interactive-coding-challenges/recursion_dynamic/max_profit_k/max_profit_solution.ipynb

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   "cell_type": "markdown",
   "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 a list of stock prices on each consecutive day, determine the max profits with k transactions.\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 k the number of sell transactions?\n",
    "    * Yes\n",
    "* Can we assume the prices input is an array of ints?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* If the prices are all decreasing and there is no opportunity to make a profit, do we just return 0?\n",
    "    * Yes\n",
    "* Should the output be the max profit and days to buy and sell?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "<pre>\n",
    "* Prices: None or k: None -> None\n",
    "* Prices: [] or k <= 0 -> []\n",
    "* Prices: [0, -1, -2, -3, -4, -5]\n",
    "    * (max profit, list of transactions)\n",
    "    * (0, [])\n",
    "* Prices: [2, 5, 7, 1, 4, 3, 1, 3] k: 3\n",
    "    * (max profit, list of transactions)\n",
    "    * (10, [Type.SELL day: 7 price: 3, \n",
    "            Type.BUY  day: 6 price: 1, \n",
    "            Type.SELL day: 4 price: 4, \n",
    "            Type.BUY  day: 3 price: 1, \n",
    "            Type.SELL day: 2 price: 7, \n",
    "            Type.BUY  day: 0 price: 2])\n",
    "</pre>"
   ]
  },
  {
   "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 the prices.\n",
    "The columns (j) represent the number of transactions (k).\n",
    "\n",
    "T[i][j] = max(T[i][j - 1],\n",
    "              prices[j] - price[m] + T[i - 1][m])\n",
    "\n",
    "m = 0...j-1\n",
    "\n",
    "      0   1   2   3   4   5   6   7\n",
    "--------------------------------------\n",
    "|   | 2 | 5 | 7 | 1 | 4 | 3 | 1 | 3  |\n",
    "--------------------------------------\n",
    "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0  |\n",
    "| 1 | 0 | 3 | 5 | 5 | 5 | 5 | 5 | 5  |\n",
    "| 2 | 0 | 3 | 5 | 5 | 8 | 8 | 8 | 8  |\n",
    "| 3 | 0 | 3 | 5 | 5 | 8 | 8 | 8 | 10 |\n",
    "--------------------------------------\n",
    "\n",
    "Optimization:\n",
    "\n",
    "max_diff = max(max_diff,\n",
    "               T[i - 1][j - 1] - prices[j - 1])\n",
    "\n",
    "T[i][j] = max(T[i][j - 1],\n",
    "              prices[j] + max_diff)\n",
    "\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n * k)\n",
    "* Space: O(n * k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from enum import Enum  # Python 2 users: Run pip install enum34\n",
    "\n",
    "\n",
    "class Type(Enum):\n",
    "    SELL = 0\n",
    "    BUY = 1\n",
    "\n",
    "\n",
    "class Transaction(object):\n",
    "\n",
    "    def __init__(self, type, day, price):\n",
    "        self.type = type\n",
    "        self.day = day\n",
    "        self.price = price\n",
    "\n",
    "    def __eq__(self, other):\n",
    "        return self.type == other.type and \\\n",
    "            self.day == other.day and \\\n",
    "            self.price == other.price\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str(self.type) + ' day: ' + \\\n",
    "            str(self.day) + ' price: ' + \\\n",
    "            str(self.price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "\n",
    "class StockTrader(object):\n",
    "\n",
    "    def find_max_profit(self, prices, k):\n",
    "        if prices is None or k is None:\n",
    "            raise TypeError('prices or k cannot be None')\n",
    "        if not prices or k <= 0:\n",
    "            return []\n",
    "        num_rows = k + 1  # 0th transaction for dp table\n",
    "        num_cols = len(prices)\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",
    "                    continue\n",
    "                max_profit = -sys.maxsize\n",
    "                for m in range(j):\n",
    "                    profit = prices[j] - prices[m] + T[i - 1][m]\n",
    "                    if profit > max_profit:\n",
    "                        max_profit = profit\n",
    "                T[i][j] = max(T[i][j - 1], max_profit)\n",
    "        return self._find_max_profit_transactions(T, prices)\n",
    "\n",
    "    def find_max_profit_optimized(self, prices, k):\n",
    "        if prices is None or k is None:\n",
    "            raise TypeError('prices or k cannot be None')\n",
    "        if not prices or k <= 0:\n",
    "            return []\n",
    "        num_rows = k + 1\n",
    "        num_cols = len(prices)\n",
    "        T = [[None] * num_cols for _ in range(num_rows)]\n",
    "        for i in range(num_rows):\n",
    "            max_diff = prices[0] * -1\n",
    "            for j in range(num_cols):\n",
    "                if i == 0 or j == 0:\n",
    "                    T[i][j] = 0\n",
    "                    continue\n",
    "                max_diff = max(\n",
    "                    max_diff,\n",
    "                    T[i - 1][j - 1] - prices[j - 1])\n",
    "                T[i][j] = max(\n",
    "                    T[i][j - 1],\n",
    "                    prices[j] + max_diff)\n",
    "        return self._find_max_profit_transactions(T, prices)\n",
    "\n",
    "    def _find_max_profit_transactions(self, T, prices):\n",
    "        results = []\n",
    "        i = len(T) - 1\n",
    "        j = len(T[0]) - 1\n",
    "        max_profit = T[i][j]\n",
    "        while i != 0 and j != 0:\n",
    "            if T[i][j] == T[i][j - 1]:\n",
    "                j -= 1\n",
    "            else:\n",
    "                sell_price = prices[j]\n",
    "                results.append(Transaction(Type.SELL, j, sell_price))\n",
    "                profit = T[i][j] - T[i - 1][j - 1]\n",
    "                i -= 1\n",
    "                j -= 1\n",
    "                for m in range(j + 1)[::-1]:\n",
    "                    if sell_price - prices[m] == profit:\n",
    "                        results.append(Transaction(Type.BUY, m, prices[m]))\n",
    "                        break\n",
    "        return (max_profit, results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_max_profit.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_max_profit.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestMaxProfit(unittest.TestCase):\n",
    "\n",
    "    def test_max_profit(self):\n",
    "        stock_trader = StockTrader()\n",
    "        self.assertRaises(TypeError, stock_trader.find_max_profit, None, None)\n",
    "        self.assertEqual(stock_trader.find_max_profit(prices=[], k=0), [])\n",
    "        prices = [5, 4, 3, 2, 1]\n",
    "        k = 3\n",
    "        self.assertEqual(stock_trader.find_max_profit(prices, k), (0, []))\n",
    "        prices = [2, 5, 7, 1, 4, 3, 1, 3]\n",
    "        profit, transactions = stock_trader.find_max_profit(prices, k)\n",
    "        self.assertEqual(profit, 10)\n",
    "        self.assertTrue(Transaction(Type.SELL,\n",
    "                                day=7,\n",
    "                                price=3) in transactions)\n",
    "        self.assertTrue(Transaction(Type.BUY,\n",
    "                                day=6,\n",
    "                                price=1) in transactions)\n",
    "        self.assertTrue(Transaction(Type.SELL,\n",
    "                                day=4,\n",
    "                                price=4) in transactions)\n",
    "        self.assertTrue(Transaction(Type.BUY,\n",
    "                                day=3,\n",
    "                                price=1) in transactions)\n",
    "        self.assertTrue(Transaction(Type.SELL,\n",
    "                                day=2,\n",
    "                                price=7) in transactions)\n",
    "        self.assertTrue(Transaction(Type.BUY,\n",
    "                                day=0,\n",
    "                                price=2) in transactions)\n",
    "        print('Success: test_max_profit')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestMaxProfit()\n",
    "    test.test_max_profit()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_max_profit\n"
     ]
    }
   ],
   "source": [
    "%run -i test_max_profit.py"
   ]
  }
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