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chapter 13: graphs
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‎src/13-graph/01-airline-system.js

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// src/13-graph/01-airline-system.js
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// import the Graph class
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const Graph = require('./graph');
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const airline = new Graph();
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const airports = 'MCO TPA JFK LAX SFO'.split(' ');
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airports.forEach(airport =>
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airline.addVertex(airport)
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);
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airline.addEdge('MCO', 'JFK');
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airline.addEdge('MCO', 'LAX');
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airline.addEdge('TPA', 'JFK');
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airline.addEdge('TPA', 'LAX');
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airline.addEdge('JFK', 'LAX');
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airline.addEdge('JFK', 'SFO');
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airline.addEdge('LAX', 'SFO');
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console.log(airline.toString());
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// Output:
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// MCO -> JFK LAX
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// TPA -> JFK LAX
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// JFK -> MCO TPA LAX SFO
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// LAX -> MCO TPA JFK SFO
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// SFO -> JFK LAX
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// to see the output of this file use the command: node src/13-graph/01-airline-system.js

‎src/13-graph/02-using-bfs.js

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// src/13-graph/02-using-bfs.js
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const Graph = require('./graph');
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const { breadthFirstSearch, bfsShortestPath} = require('./bfs');
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const airline = new Graph();
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const airports = 'SEA SFO LAX LAS DEN DFW STL MDW JFK ATL MCO MIA'.split(' ');
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airports.forEach(airport =>
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airline.addVertex(airport)
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);
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airline.addEdge('SEA', 'SFO');
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airline.addEdge('SEA', 'DEN');
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airline.addEdge('SEA', 'MDW');
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airline.addEdge('SFO', 'LAX');
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airline.addEdge('LAX', 'LAS');
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airline.addEdge('DEN', 'DFW');
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airline.addEdge('DEN', 'STL');
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airline.addEdge('STL', 'MDW');
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airline.addEdge('STL', 'MCO');
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airline.addEdge('MDW', 'ATL');
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airline.addEdge('MDW', 'JFK');
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airline.addEdge('ATL', 'JFK');
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airline.addEdge('JFK', 'MCO');
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airline.addEdge('JFK', 'MIA');
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console.log(airline.toString());
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// Output:
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// SEA -> SFO DEN MDW
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// SFO -> SEA LAX
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// LAX -> SFO LAS
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// LAS -> LAX
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// DEN -> SEA DFW STL
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// DFW -> DEN
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// STL -> DEN MDW MCO
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// MDW -> SEA STL ATL JFK
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// JFK -> MDW ATL MCO MIA
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// ATL -> MDW JFK
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// MCO -> STL JFK
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// MIA -> JFK
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console.log('--- BFS ---');
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const printAirport = (value) => console.log('Visited airport: ' + value);
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breadthFirstSearch(airline,'SEA', printAirport);
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// Output:
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// --- BFS ---
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// Visited airport: SEA
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// Visited airport: SFO
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// Visited airport: DEN
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// Visited airport: MDW
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// Visited airport: LAX
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// Visited airport: DFW
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// Visited airport: STL
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// Visited airport: ATL
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// Visited airport: JFK
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// Visited airport: LAS
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// Visited airport: MCO
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// Visited airport: MIA
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console.log('--- BFS Shortest Path ---');
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const shortestPath = bfsShortestPath(airline, 'SEA');
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console.log(shortestPath);
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// { distances: { SEA: 0, SFO: 1, LAX: 2, LAS: 3, DEN: 1, DFW: 2, STL: 2, MDW: 1, JFK: 2, ATL: 2, MCO: 3, MIA: 3 },
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// predecessors: { SEA: null, SFO: 'SEA', LAX: 'SFO', LAS: 'LAX', DEN: 'SEA', DFW: 'DEN', STL: 'DEN', MDW: 'SEA', JFK: 'MDW', ATL: 'MDW', MCO: 'STL', MIA: 'JFK'}
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// }
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// find the shortest path from SEA to JFK
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let path = [];
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for (let v = 'JFK'; v !== 'SEA'; v = shortestPath.predecessors[v]) {
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path.push(v);
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}
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path.push('SEA');
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path.reverse();
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console.log('Shortest path from SEA to JFK: ' + path.join(' -> '));
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// Shortest path from SEA to JFK: SEA -> MDW -> JFK
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// to see the output of this file use the command: node src/13-graph/02-using-bfs.js

‎src/13-graph/03-using-dfs.js

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// src/13-graph/03-using-dfs.js
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const Graph = require('./graph');
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const { depthFirstSearch, enhancedDepthFirstSearch } = require('./dfs');
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const caveSystem = new Graph();
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const caves = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'];
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caves.forEach(cave => caveSystem.addVertex(cave));
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caveSystem.addEdge('A', 'B');
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caveSystem.addEdge('A', 'C');
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caveSystem.addEdge('A', 'D');
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caveSystem.addEdge('C', 'D');
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caveSystem.addEdge('C', 'G');
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caveSystem.addEdge('D', 'G');
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caveSystem.addEdge('D', 'H');
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caveSystem.addEdge('B', 'E');
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caveSystem.addEdge('B', 'F');
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caveSystem.addEdge('E', 'I');
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console.log('********* DFS - cave ***********');
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depthFirstSearch(caveSystem, (cave) => console.log('Visited cave:',cave));
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// ********* DFS - cave ***********
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// Visited cave: A
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// Visited cave: B
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// Visited cave: E
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// Visited cave: I
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// Visited cave: F
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// Visited cave: C
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// Visited cave: D
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// Visited cave: G
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// Visited cave: H
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console.log('********* Enhanced DFS - cave ***********');
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const result = enhancedDepthFirstSearch(caveSystem);
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console.log(result);
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console.log('********* Topological sort using DFS ***********');
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const tasks = new Graph(true); // this is a directed graph
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['A', 'B', 'C', 'D', 'E', 'F'].forEach(task => tasks.addVertex(task));
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// add the arrows, task dependencies:
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tasks.addEdge('A', 'C');
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tasks.addEdge('A', 'D');
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tasks.addEdge('B', 'D');
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tasks.addEdge('B', 'E');
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tasks.addEdge('C', 'F');
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tasks.addEdge('F', 'E');
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// DFS traversal
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const dfsTasks = enhancedDepthFirstSearch(tasks);
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console.log(dfsTasks);
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// {
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// discovery: { A: 1, B: 11, C: 2, D: 8, E: 4, F: 3 },
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// finished: { A: 10, B: 12, C: 7, D: 9, E: 5, F: 6 },
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// predecessors: { A: null, B: null, C: 'A', D: 'A', E: 'F', F: 'C' }
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// }
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// sort tasks in decreasing order of finish time
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// dfsTasks.finished = { A: 10, B: 12, C: 7, D: 9, E: 5, F: 6 }
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const sortedTasks = Object.keys(dfsTasks.finished).sort((a, b) => dfsTasks.finished[b] - dfsTasks.finished[a]);
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console.log(sortedTasks);
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// [ 'B', 'A', 'D', 'C', 'F', 'E' ]
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// to see the output of this file use the command: node src/13-graph/03-using-dfs.js

‎src/13-graph/04-using-dijkstra.js

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// src/13-graph/04-using-dijkstra.js
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const Graph = require('./graph');
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const dijkstra = require('./dijkstra');
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const flightCosts = [
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// SEA, MDW, DEN, MCO, STL, JFK, ATL
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[0, 300, 220, 1000, 0, 0, 0], // SEA
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[300, 0, 0, 0, 50, 210, 190], // MDW
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[220, 0, 0, 0, 350, 0, 0], // DEN
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[1000, 0, 0, 0, 150, 250, 0], // MCO
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[0, 50, 350, 150, 0, 0, 0], // STL
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[0, 210, 0, 250, 0, 0, 200], // JFK
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[0, 190, 0, 0, 0, 200, 0], // ATL
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];
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console.log('********* Dijkstra\'s Algorithm - Shortest Path ***********');
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const prices = dijkstra(flightCosts, 0); // SEA
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// prices output:
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// {
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// distances: [
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// 0, 300, 220,
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// 500, 350, 510,
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// 490
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// ],
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// predecessors: {
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// '0': [ 0 ],
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// '1': [ 0, 1 ],
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// '2': [ 0, 2 ],
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// '3': [ 0, 1, 4, 3 ],
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// '4': [ 0, 1, 4 ],
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// '5': [ 0, 1, 5 ],
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// '6': [ 0, 1, 6 ]
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// }
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// }
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console.log('Prices from SEA to all airports:');
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const airports = ['SEA', 'MDW', 'DEN', 'MCO', 'STL', 'JFK', 'ATL'];
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for (let i = 1; i < airports.length; i++) {
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const flights = prices.predecessors[i].map(airport => airports[airport]).join(' -> ');
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console.log(`SEA -> ${airports[i]}: $${prices.distances[i]} via ${flights}`);
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}
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// Prices from SEA to all airports:
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// SEA -> MDW: $300 via SEA -> MDW
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// SEA -> DEN: $220 via SEA -> DEN
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// SEA -> MCO: $500 via SEA -> MDW -> STL -> MCO
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// SEA -> STL: $350 via SEA -> MDW -> STL
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// SEA -> JFK: $510 via SEA -> MDW -> JFK
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// SEA -> ATL: $490 via SEA -> MDW -> ATL
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// to see the output of this file use the command: node src/13-graph/04-using-dijkstra.js

‎src/13-graph/05-using-floyd-warshall.js

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// src/13-graph/05-using-floyd-warshall.js
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const floydWarshall = require('./floyd-warshall');
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const INF = Infinity;
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const flightCosts = [
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// SEA, MDW, DEN, MCO, STL, JFK, ATL
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[INF, 300, 220, 1000, INF, INF, INF], // SEA
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[300, INF, INF, INF, 50, 210, 190], // MDW
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[220, INF, INF, INF, 350, INF, INF], // DEN
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[1000, INF, INF, INF, 150, 250, INF], // MCO
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[INF, 50, 350, 150, INF, INF, INF], // STL
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[INF, 210, INF, 250, INF, INF, 200], // JFK
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[INF, 190, INF, INF, INF, 200, INF], // ATL
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];
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console.log('********* Floyd-Warshall Algorithm - Shortest Path ***********');
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const distances = floydWarshall(flightCosts);
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console.log('Distances between all airports:');
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const airports = ['SEA', 'MDW', 'DEN', 'MCO', 'STL', 'JFK', 'ATL'];
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console.table(airports.map((airport, i) => {
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return airports.reduce((acc, dest, j) => {
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acc[dest] = distances[i][j];
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return acc;
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}, {});
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}));
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// ┌─────────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┐
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// │ Airport │ SEA │ MDW │ DEN │ MCO │ STL │ JFK │ ATL │
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// ├─────────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
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// │ SEA │ 0 │ 300 │ 220 │ 500 │ 350 │ 510 │ 490 │
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// │ MDW │ 300 │ 0 │ 400 │ 200 │ 50 │ 210 │ 190 │
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// │ DEN │ 220 │ 400 │ 0 │ 500 │ 350 │ 610 │ 590 │
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// │ MCO │ 500 │ 200 │ 500 │ 0 │ 150 │ 250 │ 390 │
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// │ STL │ 350 │ 50 │ 350 │ 150 │ 0 │ 260 │ 240 │
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// │ JFK │ 510 │ 210 │ 610 │ 250 │ 260 │ 0 │ 200 │
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// │ ATL │ 490 │ 190 │ 590 │ 390 │ 240 │ 200 │ 0 │
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// └─────────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘
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// to see the output of this file use the command: node src/13-graph/05-using-floyd-warshall.js

‎src/13-graph/06-using-prim.js

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// src/13-graph/06-using-prim.js
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const prim = require('./prim');
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const cityNames = ['Erebor', 'Rivendell', 'Hobbiton', 'Isengard', 'Rohan', 'Lothlorien'];
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const cities = [
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[0, 2, 4, 0, 0, 0],
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[2, 0, 2, 4, 2, 0],
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[4, 2, 0, 0, 3, 0],
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[0, 4, 0, 0, 3, 2],
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[0, 2, 3, 3, 0, 2],
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[0, 0, 0, 2, 2, 0]
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];
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const mst = prim(cities);
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console.log('Minimum Spanning Tree:', mst);
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// [ -1, 0, 1, 5, 1, 4 ]
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// to see the output of this file use the command: node src/13-graph/06-using-prim.js

‎src/13-graph/07-using-kruskal.js

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// src/13-graph/07-using-kruskal.js
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const kruskal = require('./kruskal');
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const cityNames = ['Erebor', 'Rivendell', 'Hobbiton', 'Isengard', 'Rohan', 'Lothlorien'];
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const cities = [
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[0, 2, 4, 0, 0, 0],
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[2, 0, 2, 4, 2, 0],
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[4, 2, 0, 0, 3, 0],
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[0, 4, 0, 0, 3, 2],
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[0, 2, 3, 3, 0, 2],
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[0, 0, 0, 2, 2, 0]
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];
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const mst = kruskal(cities);
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console.log('Minimum Spanning Tree with Kruskal:', mst);
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// [ [ 0, 1 ], [ 1, 2 ], [ 1, 4 ], [ 3, 5 ], [ 4, 5 ] ]
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// to see the output of this file use the command: node src/13-graph/07-using-kruskal.js

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