From 9c0035f330dc716959dbe8a29ff5786cd7d4f177 Mon Sep 17 00:00:00 2001
From: Donne Martin <donne.martin@gmail.com>
Date: Mon, 27 Mar 2017 05:21:02 -0400
Subject: [PATCH] Add permutations challenge

---
 recursion_dynamic/permutations/__init__.py    |   0
 .../permutations/permutations_challenge.ipynb | 179 ++++++++++++++
 .../permutations/permutations_solution.ipynb  | 234 ++++++++++++++++++
 .../permutations/test_permutations.py         |  26 ++
 4 files changed, 439 insertions(+)
 create mode 100644 recursion_dynamic/permutations/__init__.py
 create mode 100644 recursion_dynamic/permutations/permutations_challenge.ipynb
 create mode 100644 recursion_dynamic/permutations/permutations_solution.ipynb
 create mode 100644 recursion_dynamic/permutations/test_permutations.py

diff --git a/recursion_dynamic/permutations/__init__.py b/recursion_dynamic/permutations/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/recursion_dynamic/permutations/permutations_challenge.ipynb b/recursion_dynamic/permutations/permutations_challenge.ipynb
new file mode 100644
index 0000000..696ccdb
--- /dev/null
+++ b/recursion_dynamic/permutations/permutations_challenge.ipynb
@@ -0,0 +1,179 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Challenge Notebook"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Find all permutations of an input string.\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",
+    "\n",
+    "* Can the input have duplicates?\n",
+    "    * Yes\n",
+    "* Can the output have duplicates?\n",
+    "    * No\n",
+    "* Is the output a list of strings?\n",
+    "    * Yes\n",
+    "* Do we have to output the results in sorted order?\n",
+    "    * No\n",
+    "* Can we assume the inputs are valid?\n",
+    "    * No\n",
+    "* Can we assume this fits memory?\n",
+    "    * Yes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Cases\n",
+    "\n",
+    "<pre>\n",
+    "* None -> None\n",
+    "* '' -> ''\n",
+    "* 'AABC' -> ['AABC', 'AACB', 'ABAC', 'ABCA',\n",
+    "             'ACAB', 'ACBA', 'BAAC', 'BACA',\n",
+    "             'BCAA', 'CAAB', 'CABA', 'CBAA']\n",
+    "</pre>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm\n",
+    "\n",
+    "Refer to the [Solution Notebook]().  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": false
+   },
+   "outputs": [],
+   "source": [
+    "class Permutations(object):\n",
+    "\n",
+    "    def find_permutations(self, string):\n",
+    "        # TODO: Implement me\n",
+    "        pass"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**The following unit test is expected to fail until you solve the challenge.**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# %load test_permutations.py\n",
+    "from nose.tools import assert_equal\n",
+    "\n",
+    "\n",
+    "class TestPermutations(object):\n",
+    "\n",
+    "    def test_permutations(self):\n",
+    "        permutations = Permutations()\n",
+    "        assert_equal(permutations.find_permutations(None), None)\n",
+    "        assert_equal(permutations.find_permutations(''), '')\n",
+    "        string = 'AABC'\n",
+    "        expected = [\n",
+    "            'AABC', 'AACB', 'ABAC', 'ABCA',\n",
+    "            'ACAB', 'ACBA', 'BAAC', 'BACA',\n",
+    "            'BCAA', 'CAAB', 'CABA', 'CBAA'\n",
+    "        ]\n",
+    "        assert_equal(permutations.find_permutations(string), expected)\n",
+    "        print('Success: test_permutations')\n",
+    "\n",
+    "\n",
+    "def main():\n",
+    "    test = TestPermutations()\n",
+    "    test.test_permutations()\n",
+    "\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    main()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Solution Notebook\n",
+    "\n",
+    "Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/recursion_dynamic/permutations/permutations_solution.ipynb b/recursion_dynamic/permutations/permutations_solution.ipynb
new file mode 100644
index 0000000..4fe81eb
--- /dev/null
+++ b/recursion_dynamic/permutations/permutations_solution.ipynb
@@ -0,0 +1,234 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Solution Notebook"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Find all permutations of an input string.\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",
+    "\n",
+    "* Can the input have duplicates?\n",
+    "    * Yes\n",
+    "* Can the output have duplicates?\n",
+    "    * No\n",
+    "* Is the output a list of strings?\n",
+    "    * Yes\n",
+    "* Do we have to output the results in sorted order?\n",
+    "    * No\n",
+    "* Can we assume the inputs are valid?\n",
+    "    * No\n",
+    "* Can we assume this fits memory?\n",
+    "    * Yes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Cases\n",
+    "\n",
+    "<pre>\n",
+    "* None -> None\n",
+    "* '' -> ''\n",
+    "* 'AABC' -> ['AABC', 'AACB', 'ABAC', 'ABCA',\n",
+    "             'ACAB', 'ACBA', 'BAAC', 'BACA',\n",
+    "             'BCAA', 'CAAB', 'CABA', 'CBAA']\n",
+    "</pre>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm\n",
+    "\n",
+    "* Build a dictionary of {chars: counts} where counts is the number of times each char is found in the input\n",
+    "* Loop through each item in the dictionary\n",
+    "    * If the counts is 0, continue\n",
+    "    * Decrement the current char's count in the dictionary\n",
+    "    * Add the current char to the current results\n",
+    "    * If the current result is the same length as the input, add it to the results\n",
+    "    * Else, recurse\n",
+    "    * Backtrack by:\n",
+    "        * Removing the just added current char from the current results\n",
+    "        * Incrementing the current char's acount in the dictionary\n",
+    "\n",
+    "Complexity:\n",
+    "* Time: O(n!)\n",
+    "* Space: O(n!) since we are storing the results in an array, or O(n) if we are just printing each result"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "from collections import OrderedDict\n",
+    "\n",
+    "\n",
+    "class Permutations(object):\n",
+    "\n",
+    "    def _build_counts_map(self, string):\n",
+    "        counts_map = OrderedDict()\n",
+    "        for char in string:\n",
+    "            if char in counts_map:\n",
+    "                counts_map[char] += 1\n",
+    "            else:\n",
+    "                counts_map[char] = 1\n",
+    "        return counts_map\n",
+    "\n",
+    "    def find_permutations(self, string):\n",
+    "        if string is None or string == '':\n",
+    "            return string\n",
+    "        counts_map = self._build_counts_map(string)\n",
+    "        curr_results = []\n",
+    "        results = []\n",
+    "        self._find_permutations(counts_map, curr_results, results, len(string))\n",
+    "        return results\n",
+    "\n",
+    "    def _find_permutations(self, counts_map, curr_result,\n",
+    "                           results, input_length):\n",
+    "        for char in counts_map:\n",
+    "            if counts_map[char] == 0:\n",
+    "                continue\n",
+    "            curr_result.append(char)\n",
+    "            counts_map[char] -= 1\n",
+    "            if len(curr_result) == input_length:\n",
+    "                results.append(''.join(curr_result))\n",
+    "            else:\n",
+    "                self._find_permutations(counts_map, curr_result,\n",
+    "                                        results, input_length)\n",
+    "            counts_map[char] += 1\n",
+    "            curr_result.pop()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Overwriting test_permutations.py\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%writefile test_permutations.py\n",
+    "from nose.tools import assert_equal\n",
+    "\n",
+    "\n",
+    "class TestPermutations(object):\n",
+    "\n",
+    "    def test_permutations(self):\n",
+    "        permutations = Permutations()\n",
+    "        assert_equal(permutations.find_permutations(None), None)\n",
+    "        assert_equal(permutations.find_permutations(''), '')\n",
+    "        string = 'AABC'\n",
+    "        expected = [\n",
+    "            'AABC', 'AACB', 'ABAC', 'ABCA',\n",
+    "            'ACAB', 'ACBA', 'BAAC', 'BACA',\n",
+    "            'BCAA', 'CAAB', 'CABA', 'CBAA'\n",
+    "        ]\n",
+    "        assert_equal(permutations.find_permutations(string), expected)\n",
+    "        print('Success: test_permutations')\n",
+    "\n",
+    "\n",
+    "def main():\n",
+    "    test = TestPermutations()\n",
+    "    test.test_permutations()\n",
+    "\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    main()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success: test_permutations\n"
+     ]
+    }
+   ],
+   "source": [
+    "%run -i test_permutations.py"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/recursion_dynamic/permutations/test_permutations.py b/recursion_dynamic/permutations/test_permutations.py
new file mode 100644
index 0000000..b319ac5
--- /dev/null
+++ b/recursion_dynamic/permutations/test_permutations.py
@@ -0,0 +1,26 @@
+from nose.tools import assert_equal
+
+
+class TestPermutations(object):
+
+    def test_permutations(self):
+        permutations = Permutations()
+        assert_equal(permutations.find_permutations(None), None)
+        assert_equal(permutations.find_permutations(''), '')
+        string = 'AABC'
+        expected = [
+            'AABC', 'AACB', 'ABAC', 'ABCA',
+            'ACAB', 'ACBA', 'BAAC', 'BACA',
+            'BCAA', 'CAAB', 'CABA', 'CBAA'
+        ]
+        assert_equal(permutations.find_permutations(string), expected)
+        print('Success: test_permutations')
+
+
+def main():
+    test = TestPermutations()
+    test.test_permutations()
+
+
+if __name__ == '__main__':
+    main()
\ No newline at end of file