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   "source": [
    "<small><i>This notebook was prepared by [Donne Martin](http://donnemartin.com). 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: Determine if a string is a permutation of another string\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm: Compare Sorted Strings](#Algorithm:-Compare-Sorted-Strings)\n",
    "* [Code: Compare Sorted Strings](#Code:-Compare-Sorted-Strings)\n",
    "* [Algorithm: Hashmap Lookup](#Algorithm:-Hash-Map-Lookup)\n",
    "* [Code: Hashmap Lookup](#Code:-Hash-Map-Lookup)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Can we assume the string is ASCII?\n",
    "    * Yes\n",
    "    * Note: Unicode strings could require special handling depending on your language\n",
    "* Is whitespace important?\n",
    "    * Yes\n",
    "* Is this case sensitive?  'Nib', 'bin' is not a match?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* One or more empty strings -> False\n",
    "* 'Nib', 'bin' -> False\n",
    "* 'act', 'cat' -> True\n",
    "* 'a ct', 'ca t' -> True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm: Compare Sorted Strings\n",
    "\n",
    "Permutations contain the same strings but in different orders.  This approach could be slow for large strings due to sorting.\n",
    "\n",
    "* Sort both strings\n",
    "* If both sorted strings are equal\n",
    "    * return True\n",
    "* Else\n",
    "    * return False\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n log n) from the sort, in general\n",
    "* Space: O(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code: Compare Sorted Strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def permutations(str1, str2):\n",
    "    return sorted(str1) == sorted(str2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm: Hash Map Lookup\n",
    "\n",
    "We'll keep a hash map (dict) to keep track of characters we encounter.  \n",
    "\n",
    "Steps:\n",
    "* Scan each character\n",
    "* For each character in each string:\n",
    "    * If the character does not exist in a hash map, add the character to a hash map\n",
    "    * Else, increment the character's count\n",
    "* If the hash maps for each string are equal\n",
    "    * Return True\n",
    "* Else\n",
    "    * Return False\n",
    "\n",
    "Notes:\n",
    "* Since the characters are in ASCII, we could potentially use an array of size 128 (or 256 for extended ASCII), where each array index is equivalent to an ASCII value\n",
    "* Instead of using two hash maps, you could use one hash map and increment character values based on the first string and decrement based on the second string\n",
    "* You can short circuit if the lengths of each string are not equal, although len() in Python is generally O(1) unlike other languages like C where getting the length of a string is O(n)\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code: Hash Map Lookup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "\n",
    "\n",
    "def unique_counts(string):\n",
    "    dict_chars = defaultdict(int)\n",
    "    for char in string:\n",
    "        dict_chars[char] += 1\n",
    "    return dict_chars\n",
    "\n",
    "\n",
    "def permutations_alt(str1, str2):\n",
    "    if len(str1) != len(str2):\n",
    "        return False\n",
    "    unique_counts1 = unique_counts(str1)\n",
    "    unique_counts2 = unique_counts(str2)\n",
    "    return unique_counts1 == unique_counts2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_permutation_solution.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_permutation_solution.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestPermutation(object):\n",
    "\n",
    "    def test_permutation(self, func):\n",
    "        assert_equal(func('', 'foo'), False)\n",
    "        assert_equal(func('Nib', 'bin'), False)\n",
    "        assert_equal(func('act', 'cat'), True)\n",
    "        assert_equal(func('a ct', 'ca t'), True)\n",
    "        print('Success: test_permutation')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestPermutation()\n",
    "    test.test_permutation(permutations)\n",
    "    try:\n",
    "        test.test_permutation(permutations_alt)\n",
    "    except NameError:\n",
    "        # Alternate solutions are only defined\n",
    "        # in the solutions file\n",
    "        pass\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_permutation\n",
      "Success: test_permutation\n"
     ]
    }
   ],
   "source": [
    "run -i test_permutation_solution.py"
   ]
  }
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