interactive-coding-challenges/online_judges/prod_three/prod_three_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 highest product of three numbers in a list.\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",
    "* Is the input a list of integers?\n",
    "    * Yes\n",
    "* Can we get negative inputs?\n",
    "    * Yes\n",
    "* Can there be duplicate entries in the input?\n",
    "    * Yes\n",
    "* Will there always be at least three integers?\n",
    "    * No\n",
    "* Can we assume the inputs are valid?\n",
    "    * No, check for None input\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> TypeError\n",
    "* Less than three ints -> ValueError\n",
    "* [5, -2, 3] -> -30\n",
    "* [5, -2, 3, 1, -1, 4] -> 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "### Brute force:\n",
    "\n",
    "Use three loops and multiple each numbers.\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n^3)\n",
    "* Space: O(1)\n",
    "\n",
    "### Sorting:\n",
    "\n",
    "Sort the list, multiply the last three elements.\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n log(n))\n",
    "* Space: O(1)\n",
    "\n",
    "### Greedy:\n",
    "\n",
    "<pre>\n",
    " 0   1  2  3   4  5\n",
    "[5, -2, 3, 1, -1, 4] -> 60\n",
    "\n",
    "max_prod_of_three = -30\n",
    "max_prod_of_two = -10\n",
    "max_num = 5\n",
    "min_prod_of_two = -10\n",
    "min_num = -2\n",
    "\n",
    " 0   1  2  3   4  5\n",
    "[5, -2, 3, 1, -1, 4] -> 60\n",
    "        ^\n",
    "max_prod_of_three = -30\n",
    "max_prod_of_two = 15\n",
    "max_num = 5\n",
    "min_prod_of_two = -10\n",
    "min_num = -2\n",
    "\n",
    " 0   1  2  3   4  5\n",
    "[5, -2, 3, 1, -1, 4] -> 60\n",
    "           ^\n",
    "max_prod_of_three = 15\n",
    "max_prod_of_two = 15\n",
    "max_num = 5\n",
    "min_prod_of_two = -10\n",
    "min_num = -2\n",
    "\n",
    " 0   1  2  3   4  5\n",
    "[5, -2, 3, 1, -1, 4] -> 60\n",
    "               ^\n",
    "max_prod_of_three = 15\n",
    "max_prod_of_two = 15\n",
    "max_num = 5\n",
    "min_prod_of_two = -10\n",
    "min_num = -2\n",
    "\n",
    " 0   1  2  3   4  5\n",
    "[5, -2, 3, 1, -1, 4] -> 60\n",
    "                  ^\n",
    "max_prod_of_three = 60\n",
    "max_prod_of_two = 15\n",
    "max_num = 5\n",
    "min_prod_of_two = -10\n",
    "min_num = -2\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(1)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "source": [
    "class Solution(object):\n",
    "\n",
    "    def max_prod_three_nlogn(self, array):\n",
    "        if array is None:\n",
    "            raise TypeError('array cannot be None')\n",
    "        if len(array) < 3:\n",
    "            raise ValueError('array must have 3 or more ints')\n",
    "        array.sort()\n",
    "        product = 1\n",
    "        for item in array[-3:]:\n",
    "            product *= item\n",
    "        return product\n",
    "\n",
    "    def max_prod_three(self, array):\n",
    "        if array is None:\n",
    "            raise TypeError('array cannot be None')\n",
    "        if len(array) < 3:\n",
    "            raise ValueError('array must have 3 or more ints')\n",
    "        curr_max_prod_three = array[0] * array[1] * array[2]\n",
    "        max_prod_two = array[0] * array[1]\n",
    "        min_prod_two = array[0] * array[1]\n",
    "        max_num = max(array[0], array[1])\n",
    "        min_num = min(array[0], array[1])\n",
    "        for i in range(2, len(array)):\n",
    "            curr_max_prod_three = max(curr_max_prod_three,\n",
    "                                      max_prod_two * array[i],\n",
    "                                      min_prod_two * array[i])\n",
    "            max_prod_two = max(max_prod_two,\n",
    "                               max_num * array[i],\n",
    "                               min_num * array[i])\n",
    "            min_prod_two = min(min_prod_two,\n",
    "                               max_num * array[i],\n",
    "                               min_num * array[i])\n",
    "            max_num = max(max_num, array[i])\n",
    "            min_num = min(min_num, array[i])\n",
    "        return curr_max_prod_three"
   ]
  },
  {
   "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_prod_three.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_prod_three.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestProdThree(object):\n",
    "\n",
    "    def test_prod_three(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.max_prod_three, None)\n",
    "        assert_raises(ValueError, solution.max_prod_three, [1, 2])\n",
    "        assert_equal(solution.max_prod_three([5, -2, 3]), -30)\n",
    "        assert_equal(solution.max_prod_three([5, -2, 3, 1, -1, 4]), 60)\n",
    "        print('Success: test_prod_three')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestProdThree()\n",
    "    test.test_prod_three()\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_prod_three\n"
     ]
    }
   ],
   "source": [
    "%run -i test_prod_three.py"
   ]
  }
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