interactive-coding-challenges/recursion_dynamic/longest_inc_subseq/longest_inc_subseq_solution.ipynb

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   "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)."
   ]
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   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Find the longest increasing subsequence.\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",
    "* Are duplicates possible?\n",
    "    * Yes\n",
    "* Can we assume the inputs are integers?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Do we expect the result to be an array of the longest increasing subsequence?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> Exception\n",
    "* [] -> []\n",
    "* [3, 4, -1, 0, 6, 2, 3] -> [-1, 0, 2, 3]"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We'll use bottom up dynamic programming to build a table.\n",
    "\n",
    "<pre>\n",
    "Init a temp array of size len(input) to 1.  \n",
    "We'll use l and r to iterate through the input.\n",
    "Array prev will hold the index of the prior smaller value, used to reconstruct the final sequence.\n",
    "\n",
    "if input[l] < input[r]:\n",
    "    if temp[r] < temp[l] + 1:\n",
    "        temp[r] = temp[l] + 1\n",
    "        prev[r] = l\n",
    "\n",
    "        l  r\n",
    "index:  0  1  2  3  4  5  6\n",
    "---------------------------\n",
    "input:  3  4 -1  0  6  2  3\n",
    "temp:   1  2  1  1  1  1  1\n",
    "prev:   x  x  x  x  x  x  x\n",
    "\n",
    "End result:\n",
    "\n",
    "index:  0  1  2  3  4  5  6\n",
    "---------------------------\n",
    "input:  3  4 -1  0  6  2  3\n",
    "temp:   1  2  1  2  3  3  4\n",
    "prev:   x  0  x  2  1  3  5\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n^2)\n",
    "* Space: O(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Subsequence(object):\n",
    "\n",
    "    def longest_inc_subseq(self, seq):\n",
    "        if seq is None:\n",
    "            raise TypeError('seq cannot be None')\n",
    "        if not seq:\n",
    "            return []\n",
    "        temp = [1] * len(seq)\n",
    "        prev = [None] * len(seq)\n",
    "        for r in range(1, len(seq)):\n",
    "            for l in range(r):\n",
    "                if seq[l] < seq[r]:\n",
    "                    if temp[r] < temp[l] + 1:\n",
    "                        temp[r] = temp[l] + 1\n",
    "                        prev[r] = l\n",
    "        max_val = 0\n",
    "        max_index = -1\n",
    "        results = []\n",
    "        for index, value in enumerate(temp):\n",
    "            if value > max_val:\n",
    "                max_val = value\n",
    "                max_index = index\n",
    "        curr_index = max_index\n",
    "        while curr_index is not None:\n",
    "            results.append(seq[curr_index])\n",
    "            curr_index = prev[curr_index]\n",
    "        return results[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_longest_increasing_subseq.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_longest_increasing_subseq.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestLongestIncreasingSubseq(unittest.TestCase):\n",
    "\n",
    "    def test_longest_increasing_subseq(self):\n",
    "        subseq = Subsequence()\n",
    "        self.assertRaises(TypeError, subseq.longest_inc_subseq, None)\n",
    "        self.assertEqual(subseq.longest_inc_subseq([]), [])\n",
    "        seq = [3, 4, -1, 0, 6, 2, 3]\n",
    "        expected = [-1, 0, 2, 3]\n",
    "        self.assertEqual(subseq.longest_inc_subseq(seq), expected)\n",
    "        print('Success: test_longest_increasing_subseq')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestLongestIncreasingSubseq()\n",
    "    test.test_longest_increasing_subseq()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_longest_increasing_subseq\n"
     ]
    }
   ],
   "source": [
    "%run -i test_longest_increasing_subseq.py"
   ]
  }
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