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