diff --git a/recursion_dynamic/coin_change_min/__init__.py b/recursion_dynamic/coin_change_min/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/recursion_dynamic/coin_change_min/coin_change_min_challenge.ipynb b/recursion_dynamic/coin_change_min/coin_change_min_challenge.ipynb new file mode 100644 index 0000000..5acd777 --- /dev/null +++ b/recursion_dynamic/coin_change_min/coin_change_min_challenge.ipynb @@ -0,0 +1,169 @@ +{ + "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 minimum number of 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] or [3, 2, 1] -> 2" + ] + }, + { + "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_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." + ] + }, + { + "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", + " pass" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**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_min.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestCoinChange(object):\n", + "\n", + " def test_coin_change(self):\n", + " coin_changer = CoinChanger()\n", + " assert_raises(TypeError, coin_changer.make_change, None, None)\n", + " assert_equal(coin_changer.make_change([], 0), 0)\n", + " assert_equal(coin_changer.make_change([1, 2, 3], 5), 2)\n", + " assert_equal(coin_changer.make_change([3, 2, 1], 5), 2)\n", + " assert_equal(coin_changer.make_change([3, 2, 1], 8), 3)\n", + " print('Success: test_coin_change')\n", + "\n", + "\n", + "def main():\n", + " test = TestCoinChange()\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_min/coin_change_min_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_min/coin_change_min_solution.ipynb b/recursion_dynamic/coin_change_min/coin_change_min_solution.ipynb new file mode 100644 index 0000000..d1960fb --- /dev/null +++ b/recursion_dynamic/coin_change_min/coin_change_min_solution.ipynb @@ -0,0 +1,242 @@ +{ + "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 minimum number of 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] or [3, 2, 1], n: 5 -> 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "We'll use top down dynamic programming with memoization.\n", + "\n", + "* Base case: If the total is 0, return 0\n", + "* If the total is already in the memo, return it\n", + "* For each coin denomination:\n", + " * If this coin > total, continue\n", + " * Recurse, decreasing total by the coin denomination, keeping track of the min return\n", + "* Set memo[total] to the min value + 1\n", + "* Return the memo[total]\n", + "\n", + "
\n",
+    "total: 5\n",
+    "coins: [1,2,3]\n",
+    "memo key: total value: min ways\n",
+    "memo = {\n",
+    "    1: 1,\n",
+    "    2: 1,\n",
+    "    3: 1,\n",
+    "    4: 2,\n",
+    "    5: 2\n",
+    "}\n",
+    "                              5\n",
+    "                           1, 2, 3\n",
+    "                          /\n",
+    "                         4\n",
+    "                      1, 2, 3\n",
+    "                     /\n",
+    "                    3\n",
+    "              1,    2,    3\n",
+    "             /       \\     \\____\n",
+    "            2         1         0\n",
+    "         1, 2, 3   1, 2, 3\n",
+    "        /   |\n",
+    "       1    0\n",
+    "    1, 2, 3\n",
+    "   /\n",
+    "  0\n",
+    "
\n", + "\n", + "Complexity:\n", + "* Time: O(t * n), where t is the total and n is the number of coin denominations\n", + "* Space: O(t) for the recursion depth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import sys\n", + "\n", + "\n", + "class CoinChanger(object):\n", + "\n", + " def make_change(self, coins, total):\n", + " if coins is None or total is None:\n", + " raise TypeError('coins or total cannot be None')\n", + " if not coins or total == 0:\n", + " return 0\n", + " cache = {}\n", + " return self._make_change(coins, total, cache)\n", + "\n", + " def _make_change(self, coins, total, cache):\n", + " if total == 0:\n", + " return 0\n", + " if total in cache:\n", + " return cache[total]\n", + " min_ways = sys.maxsize\n", + " for coin in coins:\n", + " if total - coin < 0:\n", + " continue\n", + " ways = self._make_change(coins, total - coin, cache)\n", + " if ways < min_ways:\n", + " min_ways = ways\n", + " cache[total] = min_ways + 1\n", + " return cache[total]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting test_coin_change_min.py\n" + ] + } + ], + "source": [ + "%%writefile test_coin_change_min.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestCoinChange(object):\n", + "\n", + " def test_coin_change(self):\n", + " coin_changer = CoinChanger()\n", + " assert_raises(TypeError, coin_changer.make_change, None, None)\n", + " assert_equal(coin_changer.make_change([], 0), 0)\n", + " assert_equal(coin_changer.make_change([1, 2, 3], 5), 2)\n", + " assert_equal(coin_changer.make_change([3, 2, 1], 5), 2)\n", + " assert_equal(coin_changer.make_change([3, 2, 1], 8), 3)\n", + " print('Success: test_coin_change')\n", + "\n", + "\n", + "def main():\n", + " test = TestCoinChange()\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_min.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_min/test_coin_change_min.py b/recursion_dynamic/coin_change_min/test_coin_change_min.py new file mode 100644 index 0000000..2440185 --- /dev/null +++ b/recursion_dynamic/coin_change_min/test_coin_change_min.py @@ -0,0 +1,22 @@ +from nose.tools import assert_equal, assert_raises + + +class TestCoinChange(object): + + def test_coin_change(self): + coin_changer = CoinChanger() + assert_raises(TypeError, coin_changer.make_change, None, None) + assert_equal(coin_changer.make_change([], 0), 0) + assert_equal(coin_changer.make_change([1, 2, 3], 5), 2) + assert_equal(coin_changer.make_change([3, 2, 1], 5), 2) + assert_equal(coin_changer.make_change([3, 2, 1], 8), 3) + print('Success: test_coin_change') + + +def main(): + test = TestCoinChange() + test.test_coin_change() + + +if __name__ == '__main__': + main() \ No newline at end of file