Finding all combinations of well-formed brackets

Question

This came up while talking to a friend and I thought I\'d ask here since it\'s an interesting problem and would like to see other people\'s solutions.

The task is to

Answer 1

Simple solution in C++:

#include 
#include 

void brackets(string output, int open, int close, int pairs)
{
    if(open == pairs && close == pairs)
            cout << output << endl;
    else
    {
            if(open

Output:

Combination for i = 1
()
Combination for i = 2
(())
()()
Combination for i = 3
((()))
(()())
(())()
()(())
()()()