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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: Given two strings, find the longest common substring.\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 a string as a result?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* str0 or str1 is None -> Exception\n",
    "* str0 or str1 equals 0 -> ''\n",
    "* General case\n",
    "\n",
    "str0 = 'ABCDEFGHIJ'\n",
    "str1 = 'FOOBCDBCDE'\n",
    "\n",
    "result: 'BCDE'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We'll use bottom up dynamic programming to build a table.  \n",
    "\n",
    "<pre>\n",
    "\n",
    "The rows (i) represent str0.\n",
    "The columns (j) represent str1.\n",
    "\n",
    "                       str1\n",
    "  -------------------------------------------------\n",
    "  |   |   | A | B | C | D | E | F | G | H | I | J |\n",
    "  -------------------------------------------------\n",
    "  |   | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
    "  | F | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |\n",
    "  | O | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |\n",
    "s | O | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |\n",
    "t | B | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |\n",
    "r | C | 0 | 0 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |\n",
    "0 | D | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | B | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | C | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | D | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | E | 0 | 0 | 1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 |\n",
    "  -------------------------------------------------\n",
    "\n",
    "if str1[j] != str0[i]:\n",
    "    T[i][j] = max(\n",
    "        T[i][j-1],\n",
    "        T[i-1][j])\n",
    "else:\n",
    "    T[i][j] = T[i-1][j-1] + 1\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(m * n), where m is the length of str0 and n is the length of str1\n",
    "* Space: O(m * n), where m is the length of str0 and n is the length of str1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class StringCompare(object):\n",
    "\n",
    "    def longest_common_substr(self, str0, str1):\n",
    "        if str0 is None or str1 is None:\n",
    "            raise TypeError('str input cannot be None')\n",
    "        # Add one to number of rows and cols for the dp table's\n",
    "        # first row of 0's and first col of 0's\n",
    "        num_rows = len(str0) + 1\n",
    "        num_cols = len(str1) + 1\n",
    "        T = [[None] * num_cols for _ in range(num_rows)]\n",
    "        for i in range(num_rows):\n",
    "            for j in range(num_cols):\n",
    "                if i == 0 or j == 0:\n",
    "                    T[i][j] = 0\n",
    "                elif str0[j-1] != str1[i-1]:\n",
    "                    T[i][j] = max(T[i][j-1],\n",
    "                                  T[i-1][j])\n",
    "                else:\n",
    "                    T[i][j] = T[i-1][j-1] + 1\n",
    "        results = ''\n",
    "        i = num_rows - 1\n",
    "        j = num_cols - 1\n",
    "        # Walk backwards to determine the substring\n",
    "        while T[i][j]:\n",
    "            if T[i][j] == T[i][j-1]:\n",
    "                j -= 1\n",
    "            elif T[i][j] == T[i-1][j]:\n",
    "                i -= 1\n",
    "            elif T[i][j] == T[i-1][j-1] + 1:\n",
    "                results += str1[i-1]\n",
    "                i -= 1\n",
    "                j -= 1\n",
    "            else:\n",
    "                raise Exception('Error constructing table')\n",
    "        # Walking backwards results in a string in reverse order\n",
    "        return results[::-1]                "
   ]
  },
  {
   "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_common_substr.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_longest_common_substr.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestLongestCommonSubstr(object):\n",
    "\n",
    "    def test_longest_common_substr(self):\n",
    "        str_comp = StringCompare()\n",
    "        assert_raises(TypeError, str_comp.longest_common_substr, None, None)\n",
    "        assert_equal(str_comp.longest_common_substr('', ''), '')\n",
    "        str0 = 'ABCDEFGHIJ'\n",
    "        str1 = 'FOOBCDBCDE'\n",
    "        expected = 'BCDE'\n",
    "        assert_equal(str_comp.longest_common_substr(str0, str1), expected)\n",
    "        print('Success: test_longest_common_substr')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestLongestCommonSubstr()\n",
    "    test.test_longest_common_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_common_substr\n"
     ]
    }
   ],
   "source": [
    "%run -i test_longest_common_substr.py"
   ]
  }
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