数据结构与算法JavaScript描述练习------第11章图和图算法

1. 编写一个程序，测试广度优先和深度优先这两种图搜索算法哪一种速度更快。请使用不 同大小的图来测试你的程序。


function Graph(v) {this.vertices = v;this.edges = 0;this.adj = [];this.marked = [];this.edgeTo = [];for (var i = 0; i < this.vertices; i++) {this.adj[i] = [];this.marked[i] = false;this.edgeTo[i] = null;}this.addEdge = addEdge;this.showGraph = showGraph;this.pathTo = pathTo; this.hasPathTo = hasPathTo;this.dfs = dfs;this.nonRecursiveDfs = nonRecursiveDfs;this.bfs = bfs;this.reset = reset;
}function addEdge(v, w) {this.adj[v].push(w);this.adj[w].push(v);this.edges++;
}function showGraph() {for (var i = 0; i < this.vertices; i++) {console.log(i + " -> ");for (var j = 0; j < this.vertices; j++) {if (this.adj[i][j] != undefined) {console.log(this.adj[i][j] + ' ');}}}
}function dfs(v) {this.marked[v] = true;if (this.adj[v] != undefined) {console.log("Visited vertex: " + v);}if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) {if (!this.marked[w]) {this.dfs(w);}}}
}function nonRecursiveDfs(s) {let stack = [];this.marked[s] = true;stack.push(s);while (stack.length > 0) {let v = stack.pop();console.log("Visited vertex: " + v);for (let w of this.adj[v]) {if (!this.marked[w]) {this.marked[w] = true;this.edgeTo[w] = v;stack.push(w);}}}
}function bfs(s) { var queue = []; this.marked[s] = true; queue.push(s); while (queue.length > 0) { var v = queue.shift(); console.log("Visisted vertex: " + v); if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) { if (!this.marked[w]) { this.edgeTo[w] = v; this.marked[w] = true; queue.push(w); } }} } 
}function hasPathTo(v) {return this.marked[v];
}function pathTo(v) {var source = 0;if (!this.hasPathTo(v)) {return undefined;}var path = [];for (var i = v; i !== source; i = this.edgeTo[i]) {if (this.edgeTo[i] === null) {console.error("Invalid edgeTo value:", i);return undefined;}path.push(i);}path.push(source);return path;
}function reset() {for (var i = 0; i < this.vertices; i++) {this.marked[i] = false;this.edgeTo[i] = null;}
}	function generateRandomGraph(vertices, edges) {var graph = new Graph(vertices);while (graph.edges < edges) {var v = Math.floor(Math.random() * vertices);var w = Math.floor(Math.random() * vertices);if (v !== w && !graph.adj[v].includes(w)) {graph.addEdge(v, w);}}return graph;
}function benchmarkSearchAlgorithms(verticesCount, edgesCount) {const graph = generateRandomGraph(verticesCount, edgesCount);const source = 0;console.log("Benchmarking BFS and DFS for " + verticesCount + " vertices and " + edgesCount + " edges:");const startTimeBFS = performance.now();graph.reset();graph.bfs(source);const endTimeBFS = performance.now();const bfsTime = endTimeBFS - startTimeBFS;const startTimeDFS = performance.now();graph.reset();graph.nonRecursiveDfs(source);const endTimeDFS = performance.now();const dfsTime = endTimeDFS - startTimeDFS;console.log("BFS took "bfsTime.toFixed(2) + " ms");console.log("DFS took "dfsTime.toFixed(2) + " ms");if (bfsTime < dfsTime) {console.log('BFS is faster.');} else if (bfsTime > dfsTime) {console.log('DFS is faster.');} else {console.log('BFS and DFS are equally fast.');}
}var sizes = [100, 500, 1000, 5000]; 
var densities = [1000, 5000, 10000, 50000]; sizes.forEach((vertices, index) => {benchmarkSearchAlgorithms(vertices, densities[index]);
});

2. 编写一个用文件来存储图的程序。

<!doctype html>
<html lang="en"><head><title>Graph File Reader</title><meta charset="utf-8"></head><body><h1>Graph File Reader</h1><input type="file" id="fileInput" /><button onclick="saveGraphToFile()">Save Graph to File</button><pre id="output"></pre><script src = "2.js"></script></body>
</html>
5 6
0 1
0 2
1 2
1 3
2 3
3 4
function Graph(v) {this.vertices = v;this.edges = 0;this.adj = [];this.marked = [];this.edgeTo = [];for (var i = 0; i < this.vertices; i++) {this.adj[i] = [];this.marked[i] = false;this.edgeTo[i] = null;}this.addEdge = addEdge;this.showGraph = showGraph;this.pathTo = pathTo; this.hasPathTo = hasPathTo;this.dfs = dfs;this.bfs = bfs;
}function addEdge(v, w) {this.adj[v].push(w);this.adj[w].push(v);this.edges++;
}
/*
function showGraph() {for (var i = 0; i < this.vertices; i++) {console.log(i + " -> ");for (var j = 0; j < this.vertices; j++) {if (this.adj[i][j] != undefined) {console.log(this.adj[i][j] + ' ');}}}
}
*/
function dfs(v) {this.marked[v] = true;if (this.adj[v] != undefined) {console.log("Visited vertex: " + v);}if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) {if (!this.marked[w]) {this.dfs(w);}}}
}function bfs(s) { var queue = []; this.marked[s] = true; queue.push(s); // 添加到队尾 while (queue.length > 0) { var v = queue.shift(); // 从队首移除 console.log("Visisted vertex: " + v); if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) { if (!this.marked[w]) { this.edgeTo[w] = v; this.marked[w] = true; queue.push(w); } }} } 
}function hasPathTo(v) {return this.marked[v];
}function pathTo(v) {var source = 0;if (!this.hasPathTo(v)) {return undefined;}var path = [];for (var i = v; i !== source; i = this.edgeTo[i]) {if (this.edgeTo[i] === null) {console.error("Invalid edgeTo value:", i);return undefined;}path.push(i);}path.push(source);return path;
}function showGraph() {var output = '';for (var i = 0; i < this.vertices; i++) {output += `${i} -> ${this.adj[i].join(' ')}\n`;}document.getElementById('output').innerText = output;
}function readGraphFromFile(filePath) {var fileInput = document.getElementById('fileInput');var file = fileInput.files[0];if (!file) {alert('Please select a file.');return;}var reader = new FileReader();reader.onload = function (event) {var data = event.target.result;var lines = data.split('\n').filter(line => line.trim() !== '');var [vertices, edges] = lines[0].split(' ').map(Number);var graph = new Graph(vertices);for (var i = 1; i <= edges; i++) {var [v, w] = lines[i].split(' ').map(Number);graph.addEdge(v, w);}graph.showGraph();};reader.onerror = function (error) {console.error('Error reading file:', error);};reader.readAsText(file);
}document.getElementById('fileInput').addEventListener('change', readGraphFromFile);function saveGraphToFile() {var graph = new Graph(5); graph.addEdge(0, 1);graph.addEdge(0, 2);graph.addEdge(1, 2);graph.addEdge(2, 3);graph.addEdge(3, 4);var data = `${graph.vertices} ${graph.edges}\n`;var edgesSet = new Set();for (var i = 0; i < graph.vertices; i++) {for (var j = 0; j < graph.adj[i].length; j++) {var w = graph.adj[i][j];if (i < w && !edgesSet.has(`${i}-${w}`)) {edgesSet.add(`${i}-${w}`);data += `${i} ${w}\n`;}}}var blob = new Blob([data], { type: 'text/plain' });var link = document.createElement('a');link.href = URL.createObjectURL(blob);link.download = 'graph.txt';link.click();
}

3. 编写一个从文件读取图的程序。

        同2

4. 构建一个图，用它为你居住地的地图建模。测试一下从一个开始顶点到最后顶点的最短路径。

function Graph(v) {this.vertices = v;this.edges = 0;this.adj = [];this.marked = [];this.edgeTo = [];for (var i = 0; i < this.vertices; i++) {this.adj[i] = [];this.marked[i] = false;this.edgeTo[i] = null;}this.addEdge = addEdge;this.showGraph = showGraph;this.pathTo = pathTo; this.hasPathTo = hasPathTo;this.dfs = dfs;this.bfs = bfs;this.reset = reset;
}function addEdge(v, w) {this.adj[v].push(w);this.adj[w].push(v);this.edges++;
}function showGraph() {for (var i = 0; i < this.vertices; i++) {console.log(i + " -> ");for (var j = 0; j < this.vertices; j++) {if (this.adj[i][j] != undefined) {console.log(this.adj[i][j] + ' ');}}}
}function dfs(v) {this.marked[v] = true;if (this.adj[v] != undefined) {console.log("Visited vertex: " + v);}if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) {if (!this.marked[w]) {this.dfs(w);}}}
}function bfs(s) { var queue = []; this.marked[s] = true; queue.push(s); // 添加到队尾 while (queue.length > 0) { var v = queue.shift(); // 从队首移除 console.log("Visisted vertex: " + v); if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) { if (!this.marked[w]) { this.edgeTo[w] = v; this.marked[w] = true; queue.push(w); } }} } 
}function hasPathTo(v) {return this.marked[v];
}function pathTo(v) {var source = 0;if (!this.hasPathTo(v)) {return undefined;}var path = [];for (var i = v; i !== source; i = this.edgeTo[i]) {if (this.edgeTo[i] === null) {console.error("Invalid edgeTo value:", i);return undefined;}path.push(i);}path.push(source);return path.reverse();
}function reset() {for (var i = 0; i < this.vertices; i++) {this.marked[i] = false;this.edgeTo[i] = null;}
}var graph = new Graph(6);
graph.addEdge(0, 1);
graph.addEdge(0, 3);
graph.addEdge(1, 2);
graph.addEdge(1, 4);
graph.addEdge(2, 5);
graph.addEdge(3, 4);
graph.addEdge(4, 5);
graph.showGraph();
graph.reset();
graph.bfs(0);
var shortestPath = graph.pathTo(5);
console.log("Shortest path from 0 to 5:", shortestPath);graph.reset();
console.log("DFS traversal:");
graph.dfs(0);
graph.reset();
console.log("BFS traversal:");
graph.bfs(0);

5. 对上一题中创建的图执行深度优先搜索和广度优先搜索。

        同4

拓扑排序：

function Graph(v) {this.vertices = v;this.vertexList = [];this.edges = 0;this.adj = [];this.marked = [];this.edgeTo = [];for (var i = 0; i < this.vertices; i++) {this.adj[i] = [];this.marked[i] = false;this.edgeTo[i] = null;}this.addEdge = addEdge;this.showGraph = showGraph;this.pathTo = pathTo; this.hasPathTo = hasPathTo;this.dfs = dfs;this.bfs = bfs;this.topSortHelper = topSortHelper;this.topSort = topSort;
}function addEdge(v, w) {this.adj[v].push(w);this.adj[w].push(v);this.edges++;
}function showGraph() {var visited = [];for (var i = 0; i < this.vertices; i++) {console.log(this.vertexList[i] + " -> ");visited.push(this.vertexList[i]);for (var j = 0; j < this.vertices; j++) {if (this.adj[i][j] != undefined) {if (visited.indexOf(this.vertexList[j]) < 0) {console.log(this.vertexList[j] + ' ');}}}visited.pop();}
}function dfs(v) {this.marked[v] = true;if (this.adj[v] != undefined) {console.log("Visited vertex: " + v);}if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) {if (!this.marked[w]) {this.dfs(w);}}}
}function bfs(s) { var queue = []; this.marked[s] = true; queue.unshift(s); while (queue.length > 0) { var v = queue.shift(); if (typeof(v) !== 'string') {console.log("Visisted vertex: " + v); }if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) { if (!this.marked[w]) { this.edgeTo[w] = v; this.marked[w] = true; queue.unshift(w); } }} } 
}function hasPathTo(v) {return this.marked[v];
}function pathTo(v) {var source = 0;if (!this.hasPathTo(v)) {return undefined;}var path = [];for (var i = v; i !== source; i = this.edgeTo[i]) {if (this.edgeTo[i] === null) {console.error("Invalid edgeTo value:", i);return undefined;}path.push(i);}path.push(source);return path;
}function topSort() {var stack = [];var visited = [];for (var i = 0; i < this.vertices; i++) {visited[i] = false;}for (var i = 0; i < stack.length; i++) {if (visited[i] === false) {this.topSortHelper(i, visited, stack);}}for (var i = 0; i < stack.length; i++) {if (stack[i] != undefined && stack[i] != false) {console.log(this.vertexList[stack[i]]);}}
}function topSortHelper(v, visited, stack) {visited[v] = true;if (this.adj[v] && Array.isArray(this.adj[v])) {for (var w of this.adj[v]) {if (!visited[w]) {this.topSortHelper(visited[w], visited, stack);}}stack.push(v);}
}

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