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https://github.com/donnemartin/interactive-coding-challenges
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Add k max profit challenge
This commit is contained in:
Donne Martin
0
recursion_dynamic/max_profit_k/__init__.py
Normal file
0
recursion_dynamic/max_profit_k/__init__.py
Normal file
240
recursion_dynamic/max_profit_k/max_profit_challenge.ipynb
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240
recursion_dynamic/max_profit_k/max_profit_challenge.ipynb
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@@ -0,0 +1,240 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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||||
"source": [
|
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"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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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Challenge Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Given a list of stock prices on each consecutive day, determine the max profits with k transactions.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Is k the number of sell transactions?\n",
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" * Yes\n",
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"* Can we assume the prices input is an array of ints?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* If the prices are all decreasing and there is no opportunity to make a profit, do we just return 0?\n",
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" * Yes\n",
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"* Should the output be the max profit and days to buy and sell?\n",
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" * Yes\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"<pre>\n",
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"* Prices: None or k: None -> None\n",
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"* Prices: [] or k <= 0 -> []\n",
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"* Prices: [0, -1, -2, -3, -4, -5]\n",
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" * (max profit, list of transactions)\n",
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" * (0, [])\n",
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"* Prices: [2, 5, 7, 1, 4, 3, 1, 3] k: 3\n",
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" * (max profit, list of transactions)\n",
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" * (10, [Type.SELL day: 7 price: 3, \n",
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" Type.BUY day: 6 price: 1, \n",
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" Type.SELL day: 4 price: 4, \n",
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" Type.BUY day: 3 price: 1, \n",
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" Type.SELL day: 2 price: 7, \n",
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" Type.BUY day: 0 price: 2])\n",
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"</pre>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"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."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"from enum import Enum # Python 2 users: Run pip install enum34\n",
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"\n",
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"\n",
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"class Type(Enum):\n",
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" SELL = 0\n",
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" BUY = 1\n",
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"\n",
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"\n",
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"class Transaction(object):\n",
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"\n",
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" def __init__(self, type, day, price):\n",
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" self.type = type\n",
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" self.day = day\n",
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" self.price = price\n",
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"\n",
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" def __eq__(self, other):\n",
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" return self.type == other.type and \\\n",
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" self.day == other.day and \\\n",
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" self.price == other.price\n",
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"\n",
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" def __repr__(self):\n",
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" return str(self.type) + ' day: ' + \\\n",
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" str(self.day) + ' price: ' + \\\n",
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" str(self.price)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class StockTrader(object):\n",
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"\n",
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" def find_max_profit(self, prices, k):\n",
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" # TODO: Implement me\n",
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" pass"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"## Unit Test"
|
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# %load test_max_profit.py\n",
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"from nose.tools import assert_equal\n",
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"from nose.tools import assert_raises\n",
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"from nose.tools import assert_true\n",
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"\n",
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"\n",
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"class TestMaxProfit(object):\n",
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"\n",
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" def test_max_profit(self):\n",
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" stock_trader = StockTrader()\n",
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" assert_raises(TypeError, stock_trader.find_max_profit, None, None)\n",
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" assert_equal(stock_trader.find_max_profit(prices=[], k=0), [])\n",
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" prices = [5, 4, 3, 2, 1]\n",
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" k = 3\n",
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" assert_equal(stock_trader.find_max_profit(prices, k), (0, []))\n",
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" prices = [2, 5, 7, 1, 4, 3, 1, 3]\n",
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" profit, transactions = stock_trader.find_max_profit(prices, k)\n",
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" assert_equal(profit, 10)\n",
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" assert_true(Transaction(Type.SELL,\n",
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" day=7,\n",
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" price=3) in transactions)\n",
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" assert_true(Transaction(Type.BUY,\n",
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" day=6,\n",
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" price=1) in transactions)\n",
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" assert_true(Transaction(Type.SELL,\n",
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" day=4,\n",
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" price=4) in transactions)\n",
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" assert_true(Transaction(Type.BUY,\n",
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" day=3,\n",
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" price=1) in transactions)\n",
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" assert_true(Transaction(Type.SELL,\n",
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" day=2,\n",
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" price=7) in transactions)\n",
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" assert_true(Transaction(Type.BUY,\n",
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" day=0,\n",
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" price=2) in transactions)\n",
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" print('Success: test_max_profit')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestMaxProfit()\n",
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" test.test_max_profit()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "markdown",
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||||
"metadata": {},
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"source": [
|
||||
"## Solution Notebook\n",
|
||||
"\n",
|
||||
"Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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346
recursion_dynamic/max_profit_k/max_profit_solution.ipynb
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346
recursion_dynamic/max_profit_k/max_profit_solution.ipynb
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@@ -0,0 +1,346 @@
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||||
{
|
||||
"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",
|
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" Type.BUY day: 3 price: 1, \n",
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" Type.SELL day: 2 price: 7, \n",
|
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" Type.BUY day: 0 price: 2])\n",
|
||||
"</pre>"
|
||||
]
|
||||
},
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||||
{
|
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"cell_type": "markdown",
|
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"We'll use bottom up dynamic programming to build a table.\n",
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"\n",
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"<pre>\n",
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"\n",
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"The rows (i) represent the prices.\n",
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"The columns (j) represent the number of transactions (k).\n",
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"\n",
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"T[i][j] = max(T[i][j - 1],\n",
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" prices[j] - price[m] + T[i - 1][m])\n",
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"\n",
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"m = 0...j-1\n",
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"\n",
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" 0 1 2 3 4 5 6 7\n",
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"--------------------------------------\n",
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"| | 2 | 5 | 7 | 1 | 4 | 3 | 1 | 3 |\n",
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"--------------------------------------\n",
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"| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
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"| 1 | 0 | 3 | 5 | 5 | 5 | 5 | 5 | 5 |\n",
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"| 2 | 0 | 3 | 5 | 5 | 8 | 8 | 8 | 8 |\n",
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"| 3 | 0 | 3 | 5 | 5 | 8 | 8 | 8 | 10 |\n",
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"--------------------------------------\n",
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"\n",
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"Optimization:\n",
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"\n",
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"max_diff = max(max_diff,\n",
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" T[i - 1][j - 1] - prices[j - 1])\n",
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"\n",
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"T[i][j] = max(T[i][j - 1],\n",
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" prices[j] + max_diff)\n",
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"\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n * k)\n",
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"* Space: O(n * k)"
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]
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||||
},
|
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{
|
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"## Code"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
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"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",
|
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"\n",
|
||||
" def __init__(self, type, day, price):\n",
|
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" 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
|
||||
}
|
||||
45
recursion_dynamic/max_profit_k/test_max_profit.py
Normal file
45
recursion_dynamic/max_profit_k/test_max_profit.py
Normal file
@@ -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()
|
||||
Reference in New Issue
Block a user