interactive-coding-challenges/recursion_dynamic/permutations/permutations_solution.ipynb

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   "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)"
   ]
  },
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   "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
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   "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
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_permutations\n"
     ]
    }
   ],
   "source": [
    "%run -i test_permutations.py"
   ]
  }
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