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Commit f4d93212 authored by Brady James Garvin's avatar Brady James Garvin
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# Disable line-ending conversions for this repository.
* -text
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# dependencies
/node_modules
# testing
/coverage
# production
/build
# environments
.env.local
.env.development.local
.env.test.local
.env.production.local
# logs
npm-debug.log*
yarn-debug.log*
yarn-error.log*
# misc
*~
.DS_Store
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[submodule "stylelint-config"]
path = stylelint-config
url = git@git.unl.edu:soft-core/soft-260/stylelint-config.git
[submodule "eslint-config"]
path = eslint-config
url = git@git.unl.edu:soft-core/soft-260/eslint-config.git
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{
"folders": [
{
"path": "."
}
],
"settings": {
"files.eol": "LF",
"files.exclude": {
"**/node_modules": true
},
"files.trimFinalNewlines": true,
"files.trimTrailingWhitespace": true
}
}
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# dependencies
/node_modules
# testing
/coverage
# production
/build
# environments
.env.local
.env.development.local
.env.test.local
.env.production.local
# logs
npm-debug.log*
yarn-debug.log*
yarn-error.log*
# misc
*~
.DS_Store
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Please clone the starter code linked from Canvas (with `git clone --recursive` so that you also clone the submodules), install its dependencies with `npm install`, and use "File" → "Open Workspace…" to open your clone in VSCode. Please do not run the app yet—it contains spoilers.
--------------------------------------------------------------------------------
# Graph Search vs. Dynamic Programming
* Idea behind *graph search* design:
* Frame the problem as a problem on a graph
* Explore vertices and edges using a worklist algorithm
* Compute a subproblem result for each vertex
* Postprocess to extract a final result
* Idea behind *dynamic programming* design:
* Frame the problem as a problem on a directed acyclic graph (DAG)
* Explore vertices in topological order
* Compute a subproblem result for each vertex
* Postprocess to extract a final result
--------------------------------------------------------------------------------
# Problem 1:
As long as you take no more than 10 kg, you may choose as many as you want of each of these items:
* Item A weighs 3 kg and is worth $10.
* Item B weighs 4 kg and is worth $14.
What choice of items gives you the maximum total value?
Example: The selection ⟅B, B⟆ weights 8 kg and has value $28. But there is a more valuable choice of items.
# Problem 2:
You are placing linebreaks in the following paragraph (where words are represented by 'x's):
> x x x x xxxx xxxx
so that every line is at most seven characters long, including spaces. The penalty for not filling a line is the number of unused spaces on that line squared. What wrapping gives the minimum possible total penalty?
Example: The wrapping
> x x x x
> xxxx
> xxxx
has a total penalty of `(7 - 7)² + (7 - 4)² + (7 - 4)² = 0 + 9 + 9 = 18`. But there is a wrapping with a lower total penalty.
--------------------------------------------------------------------------------
# Dynamic Programming for the Unbounded Knapsack Problem
Problem: Subject to an integer weight limit, what choice of items (allowing repeats) from a collection of items with positive integer weights gives the maximum total value?
## DAG
* Edges (actions):
* … or
* …
* Vertices (situations):
* …
* Edge weights:
* [not needed]
* Topological order:
* …
* Goal:
* …
## Backpointer Class
* Information for the final result:
* …
* Information to go back:
* …
* Information to compare quality:
* …
## Choosing a Backpointer
* Exhaustive search:
* Generate ….
* Check that ….
## Example
* Item Z ….
* Item A weighs 3 kg and is worth $10.
* Item B weighs 4 kg and is worth $14.
Backpointer
-------------------
Weight (kg) Item Total Value (Back to Weight)
----------- ------ ----------- ----------------
0 [none] $0 ⊥
1 Item … … …
2 Item … … …
3 Item … … …
4 Item … … …
5 Item … … …
6 Item … … …
7 Item … … …
8 Item … … …
9 Item … … …
10 Item … … …
Reversed Path
----
10 ← (Item …) ← …
--------------------------------------------------------------------------------
# Dynamic Programming for the Line-Wrapping Problem
Problem: Wrap a paragraph to a line length, minimizing the sum of the squares of the lengths of unused space on each line.
## DAG
* Edges (actions):
* …
* Vertices (situations):
* …
* Edge weights:
* …
* Topological order:
* …
* Goal:
* …
## Backpointer Class
* Information for the final result:
* …
* Information to go back:
* …
* Information to compare quality:
* …
## Choosing a Backpointer
* Exhaustive search:
* Generate ….
* Check that ….
## Example
> x x x x xxxx xxxx
> 0 1 2 3 4 5 6
Backpointer
-----------------------------
Index Previous Index Total Penalty
----- -------------- -------------
0 ⊥ 0
1 … …
2 … …
3 … …
4 … …
5 … …
6 … …
Reversed Path
----
6 ← …
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{
"name": "@unlsoft/dynamic-programming",
"version": "1.0.0",
"description": "Starter code for the class on dynamic programming.",
"private": true,
"license": "UNLICENSED",
"scripts": {
"lint:css": "stylelint \"**/*.css\" \"**/*.module.css\" \"!coverage/**\"",
"lint:js": "eslint --max-warnings 0 ./src",
"lint": "run-s --continue-on-error lint:**",
"test-once": "react-scripts test --watchAll=false --coverage",
"test": "react-scripts test --watchAll --coverage",
"start": "react-scripts start",
"build": "react-scripts build",
"eject": "react-scripts eject"
},
"homepage": ".",
"dependencies": {
"@reduxjs/toolkit": "^1.6.0",
"@testing-library/jest-dom": "^5.14.1",
"@testing-library/react": "^12.0.0",
"@testing-library/user-event": "^13.1.9",
"classnames": "^2.3.1",
"npm-run-all": "^4.1.5",
"react": "^17.0.2",
"react-dom": "^17.0.2",
"react-redux": "^7.2.4",
"react-router-dom": "^5.2.0",
"react-scripts": "^4.0.3",
"workbox-background-sync": "^5.1.3",
"workbox-broadcast-update": "^5.1.3",
"workbox-cacheable-response": "^5.1.3",
"workbox-core": "^5.1.3",
"workbox-expiration": "^5.1.3",
"workbox-google-analytics": "^5.1.3",
"workbox-navigation-preload": "^5.1.3",
"workbox-precaching": "^5.1.3",
"workbox-range-requests": "^5.1.3",
"workbox-routing": "^5.1.3",
"workbox-strategies": "^5.1.3",
"workbox-streams": "^5.1.3"
},
"devDependencies": {
"@unlsoft/eslint-config": "file:../eslint-config",
"@unlsoft/stylelint-config": "file:../stylelint-config",
"eslint-plugin-jest-dom": "^3.9.0",
"stylelint": "^13.13.1"
},
"stylelint": {
"extends": "@unlsoft/stylelint-config"
},
"eslintConfig": {
"extends": [
"react-app",
"@unlsoft/eslint-config/react"
]
},
"jest": {
"clearMocks": true,
"collectCoverageFrom": [
"src/features/**/*.js"
],
"resetMocks": false,
"restoreMocks": false
},
"browserslist": {
"production": [
">0.2%",
"not dead",
"not op_mini all"
],
"development": [
"last 1 chrome version",
"last 1 firefox version",
"last 1 safari version"
]
}
}
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link rel="manifest" href="%PUBLIC_URL%/manifest.json" />
<meta
name="description"
content="Starter code for the class on dynamic programming."
/>
<meta name="theme-color" content="rgba(208 0 0 / 100%)" />
<link rel="icon" href="%PUBLIC_URL%/logo.svg" />
<link rel="apple-touch-icon" href="%PUBLIC_URL%/logo.svg" />
<title>Dynamic Programming in Class</title>
</head>
<body>
<noscript>You need to enable JavaScript to run this app.</noscript>
<div id="root"></div>
</body>
</html>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 152 152">
<rect x="0" y="0" width="152" height="152" fill="rgba(0 0 0 / 100%)" />
<path d="M147,1H90V42h10V75.673L53.532,2.393,52.648,1H2V42H12v66H2v41H62V108H52V74.336l46.467,73.271L99.351,149H150V108H140V42h10V1Z" stroke-width="3" stroke="rgba(255 255 255 / 100%)" fill="rgba(208 0 0 / 100%)">
</path>
</svg>
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{
"short_name": "Dynamic Programming",
"name": "Dynamic Programming in Class",
"description": "Starter code for the class on dynamic programming.",
"icons": [
{
"src": "logo.svg",
"type": "image/svg+xml",
"sizes": "192x192 512x512",
"purpose": "any maskable"
}
],
"start_url": ".",
"display": "standalone",
"orientation": "portrait",
"theme_color": "rgba(208 0 0 / 100%)",
"background_color": "rgba(255 255 255 / 100%)"
}
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import { Route } from 'react-router-dom';
import { Solution as KnapsackSolution } from './features/knapsack/solution.js';
import { Solution as WrappingSolution } from './features/wrapping/solution.js';
export function App() {
return (
<>
<Route exact path={'/'}>
<h1>Knapsack Problem</h1>
<KnapsackSolution />
<h1>Wrapping Problem</h1>
<WrappingSolution />
</Route>
</>
);
}
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dynamic-programming/src/features/knapsack/items.js 0 → 100644
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export class Item {
constructor(weight, value) {
console.assert(weight > 0, `Tried to create an item with a nonpositive weight ${weight}.`);
console.assert(Number.isInteger(weight), `Tried to create an item with a noninteger weight ${weight}.`);
this.weight = weight;
this.value = value;
}
}
dynamic-programming/src/features/knapsack/solution.js 0 → 100644
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/* eslint-disable no-magic-numbers */
import { Item } from './items.js';
import { chooseItems } from './solver.js';
import knapsackImage from './images/knapsack.svg';
import styles from './solution.module.css';
function formatSolution(solution) {
return solution.map((item) => `(weight: ${item.weight}, value: ${item.value})`).join(', ');
}
const ITEMS = [
new Item(3, 10),
new Item(4, 14),
];
const WEIGHT_LIMIT = 10;
export function Solution() {
const solution = chooseItems(ITEMS, WEIGHT_LIMIT);
return (
<div>
<figure className={styles.diagram} >
<img src={knapsackImage} alt="A weighted directed graph corresponding to the knapsack problem." />
</figure>
<label>
Chosen Knapsack Items: <output>{formatSolution(solution)}</output>
</label>
</div>
);
}
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− 0
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.diagram {
display: block;
box-sizing: border-box;
margin: auto;
width: 100%;
overflow-x: scroll;
}
dynamic-programming/src/features/knapsack/solver.js 0 → 100644
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import { Item } from './items.js';
class Backpointer {
constructor() {
// TODO: stub
}
}
function chooseBackpointer(items, backpointers) {
const currentWeight = backpointers.length;
// TODO: stub
}
export function chooseItems(items, weightLimit) {
console.assert(Number.isInteger(weightLimit), `Tried to choose items with a noninteger weight limit ${weightLimit}.`);
return []; // TODO: stub
}
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dynamic-programming/src/features/wrapping/solution.js 0 → 100644
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/* eslint-disable no-magic-numbers */
import { wrap } from './solver.js';
import wrappingImage from './images/wrapping.svg';
import styles from './solution.module.css';
function formatSolution(solution) {
return solution.map((count) => `after ${count} word${count !== 1 ? 's' : ''}`).join(', ');
}
const WORD_LENGTHS = [1, 1, 1, 1, 4, 4];
const LINE_LENGTH = 7;
export function Solution() {
const solution = wrap(WORD_LENGTHS, LINE_LENGTH);
return (
<div>
<figure className={styles.diagram} >
<img src={wrappingImage} alt="A weighted directed graph corresponding to the line-wrapping problem." />
</figure>
<label>
Line Break Locations: <output>{formatSolution(solution)}</output>
</label>
</div>
);
}
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