# Print all the combinations of the parenthesis

Here, we are going to learn the solution to print all the combinations of the parenthesis using the recursion approach?
Submitted by Souvik Saha, on June 28, 2020

## Problem statement

Given N number of parenthesis (pair of opening and closing parenthesis), you have to print the valid combinations of the parenthesis and print the value.

```Input:
First-line contains T Testcases,
T no. of lines along with an integer number.

E.g.
3
4
3
5

Constrains:
1≤ T ≤10
1≤ N ≤ 20

Output:
Print the number of possible valid combinations
of the parenthesis.
```

Example

```T = 3

Input:
4
output:
(((()))), ((()())), ((())()), ((()))(), (()(())), (()()())
(()())(), (())(()), (())()(), ()((())),()(()()), ()(())()
()()(()), ()()()()

Input:
3
Output:
((())), (()()), (())(), ()(()), ()()()

Input:
5
Output:
((((())))), (((()()))), (((())())), (((()))()), (((())))()
((()(()))), ((()()())), ((()())()), ((()()))(), ((())(()))
((())()()), ((())())(), ((()))(()), ((()))()(), (()((())))
(()(()())), (()(())()), (()(()))(), (()()(())), (()()()())
(()()())(), (()())(()), (()())()(), (())((())), (())(()())
(())(())(), (())()(()), (())()()(), ()(((()))), ()((()()))
()((())()), ()((()))(), ()(()(())), ()(()()()), ()(()())()
()(())(()), ()(())()(), ()()((())), ()()(()()), ()()(())()
()()()(()), ()()()()()
```

Explanation with example:

To generate a valid combination with the parenthesis is a try and error process and we will solve this problem with the recursion approach.

To solve this problem, we will follow these steps,

1. We have to initialize a count variable to zero, and an open variable is for open parenthesis, and a close variable is for close parenthesis.
2. Initialize a vector to store the strings.
3. Whenever the open is less than the number then we add an open parenthesis.
4. Whenever the open parenthesis is grater the closing parenthesis then we add closing parenthesis to it.
5. If the value of open parenthesis equals the number then we add the strings into the vector.

## C++ Implementation

```#include <bits/stdc++.h>
using namespace std;

void traverse(int open, int close, int n, int& count, string str, vector<string>& v)
{
if (close == n) {
v.push_back(str);
return;
}
if (open < n) {
traverse(open + 1, close, n, count, str + "(", v);
}
if (close < open) {
traverse(open, close + 1, n, count, str + ")", v);
}
return;
}

void genarate_parenthesis(int num)
{
string str = "";
int open_brace = 0, close_brace = 0, count = 0;
vector<string> v;
traverse(open_brace, close_brace, num, count, str, v);
cout << "Posiible combination : ";
for (int i = 0; i < v.size(); i++) {
cout << v[i] << endl;
}
}

int main()
{
int t;

cout << "TestCase : ";
cin >> t;

while (t--) {
int num;

cout << "Enter the number: ";
cin >> num;

genarate_parenthesis(num);
}

return 0;
}
```

Output

```TestCase : 3
Enter the number: 4
(((())))
((()()))
((())())
((()))()
(()(()))
(()()())
(()())()
(())(())
(())()()
()((()))
()(()())
()(())()
()()(())
()()()()
Enter the number: 3
((()))
(()())
(())()
()(())
()()()
Enter the number: 5
((((()))))
(((()())))
(((())()))
(((()))())
(((())))()
((()(())))
((()()()))
((()())())
((()()))()
((())(()))
((())()())
((())())()
((()))(())
((()))()()
(()((())))
(()(()()))
(()(())())
(()(()))()
(()()(()))
(()()()())
(()()())()
(()())(())
(()())()()
(())((()))
(())(()())
(())(())()
(())()(())
(())()()()
()(((())))
()((()()))
()((())())
()((()))()
()(()(()))
()(()()())
()(()())()
()(())(())
()(())()()
()()((()))
()()(()())
()()(())()
()()()(())
()()()()()
```