Added n-pairs parentheses challenge

recursion_dynamic/n_pairs_parentheses/n_pairs_parentheses_solution.ipynb

@@ -0,0 +1,162 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<small><i>This notebook was prepared by [Rishi Rajasekaran](https://github.com/rishihot55). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).</i></small>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Solution 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)"
+   ]
+  },
+  {
+   "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",
+    "* If no_of_left == 0 and no_of right == 0, add pair_string to result\n",
+    "* Else \n",
+    "    * If (no_left > 0), parentheses_util(no_left - 1, no_right, pair_string + '(', result)\n",
+    "    * If (no_right > no_left), parentheses_util(no_left, no_right - 1, pair_string + ')', result)\n",
+    "\n",
+    "Complexity:\n",
+    "* Time: O(4^n/n^(3/2)) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def parentheses_util(no_left, no_right, pair_string, result):\n",
+    "    if no_left == 0 and no_right == 0:\n",
+    "        result.add(pair_string)\n",
+    "    else:\n",
+    "        if no_left > 0:\n",
+    "            parentheses_util(no_left - 1, no_right, pair_string + '(', result)\n",
+    "        if no_right > no_left:\n",
+    "            parentheses_util(no_left, no_right - 1, pair_string + ')', result)\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\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success: test_pair_parentheses\n"
+     ]
+    }
+   ],
+   "source": [
+    "# %load test_n_pairs_parentheses.py\n",
+    "from nose.tools import assert_equal\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",
+    "        assert_equal(solution(3), set(['((()))','(()())', '(())()', '()(())', '()()()']))\n",
+    "        print('Success: test_pair_parentheses')\n",
+    "\n",
+    "def main():\n",
+    "    test = TestPairParentheses()\n",
+    "    test.test_pair_parentheses(pair_parentheses)\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    main()"
+   ]
+  }
+ ],
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+   "language": "python",
+   "name": "python2"
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+    "version": 2
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+   "file_extension": ".py",
+   "mimetype": "text/x-python",
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+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
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