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https://github.com/donnemartin/interactive-coding-challenges.git
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Coin Change Ways Problem/Solution
This commit is contained in:
mrb00l34n
parent
502c4d77e4
commit
3370106d36
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@ -216,6 +216,7 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup
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| Print all valid combinations of n-pairs of parentheses | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
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| Implement a paint fill function | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
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| Find all permutations to represent n cents, given 1, 5, 10, 25 cent coins | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
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| Find the number of ways to represent n cents given k arbitrary cent coins | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_ways/coinchange_ways_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_ways/coinchange_ways_solution.ipynb) |
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| Add a challenge | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
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<br/>
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@ -0,0 +1,164 @@
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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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"<small><i>This notebook was prepared by [mrb00l34n](http://github.com/mrb00l34n). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).</i></small>"
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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: Counting Ways of Making Change\n",
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"\n",
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"* [Explanation](#Explanation)\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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"## Explanation\n",
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"\n",
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"How many ways are there of making change for n, given k distinct coins? For example:\n",
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"\n",
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"Input: n = 4, k = 2, coins = [1,2]\n",
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"\n",
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"Output: 3. 1+1+1+1, 1+2+1, 2+2, would be the ways of making change.\n",
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"\n",
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"Note that a coin can be used any number of times, and we are counting unique combinations."
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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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"* Input: n = 0, k = 2, coins = [1,2] -> Output: 0\n",
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"* Input: n = 100, k = 3, coins = [1,2,3] -> Output: 884\n",
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"* Input: n = 1000, k = 100, coins = [1,2,3...99,100] -> Output: 15658181104580771094597751280645\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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"## 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/coinchange_ways/coinchange_ways_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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"def change_ways(n,k,coins):\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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{
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"name":"stdout",
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"text":[],
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"output_type": "stream"
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}
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],
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"source": [
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"# %load test_coinchange_ways.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_coinchange_ways(self,solution):\n",
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" assert_equal(solution(0,2,[1,2]), 0)\n",
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" assert_equal(solution(100,3,[1,2,3]), 884)\n",
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" assert_equal(solution(1000,100,range(1,101)), 15658181104580771094597751280645)\n",
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" print('Success: test_coinchange_ways')\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_coinchange_ways(change_ways)\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/coinchange_ways/coinchange_ways_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 2",
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"language": "python",
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"name": "python2"
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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": 2
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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": "ipython2",
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"version": "2.7.6"
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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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180
recursion_dynamic/coinchange_ways/coinchange_ways_solution.ipynb
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180
recursion_dynamic/coinchange_ways/coinchange_ways_solution.ipynb
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@ -0,0 +1,180 @@
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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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"<small><i>This notebook was prepared by [mrb00l34n](http://github.com/mrb00l34n). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).</i></small>"
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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: Counting Ways of Making Change\n",
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"\n",
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"* [Hints](#Hints)\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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"## Hints\n",
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"\n",
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"* Can you think of a way to build up to a solution?\n",
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"* If there are 2 ways of making 3, and you are now given a coin of value v, how many ways can you make 3+v?\n",
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"* Can you think of a way to divide the problem into smaller subproblems?"
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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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"One possible solution using dynamic programming:\n",
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"* Create an array, s.t arr[i] = # of ways to make change for i\n",
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"* Initialize arr[0] = 1, arr[i>0] = 0\n",
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"* For each coin, and for each index from coin to n, increment arr[i] by arr[i-coin]\n",
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"\n",
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"How does this work?\n",
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"* As we iterate through each coin, we are adding the ways of making arr[i-coin] to arr[i]\n",
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"* If we have 2 ways of making 4, and are now iterating on a coin of value 3, there should be 2 ways of making 7.\n",
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"* We are essentially adding the coin we are iterating on to the # of ways of making arr[i].\n",
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"\n",
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"Complexity:\n",
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"* Time: O(mn)\n",
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"* Space: O(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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"## 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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"def change_ways(n,k,coins):\n",
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" arr = [1] + [0] * n\n",
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" for coin in coins:\n",
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" for i in xrange(coin,n + 1):\n",
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" arr[i] += arr[i - coin]\n",
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" return 0 if n == 0 else arr[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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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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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_coinchange_ways.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_coinchange_ways.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_coinchange_ways(self,solution):\n",
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" assert_equal(solution(0,2,[1,2]), 0)\n",
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" assert_equal(solution(100,3,[1,2,3]), 884)\n",
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" assert_equal(solution(1000,100,range(1,101)), 15658181104580771094597751280645)\n",
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" print('Success: test_coinchange_ways')\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_coinchange_ways(change_ways)\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_coinchange_ways\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_coinchange_ways.py"
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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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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 2",
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"language": "python",
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"name": "python2"
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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": 2
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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": "ipython2",
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"version": "2.7.6"
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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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19
recursion_dynamic/coinchange_ways/test_coinchange_ways.py
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19
recursion_dynamic/coinchange_ways/test_coinchange_ways.py
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@ -0,0 +1,19 @@
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from nose.tools import assert_equal
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class Challenge(object):
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def test_coinchange_ways(self,solution):
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assert_equal(solution(0,2,[1,2]), 0)
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assert_equal(solution(100,3,[1,2,3]), 884)
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assert_equal(solution(1000,100,range(1,101)), 15658181104580771094597751280645)
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print('Success: test_coinchange_ways')
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def main():
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test = Challenge()
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test.test_coinchange_ways(change_ways)
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if __name__ == '__main__':
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main()
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