mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Add coin change challenge
This commit is contained in:
Donne Martin
parent
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commit
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0
recursion_dynamic/coin_change/__init__.py
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0
recursion_dynamic/coin_change/__init__.py
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164
recursion_dynamic/coin_change/coin_change_challenge.ipynb
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164
recursion_dynamic/coin_change/coin_change_challenge.ipynb
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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: Determine the total number of unique ways to make n cents, given coins of denominations less than n cents.\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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"* Do the coins have to reach exactly n cents?\n",
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" * Yes\n",
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"* Can we assume we have an infinite number of coins to make n cents?\n",
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" * Yes\n",
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"* Do we need to report the combination(s) of coins that represent the minimum?\n",
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" * No\n",
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"* Can we assume the coin denominations are given in sorted order?\n",
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" * No\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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"* coins: None or n: None -> Exception\n",
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"* coins: [] or n: 0 -> 0\n",
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"* coins: [1, 2, 3], n: 5 -> 5"
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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](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change/coin_change_solution.ipynb). 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": false
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},
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"outputs": [],
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"source": [
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"class CoinChanger(object):\n",
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"\n",
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" def make_change(self, coins, total):\n",
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" # TODO: Implement me\n",
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" return n"
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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\n",
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"\n",
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"\n",
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"\n",
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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_coin_change.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class Challenge(object):\n",
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"\n",
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" def test_coin_change(self):\n",
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" coin_changer = CoinChanger()\n",
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" assert_equal(coin_changer.make_change([1, 2], 0), 0)\n",
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" assert_equal(coin_changer.make_change([1, 2, 3], 5), 5)\n",
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" assert_equal(coin_changer.make_change([1, 5, 25, 50], 10), 3)\n",
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" print('Success: test_coin_change')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = Challenge()\n",
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" test.test_coin_change()\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": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change/coin_change_solution.ipynb) 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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230
recursion_dynamic/coin_change/coin_change_solution.ipynb
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recursion_dynamic/coin_change/coin_change_solution.ipynb
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@ -0,0 +1,230 @@
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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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"# 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: Determine the total number of unique ways to make n cents, given coins of denominations less than n cents.\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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"* Do the coins have to reach exactly n cents?\n",
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" * Yes\n",
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"* Can we assume we have an infinite number of coins to make n cents?\n",
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" * Yes\n",
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"* Do we need to report the combination(s) of coins that represent the minimum?\n",
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" * No\n",
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"* Can we assume the coin denominations are given in sorted order?\n",
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" * No\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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"* coins: None or n: None -> Exception\n",
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"* coins: [] or n: 0 -> 0\n",
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"* coins: [1, 2, 3], n: 5 -> 5"
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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 a bottom-up dynamic programming approach.\n",
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"\n",
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"<pre>\n",
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"The rows (i) represent the coin values.\n",
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"The columns (j) represent the totals.\n",
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"\n",
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" -------------------------\n",
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" | 0 | 1 | 2 | 3 | 4 | 5 |\n",
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" -------------------------\n",
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"0 | 1 | 0 | 0 | 0 | 0 | 0 |\n",
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"1 | 1 | 1 | 1 | 1 | 1 | 1 |\n",
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"2 | 1 | 1 | 2 | 2 | 3 | 3 |\n",
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"3 | 1 | 1 | 2 | 3 | 4 | 5 |\n",
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" -------------------------\n",
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"\n",
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"Number of ways to get total n with coin[n] equals:\n",
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"* Number of ways to get total n with coin[n - 1] plus\n",
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"* Number of ways to get total n - coin[n]\n",
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"\n",
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"if j == 0:\n",
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" T[i][j] = 1\n",
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"if row == 0:\n",
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" T[i][j] = 0\n",
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"if coins[i] >= j\n",
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" T[i][j] = T[i - 1][j] + T[i][j - coins[i]]\n",
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"else:\n",
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" T[i][j] = T[i - 1][j]\n",
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"\n",
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"The answer will be in the bottom right corner of the matrix.\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(i * j)\n",
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"* Space: O(i * j)"
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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": true
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},
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"outputs": [],
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"source": [
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"class CoinChanger(object):\n",
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"\n",
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" def make_change(self, coins, total):\n",
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" if coins is None or total is None:\n",
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" return None\n",
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" if not coins or total == 0:\n",
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" return 0\n",
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" coins = [0] + coins\n",
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" num_rows = len(coins)\n",
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" num_cols = total + 1\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:\n",
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" T[i][j] = 0\n",
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" continue\n",
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" if j == 0:\n",
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" T[i][j] = 1\n",
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" continue\n",
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" if coins[i] <= j:\n",
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" T[i][j] = T[i - 1][j] + T[i][j - coins[i]]\n",
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" else:\n",
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" T[i][j] = T[i - 1][j]\n",
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" return T[num_rows - 1][num_cols - 1]"
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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\n",
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"\n"
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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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_coin_change.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_coin_change.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class Challenge(object):\n",
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"\n",
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" def test_coin_change(self):\n",
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" coin_changer = CoinChanger()\n",
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" assert_equal(coin_changer.make_change([1, 2], 0), 0)\n",
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" assert_equal(coin_changer.make_change([1, 2, 3], 5), 5)\n",
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" assert_equal(coin_changer.make_change([1, 5, 25, 50], 10), 3)\n",
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" print('Success: test_coin_change')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = Challenge()\n",
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" test.test_coin_change()\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": 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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"Success: test_coin_change\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_coin_change.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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20
recursion_dynamic/coin_change/test_coin_change.py
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20
recursion_dynamic/coin_change/test_coin_change.py
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@ -0,0 +1,20 @@
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from nose.tools import assert_equal
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class Challenge(object):
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def test_coin_change(self):
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coin_changer = CoinChanger()
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assert_equal(coin_changer.make_change([1, 2], 0), 0)
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assert_equal(coin_changer.make_change([1, 2, 3], 5), 5)
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assert_equal(coin_changer.make_change([1, 5, 25, 50], 10), 3)
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print('Success: test_coin_change')
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def main():
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test = Challenge()
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test.test_coin_change()
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if __name__ == '__main__':
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main()
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