{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by [Rishi Rajasekaran](https://github.com/rishihot55). Source and license info is available on [Github](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Challenge Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Print all valid combinations of n-pairs of parentheses.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)\n",
    "* [Solution Notebook](#Solution-Notebook)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "* None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* 0 -> []\n",
    "* 1 -> [()]\n",
    "* 2 -> [(()), ()()]\n",
    "* 3 -> [((())), (()()), (())(), ()(()), ()()()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/n_pairs_parentheses/n_pairs_parentheses_solution.ipynb).  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def parentheses_util(no_left, no_right, pair_string, result):\n",
    "    # TODO: implement parentheses pairing here\n",
    "    pass\n",
    "\n",
    "\n",
    "def pair_parentheses(n):\n",
    "    result_set = set()\n",
    "    if n == 0:\n",
    "        return result_set\n",
    "    parentheses_util(n, n, '', result_set)\n",
    "    return result_set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# %load test_n_pairs_parentheses.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestPairParentheses(object):\n",
    "\n",
    "    def test_pair_parentheses(self, solution):\n",
    "        assert_equal(solution(0), set([]))\n",
    "        assert_equal(solution(1), set(['()']))\n",
    "        assert_equal(solution(2), set(['(())', \n",
    "                                       '()()']))\n",
    "        assert_equal(solution(3), set(['((()))', \n",
    "                                       '(()())', \n",
    "                                       '(())()', \n",
    "                                       '()(())', \n",
    "                                       '()()()']))\n",
    "        print('Success: test_pair_parentheses')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestPairParentheses()\n",
    "    test.test_pair_parentheses(pair_parentheses)\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Notebook\n",
    "\n",
    "Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/n_pairs_parentheses/n_pairs_parentheses_solution.ipynb) for a discussion on algorithms and code solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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