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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 the length longest substring with at most k distinct characters.\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 we assume the inputs are valid?\n",
    "    * No\n",
    "* Can we assume the strings are ASCII?\n",
    "    * Yes\n",
    "* Is this case sensitive?\n",
    "    * Yes\n",
    "* Is a substring a contiguous block of chars?\n",
    "    * Yes\n",
    "* Do we expect an int as a result?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> TypeError\n",
    "* '', k = 3 -> 0\n",
    "* 'abcabcdefgghiij', k=3 -> 6\n",
    "* 'abcabcdefgghighij', k=3 -> 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We'll use a `chars_to_index_map` dictionary: char (key) to index (val) map to maintain a sliding window.\n",
    "\n",
    "The index (val) will keep track of the character index in the input string.\n",
    "\n",
    "For each character in the string:\n",
    "\n",
    "* Add the char (key) and index (value) to the map\n",
    "* If the length of our map is greater than k, then we'll need to eliminate one item\n",
    "    * Scan the map to find the lowest index and remove it\n",
    "    * The new lowest index will therefore be incremented by 1\n",
    "* The max length will be the current index minus the lower index + 1\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n*k), where n is the number of chars, k is the length of the map due to the min() call\n",
    "* Space: O(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Solution(object):\n",
    "\n",
    "    def longest_substr(self, string, k):\n",
    "        if not isinstance(string, str):\n",
    "            raise TypeError('string must be of type str')\n",
    "        if not isinstance(k, int):\n",
    "            raise TypeError('k must be of type int')\n",
    "        low_index = 0\n",
    "        max_length = 0\n",
    "        chars_to_index_map = {}\n",
    "        for index, char in enumerate(string):\n",
    "            chars_to_index_map[char] = index\n",
    "            if len(chars_to_index_map) > k:\n",
    "                low_index = min(chars_to_index_map.values())\n",
    "                del chars_to_index_map[string[low_index]]\n",
    "                low_index += 1\n",
    "            max_length = max(max_length, index - low_index + 1)\n",
    "        return max_length"
   ]
  },
  {
   "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_longest_substr.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_longest_substr.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestSolution(object):\n",
    "\n",
    "    def test_longest_substr(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.longest_substr, None)\n",
    "        assert_equal(solution.longest_substr('', k=3), 0)\n",
    "        assert_equal(solution.longest_substr('abcabcdefgghiij', k=3), 6)\n",
    "        assert_equal(solution.longest_substr('abcabcdefgghighij', k=3), 7)\n",
    "        print('Success: test_longest_substr')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestSolution()\n",
    "    test.test_longest_substr()\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_longest_substr\n"
     ]
    }
   ],
   "source": [
    "%run -i test_longest_substr.py"
   ]
  }
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