From 67f4ea99b40c6c9201a9459ad5dbadc30740b6c1 Mon Sep 17 00:00:00 2001 From: Donne Martin Date: Tue, 28 Mar 2017 05:06:47 -0400 Subject: [PATCH] Add knapsack 01 challenge --- recursion_dynamic/knapsack_01/__init__.py | 0 .../knapsack_01/knapsack_challenge.ipynb | 232 ++++++++++ .../knapsack_01/knapsack_solution.ipynb | 436 ++++++++++++++++++ .../knapsack_01/test_knapsack.py | 47 ++ 4 files changed, 715 insertions(+) create mode 100644 recursion_dynamic/knapsack_01/__init__.py create mode 100644 recursion_dynamic/knapsack_01/knapsack_challenge.ipynb create mode 100644 recursion_dynamic/knapsack_01/knapsack_solution.ipynb create mode 100644 recursion_dynamic/knapsack_01/test_knapsack.py diff --git a/recursion_dynamic/knapsack_01/__init__.py b/recursion_dynamic/knapsack_01/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/recursion_dynamic/knapsack_01/knapsack_challenge.ipynb b/recursion_dynamic/knapsack_01/knapsack_challenge.ipynb new file mode 100644 index 0000000..81b4107 --- /dev/null +++ b/recursion_dynamic/knapsack_01/knapsack_challenge.ipynb @@ -0,0 +1,232 @@ +{ + "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: Given a knapsack with a total weight capacity and a list of items with weight w(i) and value v(i), determine which items to select to maximize total value.\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", + "* Can we replace the items once they are placed in the knapsack?\n", + " * No, this is the 0/1 knapsack problem\n", + "* Can we split an item?\n", + " * No\n", + "* Can we get an input item with weight of 0 or value of 0?\n", + " * No\n", + "* Can we assume the inputs are valid?\n", + " * No\n", + "* Are the inputs in sorted order by val/weight?\n", + " * Yes, if not we'd need to sort them first\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* items or total weight is None -> Exception\n", + "* items or total weight is 0 -> 0\n", + "* General case\n", + "\n", + "
\n",
+    "total_weight = 8\n",
+    "items\n",
+    "  v | w\n",
+    "  0 | 0\n",
+    "a 2 | 2\n",
+    "b 4 | 2\n",
+    "c 6 | 4\n",
+    "d 9 | 5\n",
+    "\n",
+    "max value = 13\n",
+    "items\n",
+    "  v | w\n",
+    "b 4 | 2\n",
+    "d 9 | 5 \n",
+    "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "Refer to the [Solution Notebook](). 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": true + }, + "outputs": [], + "source": [ + "class Item(object):\n", + "\n", + " def __init__(self, label, value, weight):\n", + " self.label = label\n", + " self.value = value\n", + " self.weight = weight\n", + "\n", + " def __repr__(self):\n", + " return self.label + ' v:' + str(self.value) + ' w:' + str(self.weight)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Knapsack(object):\n", + "\n", + " def fill_knapsack(self, input_items, total_weight):\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_knapsack.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestKnapsack(object):\n", + "\n", + " def test_knapsack_bottom_up(self):\n", + " knapsack = Knapsack()\n", + " assert_raises(TypeError, knapsack.fill_knapsack, None, None)\n", + " assert_equal(knapsack.fill_knapsack(0, 0), 0)\n", + " items = []\n", + " items.append(Item(label='a', value=2, weight=2))\n", + " items.append(Item(label='b', value=4, weight=2))\n", + " items.append(Item(label='c', value=6, weight=4))\n", + " items.append(Item(label='d', value=9, weight=5))\n", + " total_weight = 8\n", + " expected_value = 13\n", + " results = knapsack.fill_knapsack(items, total_weight)\n", + " assert_equal(results[0].label, 'd')\n", + " assert_equal(results[1].label, 'b')\n", + " total_value = 0\n", + " for item in results:\n", + " total_value += item.value\n", + " assert_equal(total_value, expected_value)\n", + " print('Success: test_knapsack_bottom_up')\n", + "\n", + " def test_knapsack_top_down(self):\n", + " knapsack = KnapsackTopDown()\n", + " assert_raises(TypeError, knapsack.fill_knapsack, None, None)\n", + " assert_equal(knapsack.fill_knapsack(0, 0), 0)\n", + " items = []\n", + " items.append(Item(label='a', value=2, weight=2))\n", + " items.append(Item(label='b', value=4, weight=2))\n", + " items.append(Item(label='c', value=6, weight=4))\n", + " items.append(Item(label='d', value=9, weight=5))\n", + " total_weight = 8\n", + " expected_value = 13\n", + " assert_equal(knapsack.fill_knapsack(items, total_weight), expected_value)\n", + " print('Success: test_knapsack_top_down')\n", + "\n", + "def main():\n", + " test = TestKnapsack()\n", + " test.test_knapsack_bottom_up()\n", + " test.test_knapsack_top_down()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Notebook\n", + "\n", + "Review the [Solution Notebook]() 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/knapsack_01/knapsack_solution.ipynb b/recursion_dynamic/knapsack_01/knapsack_solution.ipynb new file mode 100644 index 0000000..aff4319 --- /dev/null +++ b/recursion_dynamic/knapsack_01/knapsack_solution.ipynb @@ -0,0 +1,436 @@ +{ + "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: Given a knapsack with a total weight capacity and a list of items with weight w(i) and value v(i), determine which items to select to maximize total value.\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", + "* Can we replace the items once they are placed in the knapsack?\n", + " * No, this is the 0/1 knapsack problem\n", + "* Can we split an item?\n", + " * No\n", + "* Can we get an input item with weight of 0 or value of 0?\n", + " * No\n", + "* Can we assume the inputs are valid?\n", + " * No\n", + "* Are the inputs in sorted order by val/weight?\n", + " * Yes, if not we'd need to sort them first\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* items or total weight is None -> Exception\n", + "* items or total weight is 0 -> 0\n", + "* General case\n", + "\n", + "
\n",
+    "total_weight = 8\n",
+    "items\n",
+    "  v | w\n",
+    "  0 | 0\n",
+    "a 2 | 2\n",
+    "b 4 | 2\n",
+    "c 6 | 4\n",
+    "d 9 | 5\n",
+    "\n",
+    "max value = 13\n",
+    "items\n",
+    "  v | w\n",
+    "b 4 | 2\n",
+    "d 9 | 5 \n",
+    "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "We'll use bottom up dynamic programming to build a table.\n", + "\n", + "The solution for the top down approach is also provided below.\n", + "\n", + "
\n",
+    "v = value\n",
+    "w = weight\n",
+    "\n",
+    "               j              \n",
+    "    -------------------------------------------------\n",
+    "    | v | w || 0 | 1 | 2 | 3 | 4 | 5 | 6  | 7  | 8  |\n",
+    "    -------------------------------------------------\n",
+    "    | 0 | 0 || 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0  |\n",
+    "i a | 2 | 2 || 0 | 0 | 2 | 2 | 2 | 2 | 2  | 2  | 2  |\n",
+    "  b | 4 | 2 || 0 | 0 | 4 | 4 | 6 | 6 | 6  | 6  | 6  |\n",
+    "  c | 6 | 4 || 0 | 0 | 4 | 4 | 6 | 6 | 10 | 10 | 12 |\n",
+    "  d | 9 | 5 || 0 | 0 | 4 | 4 | 6 | 9 | 10 | 13 | 13 |\n",
+    "    -------------------------------------------------\n",
+    "\n",
+    "i = row\n",
+    "j = col\n",
+    "\n",
+    "if j >= item[i].weight:\n",
+    "    T[i][j] = max(item[i].value + T[i - 1][j - item[i].weight],\n",
+    "                  T[i - 1][j])\n",
+    "else:\n",
+    "    T[i][j] = T[i - 1][j]\n",
+    "
\n", + "\n", + "Complexity:\n", + "* Time: O(n * w), where n is the number of items and w is the total weight\n", + "* Space: O(n * w), where n is the number of items and w is the total weight" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Item Class" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class Item(object):\n", + "\n", + " def __init__(self, label, value, weight):\n", + " self.label = label\n", + " self.value = value\n", + " self.weight = weight\n", + "\n", + " def __repr__(self):\n", + " return self.label + ' v:' + str(self.value) + ' w:' + str(self.weight)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Knapsack Bottom Up" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Knapsack(object):\n", + "\n", + " def fill_knapsack(self, input_items, total_weight):\n", + " if input_items is None or total_weight is None:\n", + " raise TypeError('input_items or total_weight cannot be None')\n", + " if not input_items or total_weight == 0:\n", + " return 0\n", + " items = list([Item(label='', value=0, weight=0)] + input_items)\n", + " num_rows = len(items)\n", + " num_cols = total_weight + 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 or j == 0:\n", + " T[i][j] = 0\n", + " elif j >= items[i].weight:\n", + " T[i][j] = max(items[i].value + T[i - 1][j - items[i].weight],\n", + " T[i - 1][j])\n", + " else:\n", + " T[i][j] = T[i - 1][j]\n", + " results = []\n", + " i = num_rows - 1\n", + " j = num_cols - 1\n", + " while T[i][j] != 0:\n", + " if T[i - 1][j] == T[i][j]:\n", + " i -= 1\n", + " elif T[i][j - 1] == T[i][j]:\n", + " j -= 1\n", + " else:\n", + " results.append(items[i])\n", + " i -= 1\n", + " j -= items[i].weight\n", + " return results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Knapsack Top Down" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class KnapsackTopDown(object):\n", + "\n", + " def fill_knapsack(self, items, total_weight):\n", + " if items is None or total_weight is None:\n", + " raise TypeError('input_items or total_weight cannot be None')\n", + " if not items or not total_weight:\n", + " return 0\n", + " memo = {}\n", + " result = self._fill_knapsack(items, total_weight, memo, index=0)\n", + " return result\n", + "\n", + "\n", + " def _fill_knapsack(self, items, total_weight, memo, index):\n", + " if total_weight < 0:\n", + " return 0\n", + " if not total_weight or index >= len(items):\n", + " return items[index - 1].value\n", + " if (total_weight, len(items) - index - 1) in memo:\n", + " return memo[(total_weight, len(items) - index - 1)] + items[index - 1].value\n", + " results = []\n", + " for i in range(index, len(items)):\n", + " total_weight -= items[i].weight\n", + " result = self._fill_knapsack(items, total_weight, memo, index=i + 1)\n", + " total_weight += items[i].weight\n", + " results.append(result)\n", + " results_index = 0\n", + " for i in range(index, len(items)):\n", + " memo[total_weight, len(items) - i] = max(results[results_index:])\n", + " results_index += 1\n", + " return max(results) + (items[index - 1].value if index > 0 else 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Knapsack Top Down Alternate" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Result(object):\n", + "\n", + " def __init__(self, total_weight, item):\n", + " self.total_weight = total_weight\n", + " self.item = item\n", + "\n", + " def __repr__(self):\n", + " return 'w:' + str(self.total_weight) + ' i:' + str(self.item)\n", + "\n", + " def __lt__(self, other):\n", + " return self.total_weight < other.total_weight\n", + "\n", + "\n", + "def knapsack_top_down_alt(items, total_weight):\n", + " if items is None or total_weight is None:\n", + " raise TypeError('input_items or total_weight cannot be None')\n", + " if not items or not total_weight:\n", + " return 0\n", + " memo = {}\n", + " result = _knapsack_top_down_alt(items, total_weight, memo, index=0)\n", + " curr_item = result.item\n", + " curr_weight = curr_item.weight\n", + " picked_items = [curr_item]\n", + " while curr_weight > 0:\n", + " total_weight -= curr_item.weight\n", + " curr_item = memo[(total_weight, len(items) - len(picked_items))].item\n", + " return result\n", + "\n", + "\n", + "def _knapsack_top_down_alt(items, total_weight, memo, index):\n", + " if total_weight < 0:\n", + " return Result(total_weight=0, item=None)\n", + " if not total_weight or index >= len(items):\n", + " return Result(total_weight=items[index - 1].value, item=items[index - 1])\n", + " if (total_weight, len(items) - index - 1) in memo:\n", + " weight=memo[(total_weight, \n", + " len(items) - index - 1)].total_weight + items[index - 1].value\n", + " return Result(total_weight=weight,\n", + " item=items[index-1])\n", + " results = []\n", + " for i in range(index, len(items)):\n", + " total_weight -= items[i].weight\n", + " result = _knapsack_top_down_alt(items, total_weight, memo, index=i + 1)\n", + " total_weight += items[i].weight\n", + " results.append(result)\n", + " results_index = 0\n", + " for i in range(index, len(items)):\n", + " memo[(total_weight, len(items) - i)] = max(results[results_index:])\n", + " results_index += 1\n", + " if index == 0:\n", + " result_item = memo[(total_weight, len(items) - 1)].item\n", + " else:\n", + " result_item = items[index - 1]\n", + " weight = max(results).total_weight + (items[index - 1].value if index > 0 else 0)\n", + " return Result(total_weight=weight,\n", + " item=result_item)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting test_knapsack.py\n" + ] + } + ], + "source": [ + "%%writefile test_knapsack.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestKnapsack(object):\n", + "\n", + " def test_knapsack_bottom_up(self):\n", + " knapsack = Knapsack()\n", + " assert_raises(TypeError, knapsack.fill_knapsack, None, None)\n", + " assert_equal(knapsack.fill_knapsack(0, 0), 0)\n", + " items = []\n", + " items.append(Item(label='a', value=2, weight=2))\n", + " items.append(Item(label='b', value=4, weight=2))\n", + " items.append(Item(label='c', value=6, weight=4))\n", + " items.append(Item(label='d', value=9, weight=5))\n", + " total_weight = 8\n", + " expected_value = 13\n", + " results = knapsack.fill_knapsack(items, total_weight)\n", + " assert_equal(results[0].label, 'd')\n", + " assert_equal(results[1].label, 'b')\n", + " total_value = 0\n", + " for item in results:\n", + " total_value += item.value\n", + " assert_equal(total_value, expected_value)\n", + " print('Success: test_knapsack_bottom_up')\n", + "\n", + " def test_knapsack_top_down(self):\n", + " knapsack = KnapsackTopDown()\n", + " assert_raises(TypeError, knapsack.fill_knapsack, None, None)\n", + " assert_equal(knapsack.fill_knapsack(0, 0), 0)\n", + " items = []\n", + " items.append(Item(label='a', value=2, weight=2))\n", + " items.append(Item(label='b', value=4, weight=2))\n", + " items.append(Item(label='c', value=6, weight=4))\n", + " items.append(Item(label='d', value=9, weight=5))\n", + " total_weight = 8\n", + " expected_value = 13\n", + " assert_equal(knapsack.fill_knapsack(items, total_weight), expected_value)\n", + " print('Success: test_knapsack_top_down')\n", + "\n", + "def main():\n", + " test = TestKnapsack()\n", + " test.test_knapsack_bottom_up()\n", + " test.test_knapsack_top_down()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Success: test_knapsack_bottom_up\n", + "Success: test_knapsack_top_down\n" + ] + } + ], + "source": [ + "%run -i test_knapsack.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/knapsack_01/test_knapsack.py b/recursion_dynamic/knapsack_01/test_knapsack.py new file mode 100644 index 0000000..5388b1b --- /dev/null +++ b/recursion_dynamic/knapsack_01/test_knapsack.py @@ -0,0 +1,47 @@ +from nose.tools import assert_equal, assert_raises + + +class TestKnapsack(object): + + def test_knapsack_bottom_up(self): + knapsack = Knapsack() + assert_raises(TypeError, knapsack.fill_knapsack, None, None) + assert_equal(knapsack.fill_knapsack(0, 0), 0) + items = [] + items.append(Item(label='a', value=2, weight=2)) + items.append(Item(label='b', value=4, weight=2)) + items.append(Item(label='c', value=6, weight=4)) + items.append(Item(label='d', value=9, weight=5)) + total_weight = 8 + expected_value = 13 + results = knapsack.fill_knapsack(items, total_weight) + assert_equal(results[0].label, 'd') + assert_equal(results[1].label, 'b') + total_value = 0 + for item in results: + total_value += item.value + assert_equal(total_value, expected_value) + print('Success: test_knapsack_bottom_up') + + def test_knapsack_top_down(self): + knapsack = KnapsackTopDown() + assert_raises(TypeError, knapsack.fill_knapsack, None, None) + assert_equal(knapsack.fill_knapsack(0, 0), 0) + items = [] + items.append(Item(label='a', value=2, weight=2)) + items.append(Item(label='b', value=4, weight=2)) + items.append(Item(label='c', value=6, weight=4)) + items.append(Item(label='d', value=9, weight=5)) + total_weight = 8 + expected_value = 13 + assert_equal(knapsack.fill_knapsack(items, total_weight), expected_value) + print('Success: test_knapsack_top_down') + +def main(): + test = TestKnapsack() + test.test_knapsack_bottom_up() + test.test_knapsack_top_down() + + +if __name__ == '__main__': + main() \ No newline at end of file