Algorithm

C. Bracket Subsequence
time limit per test
2 seconds
memory limit per test
256 megabytes
problem link- https://codeforces.com/contest/1023/problem/C
input
standard input
output
standard output

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.

Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

You are given a regular bracket sequence s� and an integer number k�. Your task is to find a regular bracket sequence of length exactly k� such that it is also a subsequence of s�.

It is guaranteed that such sequence always exists.

Input

The first line contains two integers n� and k� (2≤k≤n≤2⋅1052≤�≤�≤2⋅105, both n� and k� are even) — the length of s� and the length of the sequence you are asked to find.

The second line is a string s� — regular bracket sequence of length n�.

Output

Print a single string — a regular bracket sequence of length exactly k� such that it is also a subsequence of s�.

It is guaranteed that such sequence always exists.

Examples
input
Copy
6 4
()(())
output
Copy
()()
input
Copy
8 8
(()(()))
output
Copy
(()(()))

 



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <bits/stdc++.h>

using namespace std;

int const N = 2e5 + 1;
int n, k;
char s[N], r[N];

int main() {
  scanf("%d %d", &n, &k);
  scanf("%s", s);
  r[k] = '\0';

  int o = k / 2, c = o;
  for(int i = 0, j = 0, cur; i < n; ++i) {
    if(s[i] == '(') {
      if(o > 0)
        r[j++] = '(', ++cur;
      --o;
    } else {
      if(c > 0 && cur > 0)
        r[j++] = ')', --cur;;
      --c;
    }
  }

  printf("%s\n", r);

  return 0;
}
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Input

x
–
+
cmd
6 4
()(())

Output

x
–
+
cmd
()()
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Demonstration

Codeforces Solution-C. Bracket Subsequence-Solution in C, C++, Java, Python,Bracket Subsequence,Codeforces Solution

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