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Add knapsack 01 challenge
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Donne Martin
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commit
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0
recursion_dynamic/knapsack_01/__init__.py
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0
recursion_dynamic/knapsack_01/__init__.py
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recursion_dynamic/knapsack_01/knapsack_challenge.ipynb
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recursion_dynamic/knapsack_01/knapsack_challenge.ipynb
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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 which items to select to maximize total value.\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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" * No, this is the 0/1 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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"* 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, if not we'd need to sort them first\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 2 | 2\n",
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"b 4 | 2\n",
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"c 6 | 4\n",
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"d 9 | 5\n",
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"\n",
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"max value = 13\n",
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"items\n",
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" v | w\n",
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"b 4 | 2\n",
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"d 9 | 5 \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.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_bottom_up(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=2, weight=2))\n",
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" items.append(Item(label='b', value=4, weight=2))\n",
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" items.append(Item(label='c', value=6, weight=4))\n",
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" items.append(Item(label='d', value=9, weight=5))\n",
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" total_weight = 8\n",
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" expected_value = 13\n",
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" results = knapsack.fill_knapsack(items, total_weight)\n",
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" assert_equal(results[0].label, 'd')\n",
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" assert_equal(results[1].label, 'b')\n",
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" total_value = 0\n",
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" for item in results:\n",
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" total_value += item.value\n",
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" assert_equal(total_value, expected_value)\n",
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" print('Success: test_knapsack_bottom_up')\n",
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"\n",
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" def test_knapsack_top_down(self):\n",
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" knapsack = KnapsackTopDown()\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=2, weight=2))\n",
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" items.append(Item(label='b', value=4, weight=2))\n",
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" items.append(Item(label='c', value=6, weight=4))\n",
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" items.append(Item(label='d', value=9, weight=5))\n",
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" total_weight = 8\n",
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" expected_value = 13\n",
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" assert_equal(knapsack.fill_knapsack(items, total_weight), expected_value)\n",
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" print('Success: test_knapsack_top_down')\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_bottom_up()\n",
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" test.test_knapsack_top_down()\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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436
recursion_dynamic/knapsack_01/knapsack_solution.ipynb
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recursion_dynamic/knapsack_01/knapsack_solution.ipynb
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@ -0,0 +1,436 @@
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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": [
|
||||
"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 which items to select to maximize total value.\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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" * No, this is the 0/1 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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"* 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",
|
||||
" * Yes, if not we'd need to sort them first\n",
|
||||
"* 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 2 | 2\n",
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"b 4 | 2\n",
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"c 6 | 4\n",
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"d 9 | 5\n",
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"\n",
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"max value = 13\n",
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"items\n",
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" v | w\n",
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"b 4 | 2\n",
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"d 9 | 5 \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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"The solution for the top down approach is also provided below.\n",
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"\n",
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"<pre>\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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"i a | 2 | 2 || 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |\n",
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" b | 4 | 2 || 0 | 0 | 4 | 4 | 6 | 6 | 6 | 6 | 6 |\n",
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" c | 6 | 4 || 0 | 0 | 4 | 4 | 6 | 6 | 10 | 10 | 12 |\n",
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" d | 9 | 5 || 0 | 0 | 4 | 4 | 6 | 9 | 10 | 13 | 13 |\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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"if j >= item[i].weight:\n",
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" T[i][j] = max(item[i].value + T[i - 1][j - item[i].weight],\n",
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" T[i - 1][j])\n",
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"else:\n",
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" T[i][j] = T[i - 1][j]\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(n * w), where n is the number of items and 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, input_items, total_weight):\n",
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" if input_items is None or total_weight is None:\n",
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" raise TypeError('input_items or total_weight cannot be None')\n",
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" if not input_items or total_weight == 0:\n",
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" return 0\n",
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" items = list([Item(label='', value=0, weight=0)] + input_items)\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 = [[None] * num_cols for _ in range(num_rows)]\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 i == 0 or j == 0:\n",
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" T[i][j] = 0\n",
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" elif j >= items[i].weight:\n",
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" T[i][j] = max(items[i].value + T[i - 1][j - items[i].weight],\n",
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" T[i - 1][j])\n",
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" else:\n",
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" T[i][j] = T[i - 1][j]\n",
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" results = []\n",
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" i = num_rows - 1\n",
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" j = num_cols - 1\n",
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" while T[i][j] != 0:\n",
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" if T[i - 1][j] == T[i][j]:\n",
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" i -= 1\n",
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" elif T[i][j - 1] == T[i][j]:\n",
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" j -= 1\n",
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" else:\n",
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" results.append(items[i])\n",
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" i -= 1\n",
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" j -= items[i].weight\n",
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" return results"
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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 Top Down"
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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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"source": [
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"class KnapsackTopDown(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('input_items or total_weight cannot be None')\n",
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" if not items or not total_weight:\n",
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" return 0\n",
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" memo = {}\n",
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" result = self._fill_knapsack(items, total_weight, memo, index=0)\n",
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" return result\n",
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"\n",
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"\n",
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" def _fill_knapsack(self, items, total_weight, memo, index):\n",
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" if total_weight < 0:\n",
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" 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
|
||||
}
|
||||
47
recursion_dynamic/knapsack_01/test_knapsack.py
Normal file
47
recursion_dynamic/knapsack_01/test_knapsack.py
Normal file
|
|
@ -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()
|
||||
Loading…
Reference in New Issue
Block a user