn, or, in other words, a string s of length n, consisting of characters "(" and ")".
Sereja needs to answer m queries, each of them is described by two integers li, ri (1 ≤ li ≤ ri ≤ n). The answer to the i-th query is the length of the maximum correct bracket subsequence of sequence sli, sli + 1, ..., sri. Help Sereja answer all queries.
You can find the definitions for a subsequence and a correct bracket sequence in the notes.
Input
The first line contains a sequence of characters s1, s2, ..., sn (1 ≤ n ≤ 106) without any spaces. Each character is either a "(" or a ")". The second line contains integer m (1 ≤ m ≤ 105) — the number of queries. Each of the next m lines contains a pair of integers. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n) — the description of the i-th query.
Output
Print the answer to each question on a single line. Print the answers in the order they go in the input.
Examples
Input
())(())(())(
7
1 1
2 3
1 2
1 12
8 12
5 11
2 10
Output
0
0
2
10
4
6
6
Note
A subsequence of length |x| of string s = s1s2... s|s| (where |s| is the length of string s) is string x = sk1sk2... sk|x| (1 ≤ k1 < k2 < ... < k|x| ≤ |s|).
A correct bracket sequence is a bracket sequence that can be transformed into a correct aryphmetic expression by inserting characters "1" and "+" between the characters of the string. For example, bracket sequences "()()", "(())" are correct (the resulting expressions "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.
For the third query required sequence will be «()».
For the fourth query required sequence will be «()(())(())». | instruction | 0 | 64,328 | 21 | 128,656 |
Tags: data structures, schedules
Correct Solution:
```
import sys
import math
input=sys.stdin.readline
s=input().rstrip()
n=len(s)
q=int(input())
class segTree:
def __init__(self):
self.a=[0]*(2*n)
self.b=[0]*(2*n)
self.c=[0]*(2*n)
def build(self,arr):
for i in range(n):
self.a[i+n]=0
self.b[i+n]=1 if arr[i]=="(" else 0
self.c[i+n]=1 if arr[i]==")" else 0
for i in range(n-1,0,-1):
t=min(self.b[i<<1],self.c[i<<1|1])
self.a[i]=self.a[i<<1]+self.a[i<<1|1]+2*t
self.b[i]=self.b[i<<1]+self.b[i<<1|1]-t
self.c[i]=self.c[i<<1]+self.c[i<<1|1]-t
def query(self,l,r):
left=[]
right=[]
l+=n
r+=n
while l<=r:
if (l&1):
left.append([self.a[l],self.b[l],self.c[l]])
l+=1
if not (r&1):
right.append([self.a[r],self.b[r],self.c[r]])
r-=1
l>>=1
r>>=1
a1=b1=c1=0
for a2,b2,c2 in left+right[::-1]:
t=min(b1,c2)
a1+=a2+2*t
b1+=b2-t
c1+=c2-t
return a1
tr=segTree()
tr.build(s)
for _ in range(q):
l,r=map(int,input().split())
print(tr.query(l-1,r-1))
``` | output | 1 | 64,328 | 21 | 128,657 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja has a bracket sequence s1, s2, ..., sn, or, in other words, a string s of length n, consisting of characters "(" and ")".
Sereja needs to answer m queries, each of them is described by two integers li, ri (1 ≤ li ≤ ri ≤ n). The answer to the i-th query is the length of the maximum correct bracket subsequence of sequence sli, sli + 1, ..., sri. Help Sereja answer all queries.
You can find the definitions for a subsequence and a correct bracket sequence in the notes.
Input
The first line contains a sequence of characters s1, s2, ..., sn (1 ≤ n ≤ 106) without any spaces. Each character is either a "(" or a ")". The second line contains integer m (1 ≤ m ≤ 105) — the number of queries. Each of the next m lines contains a pair of integers. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n) — the description of the i-th query.
Output
Print the answer to each question on a single line. Print the answers in the order they go in the input.
Examples
Input
())(())(())(
7
1 1
2 3
1 2
1 12
8 12
5 11
2 10
Output
0
0
2
10
4
6
6
Note
A subsequence of length |x| of string s = s1s2... s|s| (where |s| is the length of string s) is string x = sk1sk2... sk|x| (1 ≤ k1 < k2 < ... < k|x| ≤ |s|).
A correct bracket sequence is a bracket sequence that can be transformed into a correct aryphmetic expression by inserting characters "1" and "+" between the characters of the string. For example, bracket sequences "()()", "(())" are correct (the resulting expressions "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.
For the third query required sequence will be «()».
For the fourth query required sequence will be «()(())(())». | instruction | 0 | 64,329 | 21 | 128,658 |
Tags: data structures, schedules
Correct Solution:
```
from sys import stdout, stdin, setrecursionlimit
from io import BytesIO, IOBase
from collections import *
from itertools import *
from random import *
from bisect import *
from string import *
from queue import *
from heapq import *
from math import *
from re import *
from os import *
####################################---fast-input-output----#########################################
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = read(self._fd, max(fstat(self._fd).st_size, 8192))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = read(self._fd, max(fstat(self._fd).st_size, 8192))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
stdin, stdout = IOWrapper(stdin), IOWrapper(stdout)
graph, mod, szzz = {}, 10**9 + 7, lambda: sorted(zzz())
def getStr(): return input()
def getInt(): return int(input())
def listStr(): return list(input())
def getStrs(): return input().split()
def isInt(s): return '0' <= s[0] <= '9'
def input(): return stdin.readline().strip()
def zzz(): return [int(i) for i in input().split()]
def output(answer, end='\n'): stdout.write(str(answer) + end)
def lcd(xnum1, xnum2): return (xnum1 * xnum2 // gcd(xnum1, xnum2))
dx = [-1, 1, 0, 0, 1, -1, 1, -1]
dy = [0, 0, 1, -1, 1, -1, -1, 1]
daysInMounth = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
#################################################---Some Rule For Me To Follow---#################################
"""
--instants of Reading problem continuously try to understand them.
--If you Know some-one , Then you probably don't know him !
--Try & again try, maybe you're just one statement away!
"""
##################################################---START-CODING---###############################################
s = input().strip()
n = len(s)
class segTree:
def __init__(self):
self.a = [0]*(2*n)
self.b = [0]*(2*n)
self.c = [0]*(2*n)
def build(self, arr):
for i in range(n):
self.a[i+n] = 0
self.b[i+n] = 1 if arr[i] == '(' else 0
self.c[i+n] = 1 if arr[i] == ')' else 0
for i in range(n-1,0,-1):
to_match = min(self.b[i << 1],self.c[i << 1 | 1])
self.a[i] = self.a[i << 1] + self.a[i << 1 | 1] + 2*to_match
self.b[i] = self.b[i << 1] + self.b[i << 1 | 1] - to_match
self.c[i] = self.c[i << 1] + self.c[i << 1 | 1] - to_match
def query(self, l, r):
left = []
right = []
l += n
r += n
while l <= r:
if (l & 1):
left.append((self.a[l],self.b[l],self.c[l]))
l += 1
if not (r & 1):
right.append((self.a[r],self.b[r],self.c[r]))
r -= 1
l >>= 1
r >>= 1
a1 = b1 = c1 = 0
for a2, b2, c2 in left + right[::-1]:
to_match = min(b1,c2)
a1 += a2 + 2*to_match
b1 += b2 - to_match
c1 += c2 - to_match
return a1
tree = segTree()
tree.build(s)
for m in range(getInt()):
l, r = zzz()
l -= 1
r -= 1
print(tree.query(l,r))
``` | output | 1 | 64,329 | 21 | 128,659 |
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