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

results = []
num = 0

def print_paratheses(left, right):
    global num
    global results

    # When nothing left, print the results.
    if left == 0 and right == 0:
        print results
        return

    # pos is the next postion we should insert parenthesis.
    pos = num - left - right
    if left > 0:
        results[pos] = '('
        print_paratheses(left - 1, right)

    if left < right:
        results[pos] = ')'
        print_paratheses(left, right - 1)

def print_all_permutations(n):
    global num
    global results
    num = n * 2
    results = [None] * num
    print_paratheses(n, n)

Reference: Permutations of Parentheses