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Add knapsack unbounded challenge
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Donne Martin
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0
recursion_dynamic/knapsack_unbounded/__init__.py
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0
recursion_dynamic/knapsack_unbounded/__init__.py
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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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"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)."
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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: Given a knapsack with a total weight capacity and a list of items with weight w(i) and value v(i), determine the max total value you can carry.\n",
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"\n",
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"* [Constraints](#Constraints)\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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"## Constraints\n",
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"\n",
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"* Can we replace the items once they are placed in the knapsack?\n",
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" * Yes, this is the unbounded knapsack problem\n",
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"* Can we split an item?\n",
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" * No\n",
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"* Can we get an input item with weight of 0 or value of 0?\n",
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" * No\n",
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"* Do we need to return the items that make up the max total value?\n",
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" * No, just the total value\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Are the inputs in sorted order by val/weight?\n",
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" * Yes\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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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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"* items or total weight is None -> Exception\n",
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"* items or total weight is 0 -> 0\n",
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"* General case\n",
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"\n",
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"<pre>\n",
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"total_weight = 8\n",
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"items\n",
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" v | w\n",
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" 0 | 0\n",
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"a 1 | 1\n",
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"b 3 | 2\n",
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"c 7 | 4\n",
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"\n",
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"max value = 14 \n",
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"</pre>"
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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](). 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": true
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},
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"outputs": [],
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"source": [
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"class Item(object):\n",
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"\n",
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" def __init__(self, label, value, weight):\n",
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" self.label = label\n",
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" self.value = value\n",
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" self.weight = weight\n",
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"\n",
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" def __repr__(self):\n",
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" return self.label + ' v:' + str(self.value) + ' w:' + str(self.weight)"
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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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"class Knapsack(object):\n",
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"\n",
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" def fill_knapsack(self, input_items, total_weight):\n",
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" # TODO: Implement me\n",
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" pass"
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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"
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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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"**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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"source": [
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"# %load test_knapsack_unbounded.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestKnapsack(object):\n",
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"\n",
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" def test_knapsack(self):\n",
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" knapsack = Knapsack()\n",
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" assert_raises(TypeError, knapsack.fill_knapsack, None, None)\n",
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" assert_equal(knapsack.fill_knapsack(0, 0), 0)\n",
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" items = []\n",
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" items.append(Item(label='a', value=1, weight=1))\n",
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" items.append(Item(label='b', value=3, weight=2))\n",
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" items.append(Item(label='c', value=7, weight=4))\n",
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" total_weight = 8\n",
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" expected_value = 14\n",
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" results = knapsack.fill_knapsack(items, total_weight)\n",
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" total_weight = 7\n",
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" expected_value = 11\n",
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" results = knapsack.fill_knapsack(items, total_weight)\n",
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" assert_equal(results, expected_value)\n",
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" print('Success: test_knapsack')\n",
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"\n",
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"def main():\n",
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" test = TestKnapsack()\n",
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" test.test_knapsack()\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]() 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 3",
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"language": "python",
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"name": "python3"
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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": 3
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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": "ipython3",
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"version": "3.5.0"
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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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@ -0,0 +1,298 @@
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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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"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)."
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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: Given a knapsack with a total weight capacity and a list of items with weight w(i) and value v(i), determine the max total value you can carry.\n",
|
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"\n",
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"* [Constraints](#Constraints)\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)"
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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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"## Constraints\n",
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"\n",
|
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"* Can we replace the items once they are placed in the knapsack?\n",
|
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" * Yes, this is the unbounded knapsack problem\n",
|
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"* Can we split an item?\n",
|
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" * No\n",
|
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"* Can we get an input item with weight of 0 or value of 0?\n",
|
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" * No\n",
|
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"* Do we need to return the items that make up the max total value?\n",
|
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" * No, just the total value\n",
|
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"* Can we assume the inputs are valid?\n",
|
||||
" * No\n",
|
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"* Are the inputs in sorted order by val/weight?\n",
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" * Yes\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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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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"* items or total weight is None -> Exception\n",
|
||||
"* items or total weight is 0 -> 0\n",
|
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"* General case\n",
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"\n",
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"<pre>\n",
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"total_weight = 8\n",
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"items\n",
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" v | w\n",
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" 0 | 0\n",
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"a 1 | 1\n",
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"b 3 | 2\n",
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"c 7 | 4\n",
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"\n",
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"max value = 14 \n",
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"</pre>"
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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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"We'll use bottom up dynamic programming to build a table. \n",
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"\n",
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"Taking what we learned with the 0/1 knapsack problem, we could solve the problem like the following:\n",
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"\n",
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"<pre>\n",
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"\n",
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"v = value\n",
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"w = weight\n",
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"\n",
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" j \n",
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" -------------------------------------------------\n",
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" | v | w || 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |\n",
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" -------------------------------------------------\n",
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" | 0 | 0 || 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
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" a | 1 | 1 || 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |\n",
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"i b | 3 | 2 || 0 | 1 | 3 | 4 | 6 | 7 | 9 | 10 | 12 |\n",
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" c | 7 | 4 || 0 | 1 | 3 | 4 | 7 | 8 | 10 | 11 | 14 |\n",
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" -------------------------------------------------\n",
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"\n",
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"i = row\n",
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"j = col\n",
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"\n",
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"</pre>\n",
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"\n",
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"However, unlike the 0/1 knapsack variant, we don't actually need to keep space of O(n * w), where n is the number of items and w is the total weight. We just need a single array that we update after we process each item:\n",
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"\n",
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"<pre>\n",
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"\n",
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" -------------------------------------------------\n",
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" | v | w || 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |\n",
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" -------------------------------------------------\n",
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"\n",
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" -------------------------------------------------\n",
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" a | 1 | 1 || 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |\n",
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" -------------------------------------------------\n",
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"\n",
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" -------------------------------------------------\n",
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" b | 3 | 2 || 0 | 1 | 3 | 4 | 6 | 7 | 9 | 10 | 12 |\n",
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" -------------------------------------------------\n",
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"\n",
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" -------------------------------------------------\n",
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" c | 7 | 4 || 0 | 1 | 3 | 4 | 7 | 8 | 10 | 11 | 14 |\n",
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" -------------------------------------------------\n",
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"\n",
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"if j >= items[i].weight:\n",
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" T[j] = max(items[i].value + T[j - items[i].weight],\n",
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" T[j])\n",
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"\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n * w), where n is the number of items and w is the total weight\n",
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"* Space: O(w), where w is the total weight"
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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": "markdown",
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"metadata": {},
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"source": [
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"### Item Class"
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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": true
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},
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"outputs": [],
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"source": [
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"class Item(object):\n",
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"\n",
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" def __init__(self, label, value, weight):\n",
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" self.label = label\n",
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" self.value = value\n",
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" self.weight = weight\n",
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"\n",
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" def __repr__(self):\n",
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" return self.label + ' v:' + str(self.value) + ' w:' + str(self.weight)"
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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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"### Knapsack Bottom Up"
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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": 2,
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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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"class Knapsack(object):\n",
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"\n",
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" def fill_knapsack(self, items, total_weight):\n",
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" if items is None or total_weight is None:\n",
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" raise TypeError('items or total_weight cannot be None')\n",
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" if not items or total_weight == 0:\n",
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" return 0\n",
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" num_rows = len(items)\n",
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" num_cols = total_weight + 1\n",
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" T = [0] * (num_cols)\n",
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" for i in range(num_rows):\n",
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" for j in range(num_cols):\n",
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" if j >= items[i].weight:\n",
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" T[j] = max(items[i].value + T[j - items[i].weight],\n",
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" T[j])\n",
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" return T[-1]"
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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"
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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": 3,
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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_knapsack_unbounded.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_knapsack_unbounded.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestKnapsack(object):\n",
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"\n",
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" def test_knapsack(self):\n",
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" knapsack = Knapsack()\n",
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" assert_raises(TypeError, knapsack.fill_knapsack, None, None)\n",
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" assert_equal(knapsack.fill_knapsack(0, 0), 0)\n",
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" items = []\n",
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" items.append(Item(label='a', value=1, weight=1))\n",
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" items.append(Item(label='b', value=3, weight=2))\n",
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" items.append(Item(label='c', value=7, weight=4))\n",
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" total_weight = 8\n",
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" expected_value = 14\n",
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" results = knapsack.fill_knapsack(items, total_weight)\n",
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" total_weight = 7\n",
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" expected_value = 11\n",
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" results = knapsack.fill_knapsack(items, total_weight)\n",
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" assert_equal(results, expected_value)\n",
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" print('Success: test_knapsack')\n",
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"\n",
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"def main():\n",
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" test = TestKnapsack()\n",
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" test.test_knapsack()\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,
|
||||
"metadata": {
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||||
"collapsed": false
|
||||
},
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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_knapsack\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_knapsack_unbounded.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
|
||||
}
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
from nose.tools import assert_equal, assert_raises
|
||||
|
||||
|
||||
class TestKnapsack(object):
|
||||
|
||||
def test_knapsack(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=1, weight=1))
|
||||
items.append(Item(label='b', value=3, weight=2))
|
||||
items.append(Item(label='c', value=7, weight=4))
|
||||
total_weight = 8
|
||||
expected_value = 14
|
||||
results = knapsack.fill_knapsack(items, total_weight)
|
||||
total_weight = 7
|
||||
expected_value = 11
|
||||
results = knapsack.fill_knapsack(items, total_weight)
|
||||
assert_equal(results, expected_value)
|
||||
print('Success: test_knapsack')
|
||||
|
||||
def main():
|
||||
test = TestKnapsack()
|
||||
test.test_knapsack()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
||||
Loading…
Reference in New Issue
Block a user