Prints all sets of nested parenthesis of order [number] using dynamic programming.

printKParens.py

'''
Prints all sets of nested parenthesis of order [number]

Usage: python printKParens.py number
'''
import sys

def printKParens(s, index, k_remaining):
    if(index == len(s)):
        print ''.join(s)
        return
    if k_remaining:
        s[index] = "("
        printKParens(s, index+1, k_remaining-1)
        if k_remaining < ((len(s)-index)/2.0): # python 2.X has screwy division
            s[index] = ")"
            printKParens(s, index+1, k_remaining)
    else:
        s[index] = ")"
        printKParens(s, index+1, k_remaining)

if __name__ == '__main__':
    try:
        print "Generating all trees of " + sys.argv[1] + " nested parens."
    except IndexError:
        print __doc__
        sys.exit(1)
     
    printKParens([")" for x in range(2*int(sys.argv[1]))], 0, int(sys.argv[1]))