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C++ program to find n valid bracket sequences
Suppose we have a number n. As we know, a bracket sequence is a string containing only characters "(" and ")". A valid bracket sequence is a bracket sequence which can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. So, if a bracket sequence is like "()()" this is valid because we can put 1's like "(1)+(1)". From number n, we have to find exactly n different possible valid bracket sequences of length 2n.
So, if the input is like n = 4, then the output will be ["()()()()", "(())()()", "((()))()", "(((())))"]
Steps
To solve this, we will follow these steps −
for initialize k := 1, when k <= n, update (increase k by 1), do: for initialize i := 1, when i <= k, update (increase i by 1), do: print "(" for initialize i := 1, when i <= k, update (increase i by 1), do: print ")" for initialize i := k + 1, when i <= n, update (increase i by 1), do: print "()" go to next line
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h> using namespace std; void solve(int n) { for (int k = 1; k <= n; k++) { for (int i = 1; i <= k; i++) cout << "("; for (int i = 1; i <= k; i++) cout << ")"; for (int i = k + 1; i <= n; i++) cout << "()"; cout << endl; } } int main() { int n = 4; solve(n); }
Input
4
Output
()()()() (())()() ((()))() (((())))
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