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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A string is called 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
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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
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No
output
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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