From f0bca255ee7982f599f6c41743fd96ccfac2c878 Mon Sep 17 00:00:00 2001
From: Donne Martin <donne.martin@gmail.com>
Date: Mon, 27 Mar 2017 05:22:19 -0400
Subject: [PATCH] Add k max profit challenge

---
 recursion_dynamic/max_profit_k/__init__.py    |   0
 .../max_profit_k/max_profit_challenge.ipynb   | 240 ++++++++++++
 .../max_profit_k/max_profit_solution.ipynb    | 346 ++++++++++++++++++
 .../max_profit_k/test_max_profit.py           |  45 +++
 4 files changed, 631 insertions(+)
 create mode 100644 recursion_dynamic/max_profit_k/__init__.py
 create mode 100644 recursion_dynamic/max_profit_k/max_profit_challenge.ipynb
 create mode 100644 recursion_dynamic/max_profit_k/max_profit_solution.ipynb
 create mode 100644 recursion_dynamic/max_profit_k/test_max_profit.py

diff --git a/recursion_dynamic/max_profit_k/__init__.py b/recursion_dynamic/max_profit_k/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/recursion_dynamic/max_profit_k/max_profit_challenge.ipynb b/recursion_dynamic/max_profit_k/max_profit_challenge.ipynb
new file mode 100644
index 0000000..94291e6
--- /dev/null
+++ b/recursion_dynamic/max_profit_k/max_profit_challenge.ipynb
@@ -0,0 +1,240 @@
+{
+ "cells": [
+  {
+   "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": [
+    "# Challenge 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)\n",
+    "* [Solution Notebook](#Solution-Notebook)"
+   ]
+  },
+  {
+   "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",
+    "Refer to the [Solution Notebook]().  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "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": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "class StockTrader(object):\n",
+    "\n",
+    "    def find_max_profit(self, prices, k):\n",
+    "        # TODO: Implement me\n",
+    "        pass"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**The following unit test is expected to fail until you solve the challenge.**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# %load test_max_profit.py\n",
+    "from nose.tools import assert_equal\n",
+    "from nose.tools import assert_raises\n",
+    "from nose.tools import assert_true\n",
+    "\n",
+    "\n",
+    "class TestMaxProfit(object):\n",
+    "\n",
+    "    def test_max_profit(self):\n",
+    "        stock_trader = StockTrader()\n",
+    "        assert_raises(TypeError, stock_trader.find_max_profit, None, None)\n",
+    "        assert_equal(stock_trader.find_max_profit(prices=[], k=0), [])\n",
+    "        prices = [5, 4, 3, 2, 1]\n",
+    "        k = 3\n",
+    "        assert_equal(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",
+    "        assert_equal(profit, 10)\n",
+    "        assert_true(Transaction(Type.SELL,\n",
+    "                                day=7,\n",
+    "                                price=3) in transactions)\n",
+    "        assert_true(Transaction(Type.BUY,\n",
+    "                                day=6,\n",
+    "                                price=1) in transactions)\n",
+    "        assert_true(Transaction(Type.SELL,\n",
+    "                                day=4,\n",
+    "                                price=4) in transactions)\n",
+    "        assert_true(Transaction(Type.BUY,\n",
+    "                                day=3,\n",
+    "                                price=1) in transactions)\n",
+    "        assert_true(Transaction(Type.SELL,\n",
+    "                                day=2,\n",
+    "                                price=7) in transactions)\n",
+    "        assert_true(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": "markdown",
+   "metadata": {},
+   "source": [
+    "## Solution Notebook\n",
+    "\n",
+    "Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/recursion_dynamic/max_profit_k/max_profit_solution.ipynb b/recursion_dynamic/max_profit_k/max_profit_solution.ipynb
new file mode 100644
index 0000000..fe9b866
--- /dev/null
+++ b/recursion_dynamic/max_profit_k/max_profit_solution.ipynb
@@ -0,0 +1,346 @@
+{
+ "cells": [
+  {
+   "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": {
+    "collapsed": false
+   },
+   "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": {
+    "collapsed": false
+   },
+   "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": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Overwriting test_max_profit.py\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%writefile test_max_profit.py\n",
+    "from nose.tools import assert_equal\n",
+    "from nose.tools import assert_raises\n",
+    "from nose.tools import assert_true\n",
+    "\n",
+    "\n",
+    "class TestMaxProfit(object):\n",
+    "\n",
+    "    def test_max_profit(self):\n",
+    "        stock_trader = StockTrader()\n",
+    "        assert_raises(TypeError, stock_trader.find_max_profit, None, None)\n",
+    "        assert_equal(stock_trader.find_max_profit(prices=[], k=0), [])\n",
+    "        prices = [5, 4, 3, 2, 1]\n",
+    "        k = 3\n",
+    "        assert_equal(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",
+    "        assert_equal(profit, 10)\n",
+    "        assert_true(Transaction(Type.SELL,\n",
+    "                                day=7,\n",
+    "                                price=3) in transactions)\n",
+    "        assert_true(Transaction(Type.BUY,\n",
+    "                                day=6,\n",
+    "                                price=1) in transactions)\n",
+    "        assert_true(Transaction(Type.SELL,\n",
+    "                                day=4,\n",
+    "                                price=4) in transactions)\n",
+    "        assert_true(Transaction(Type.BUY,\n",
+    "                                day=3,\n",
+    "                                price=1) in transactions)\n",
+    "        assert_true(Transaction(Type.SELL,\n",
+    "                                day=2,\n",
+    "                                price=7) in transactions)\n",
+    "        assert_true(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": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success: test_max_profit\n"
+     ]
+    }
+   ],
+   "source": [
+    "%run -i test_max_profit.py"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.4.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/recursion_dynamic/max_profit_k/test_max_profit.py b/recursion_dynamic/max_profit_k/test_max_profit.py
new file mode 100644
index 0000000..bd21cc1
--- /dev/null
+++ b/recursion_dynamic/max_profit_k/test_max_profit.py
@@ -0,0 +1,45 @@
+from nose.tools import assert_equal
+from nose.tools import assert_raises
+from nose.tools import assert_true
+
+
+class TestMaxProfit(object):
+
+    def test_max_profit(self):
+        stock_trader = StockTrader()
+        assert_raises(TypeError, stock_trader.find_max_profit, None, None)
+        assert_equal(stock_trader.find_max_profit(prices=[], k=0), [])
+        prices = [5, 4, 3, 2, 1]
+        k = 3
+        assert_equal(stock_trader.find_max_profit(prices, k), (0, []))
+        prices = [2, 5, 7, 1, 4, 3, 1, 3]
+        profit, transactions = stock_trader.find_max_profit(prices, k)
+        assert_equal(profit, 10)
+        assert_true(Transaction(Type.SELL,
+                                day=7,
+                                price=3) in transactions)
+        assert_true(Transaction(Type.BUY,
+                                day=6,
+                                price=1) in transactions)
+        assert_true(Transaction(Type.SELL,
+                                day=4,
+                                price=4) in transactions)
+        assert_true(Transaction(Type.BUY,
+                                day=3,
+                                price=1) in transactions)
+        assert_true(Transaction(Type.SELL,
+                                day=2,
+                                price=7) in transactions)
+        assert_true(Transaction(Type.BUY,
+                                day=0,
+                                price=2) in transactions)
+        print('Success: test_max_profit')
+
+
+def main():
+    test = TestMaxProfit()
+    test.test_max_profit()
+
+
+if __name__ == '__main__':
+    main()
\ No newline at end of file