From a97d35f86a478e25834cbb14d623160222a28349 Mon Sep 17 00:00:00 2001 From: Donne Martin Date: Tue, 28 Mar 2017 05:10:10 -0400 Subject: [PATCH] Add coin change challenge --- recursion_dynamic/coin_change/__init__.py | 0 .../coin_change/coin_change_challenge.ipynb | 164 +++++++++++++ .../coin_change/coin_change_solution.ipynb | 230 ++++++++++++++++++ .../coin_change/test_coin_change.py | 20 ++ 4 files changed, 414 insertions(+) create mode 100644 recursion_dynamic/coin_change/__init__.py create mode 100644 recursion_dynamic/coin_change/coin_change_challenge.ipynb create mode 100644 recursion_dynamic/coin_change/coin_change_solution.ipynb create mode 100644 recursion_dynamic/coin_change/test_coin_change.py diff --git a/recursion_dynamic/coin_change/__init__.py b/recursion_dynamic/coin_change/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/recursion_dynamic/coin_change/coin_change_challenge.ipynb b/recursion_dynamic/coin_change/coin_change_challenge.ipynb new file mode 100644 index 0000000..c552f50 --- /dev/null +++ b/recursion_dynamic/coin_change/coin_change_challenge.ipynb @@ -0,0 +1,164 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Challenge Notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Determine the total number of unique ways to make n cents, given coins of denominations less than n cents.\n", + "\n", + "* [Constraints](#Constraints)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Unit Test](#Unit-Test)\n", + "* [Solution Notebook](#Solution-Notebook)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constraints\n", + "\n", + "* Do the coins have to reach exactly n cents?\n", + " * Yes\n", + "* Can we assume we have an infinite number of coins to make n cents?\n", + " * Yes\n", + "* Do we need to report the combination(s) of coins that represent the minimum?\n", + " * No\n", + "* Can we assume the coin denominations are given in sorted order?\n", + " * No\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* coins: None or n: None -> Exception\n", + "* coins: [] or n: 0 -> 0\n", + "* coins: [1, 2, 3], n: 5 -> 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "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." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class CoinChanger(object):\n", + "\n", + " def make_change(self, coins, total):\n", + " # TODO: Implement me\n", + " return n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test\n", + "\n", + "\n", + "\n", + "**The following unit test is expected to fail until you solve the challenge.**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# %load test_coin_change.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class Challenge(object):\n", + "\n", + " def test_coin_change(self):\n", + " coin_changer = CoinChanger()\n", + " assert_equal(coin_changer.make_change([1, 2], 0), 0)\n", + " assert_equal(coin_changer.make_change([1, 2, 3], 5), 5)\n", + " assert_equal(coin_changer.make_change([1, 5, 25, 50], 10), 3)\n", + " print('Success: test_coin_change')\n", + "\n", + "\n", + "def main():\n", + " test = Challenge()\n", + " test.test_coin_change()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Notebook\n", + "\n", + "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." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/recursion_dynamic/coin_change/coin_change_solution.ipynb b/recursion_dynamic/coin_change/coin_change_solution.ipynb new file mode 100644 index 0000000..44da41f --- /dev/null +++ b/recursion_dynamic/coin_change/coin_change_solution.ipynb @@ -0,0 +1,230 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solution Notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Determine the total number of unique ways to make n cents, given coins of denominations less than n cents.\n", + "\n", + "* [Constraints](#Constraints)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Unit Test](#Unit-Test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constraints\n", + "\n", + "* Do the coins have to reach exactly n cents?\n", + " * Yes\n", + "* Can we assume we have an infinite number of coins to make n cents?\n", + " * Yes\n", + "* Do we need to report the combination(s) of coins that represent the minimum?\n", + " * No\n", + "* Can we assume the coin denominations are given in sorted order?\n", + " * No\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* coins: None or n: None -> Exception\n", + "* coins: [] or n: 0 -> 0\n", + "* coins: [1, 2, 3], n: 5 -> 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "We'll use a bottom-up dynamic programming approach.\n", + "\n", + "
\n",
+    "The rows (i) represent the coin values.\n",
+    "The columns (j) represent the totals.\n",
+    "\n",
+    "  -------------------------\n",
+    "  | 0 | 1 | 2 | 3 | 4 | 5 |\n",
+    "  -------------------------\n",
+    "0 | 1 | 0 | 0 | 0 | 0 | 0 |\n",
+    "1 | 1 | 1 | 1 | 1 | 1 | 1 |\n",
+    "2 | 1 | 1 | 2 | 2 | 3 | 3 |\n",
+    "3 | 1 | 1 | 2 | 3 | 4 | 5 |\n",
+    "  -------------------------\n",
+    "\n",
+    "Number of ways to get total n with coin[n] equals:\n",
+    "* Number of ways to get total n with coin[n - 1] plus\n",
+    "* Number of ways to get total n - coin[n]\n",
+    "\n",
+    "if j == 0:\n",
+    "    T[i][j] = 1\n",
+    "if row == 0:\n",
+    "    T[i][j] = 0\n",
+    "if coins[i] >= j\n",
+    "    T[i][j] = T[i - 1][j] + T[i][j - coins[i]]\n",
+    "else:\n",
+    "    T[i][j] = T[i - 1][j]\n",
+    "\n",
+    "The answer will be in the bottom right corner of the matrix.\n",
+    "
\n", + "\n", + "Complexity:\n", + "* Time: O(i * j)\n", + "* Space: O(i * j)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class CoinChanger(object):\n", + "\n", + " def make_change(self, coins, total):\n", + " if coins is None or total is None:\n", + " return None\n", + " if not coins or total == 0:\n", + " return 0\n", + " coins = [0] + coins\n", + " num_rows = len(coins)\n", + " num_cols = total + 1\n", + " T = [[None] * num_cols for _ in range(num_rows)]\n", + " for i in range(num_rows):\n", + " for j in range(num_cols):\n", + " if i == 0:\n", + " T[i][j] = 0\n", + " continue\n", + " if j == 0:\n", + " T[i][j] = 1\n", + " continue\n", + " if coins[i] <= j:\n", + " T[i][j] = T[i - 1][j] + T[i][j - coins[i]]\n", + " else:\n", + " T[i][j] = T[i - 1][j]\n", + " return T[num_rows - 1][num_cols - 1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting test_coin_change.py\n" + ] + } + ], + "source": [ + "%%writefile test_coin_change.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class Challenge(object):\n", + "\n", + " def test_coin_change(self):\n", + " coin_changer = CoinChanger()\n", + " assert_equal(coin_changer.make_change([1, 2], 0), 0)\n", + " assert_equal(coin_changer.make_change([1, 2, 3], 5), 5)\n", + " assert_equal(coin_changer.make_change([1, 5, 25, 50], 10), 3)\n", + " print('Success: test_coin_change')\n", + "\n", + "\n", + "def main():\n", + " test = Challenge()\n", + " test.test_coin_change()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Success: test_coin_change\n" + ] + } + ], + "source": [ + "%run -i test_coin_change.py" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.4.3" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/recursion_dynamic/coin_change/test_coin_change.py b/recursion_dynamic/coin_change/test_coin_change.py new file mode 100644 index 0000000..8d8efb2 --- /dev/null +++ b/recursion_dynamic/coin_change/test_coin_change.py @@ -0,0 +1,20 @@ +from nose.tools import assert_equal + + +class Challenge(object): + + def test_coin_change(self): + coin_changer = CoinChanger() + assert_equal(coin_changer.make_change([1, 2], 0), 0) + assert_equal(coin_changer.make_change([1, 2, 3], 5), 5) + assert_equal(coin_changer.make_change([1, 5, 25, 50], 10), 3) + print('Success: test_coin_change') + + +def main(): + test = Challenge() + test.test_coin_change() + + +if __name__ == '__main__': + main() \ No newline at end of file