mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Add coin change min challenge
This commit is contained in:
Donne Martin
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commit
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0
recursion_dynamic/coin_change_min/__init__.py
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0
recursion_dynamic/coin_change_min/__init__.py
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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 minimum number of 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] or [3, 2, 1] -> 2"
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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_min/coin_change_min_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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" 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_coin_change_min.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestCoinChange(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_raises(TypeError, coin_changer.make_change, None, None)\n",
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" assert_equal(coin_changer.make_change([], 0), 0)\n",
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" assert_equal(coin_changer.make_change([1, 2, 3], 5), 2)\n",
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" assert_equal(coin_changer.make_change([3, 2, 1], 5), 2)\n",
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" assert_equal(coin_changer.make_change([3, 2, 1], 8), 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 = TestCoinChange()\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_min/coin_change_min_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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242
recursion_dynamic/coin_change_min/coin_change_min_solution.ipynb
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recursion_dynamic/coin_change_min/coin_change_min_solution.ipynb
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@ -0,0 +1,242 @@
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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 minimum number of 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] or [3, 2, 1], n: 5 -> 2"
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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 top down dynamic programming with memoization.\n",
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"\n",
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"* Base case: If the total is 0, return 0\n",
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"* If the total is already in the memo, return it\n",
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"* For each coin denomination:\n",
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" * If this coin > total, continue\n",
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" * Recurse, decreasing total by the coin denomination, keeping track of the min return\n",
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"* Set memo[total] to the min value + 1\n",
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"* Return the memo[total]\n",
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"\n",
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"<pre>\n",
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"total: 5\n",
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"coins: [1,2,3]\n",
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"memo key: total value: min ways\n",
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"memo = {\n",
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" 1: 1,\n",
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" 2: 1,\n",
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" 3: 1,\n",
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" 4: 2,\n",
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" 5: 2\n",
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"}\n",
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" 5\n",
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" 1, 2, 3\n",
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" /\n",
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" 4\n",
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" 1, 2, 3\n",
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" /\n",
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" 3\n",
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" 1, 2, 3\n",
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" / \\ \\____\n",
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" 2 1 0\n",
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" 1, 2, 3 1, 2, 3\n",
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" / |\n",
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" 1 0\n",
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" 1, 2, 3\n",
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" /\n",
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" 0\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(t * n), where t is the total and n is the number of coin denominations\n",
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"* Space: O(t) for the recursion depth"
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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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"import sys\n",
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"\n",
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"\n",
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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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" raise TypeError('coins or total cannot be None')\n",
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" if not coins or total == 0:\n",
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" return 0\n",
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" cache = {}\n",
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" return self._make_change(coins, total, cache)\n",
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"\n",
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" def _make_change(self, coins, total, cache):\n",
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" if total == 0:\n",
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" return 0\n",
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" if total in cache:\n",
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" return cache[total]\n",
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" min_ways = sys.maxsize\n",
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" for coin in coins:\n",
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" if total - coin < 0:\n",
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" continue\n",
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" ways = self._make_change(coins, total - coin, cache)\n",
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" if ways < min_ways:\n",
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" min_ways = ways\n",
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" cache[total] = min_ways + 1\n",
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" return cache[total]"
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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": 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_min.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_min.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestCoinChange(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_raises(TypeError, coin_changer.make_change, None, None)\n",
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" assert_equal(coin_changer.make_change([], 0), 0)\n",
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" assert_equal(coin_changer.make_change([1, 2, 3], 5), 2)\n",
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" assert_equal(coin_changer.make_change([3, 2, 1], 5), 2)\n",
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" assert_equal(coin_changer.make_change([3, 2, 1], 8), 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 = TestCoinChange()\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_min.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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22
recursion_dynamic/coin_change_min/test_coin_change_min.py
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22
recursion_dynamic/coin_change_min/test_coin_change_min.py
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from nose.tools import assert_equal, assert_raises
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class TestCoinChange(object):
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def test_coin_change(self):
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coin_changer = CoinChanger()
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assert_raises(TypeError, coin_changer.make_change, None, None)
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assert_equal(coin_changer.make_change([], 0), 0)
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assert_equal(coin_changer.make_change([1, 2, 3], 5), 2)
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assert_equal(coin_changer.make_change([3, 2, 1], 5), 2)
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assert_equal(coin_changer.make_change([3, 2, 1], 8), 3)
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print('Success: test_coin_change')
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def main():
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test = TestCoinChange()
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test.test_coin_change()
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if __name__ == '__main__':
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main()
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