mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
347 lines
10 KiB
Python
347 lines
10 KiB
Python
{
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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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"# 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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"## 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)"
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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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"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"
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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": 1,
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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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"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": 2,
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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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"import sys\n",
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"\n",
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"\n",
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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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" if prices is None or k is None:\n",
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" raise TypeError('prices or k cannot be None')\n",
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" if not prices or k <= 0:\n",
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" return []\n",
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" num_rows = k + 1 # 0th transaction for dp table\n",
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" num_cols = len(prices)\n",
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" T = [[None] * num_cols for _ in range(num_rows)]\n",
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" for i in range(num_rows):\n",
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" for j in range(num_cols):\n",
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" if i == 0 or j == 0:\n",
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" T[i][j] = 0\n",
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" continue\n",
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" max_profit = -sys.maxsize\n",
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" for m in range(j):\n",
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" profit = prices[j] - prices[m] + T[i - 1][m]\n",
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" if profit > max_profit:\n",
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" max_profit = profit\n",
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" T[i][j] = max(T[i][j - 1], max_profit)\n",
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" return self._find_max_profit_transactions(T, prices)\n",
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"\n",
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" def find_max_profit_optimized(self, prices, k):\n",
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" if prices is None or k is None:\n",
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" raise TypeError('prices or k cannot be None')\n",
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" if not prices or k <= 0:\n",
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" return []\n",
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" num_rows = k + 1\n",
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" num_cols = len(prices)\n",
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" T = [[None] * num_cols for _ in range(num_rows)]\n",
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" for i in range(num_rows):\n",
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" max_diff = prices[0] * -1\n",
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" for j in range(num_cols):\n",
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" if i == 0 or j == 0:\n",
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" T[i][j] = 0\n",
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" continue\n",
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" max_diff = max(\n",
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" max_diff,\n",
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" T[i - 1][j - 1] - prices[j - 1])\n",
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" T[i][j] = max(\n",
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" T[i][j - 1],\n",
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" prices[j] + max_diff)\n",
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" return self._find_max_profit_transactions(T, prices)\n",
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"\n",
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" def _find_max_profit_transactions(self, T, prices):\n",
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" results = []\n",
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" i = len(T) - 1\n",
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" j = len(T[0]) - 1\n",
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" max_profit = T[i][j]\n",
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" while i != 0 and j != 0:\n",
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" if T[i][j] == T[i][j - 1]:\n",
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" j -= 1\n",
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" else:\n",
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" sell_price = prices[j]\n",
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" results.append(Transaction(Type.SELL, j, sell_price))\n",
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" profit = T[i][j] - T[i - 1][j - 1]\n",
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" i -= 1\n",
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" j -= 1\n",
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" for m in range(j + 1)[::-1]:\n",
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" if sell_price - prices[m] == profit:\n",
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" results.append(Transaction(Type.BUY, m, prices[m]))\n",
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" break\n",
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" return (max_profit, results)"
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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": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_max_profit.py\n"
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]
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}
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],
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"source": [
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"%%writefile 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": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Success: test_max_profit\n"
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]
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}
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],
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"source": [
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"%run -i test_max_profit.py"
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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": "3.4.3"
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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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