用Javascript完成图类
在此代码中已注释掉的功能。您也可以切换到那些。我们还将Queue，Stack和PriorityQueue类移到了可以使用import语句或require调用导入的不同模块中。这是Graph类的完整实现-
示例
const Queue = require("./Queue");
const Stack = require("./Stack");
const PriorityQueue = require("./PriorityQueue");
class Graph {
constructor() {
this.edges = {};
this.nodes = [];
}
addNode(node) {
this.nodes.push(node);
this.edges[node] = [];
}
addEdge(node1, node2, weight = 1) {
this.edges[node1].push({ node: node2, weight: weight});
this.edges[node2].push({ node: node1, weight: weight});
}
addDirectedEdge(node1, node2, weight = 1) {
this.edges[node1].push({ node: node2, weight: weight});
}
//addEdge(node1,node2){
//this.edges[node1].push(node2);
//this.edges[node2].push(node1);
//}
//addDirectedEdge(node1,node2){
//this.edges[node1].push(node2);
//}
display() {
let graph = "";
this.nodes.forEach(node => {
graph += node + "->" + this.edges[node].map(n => n.node).join(", ") + "\n";
});
console.log(graph);
}
BFS(node) {
let q = new Queue(this.nodes.length);
let explored = new Set();
q.enqueue(node);
explored.add(node);
while (!q.isEmpty()) {
let t = q.dequeue();
console.log(t);
this.edges[t].filter(n => !explored.has(n)).forEach(n => {
explored.add(n);
q.enqueue(n);
});
}
}
DFS(node) {
//创建一个堆栈并在其中添加我们的初始节点
let s = new Stack(this.nodes.length);
let explored = new Set();
s.push(node);
//将第一个节点标记为已浏览
explored.add(node);
//我们将继续直到堆栈变空
while (!s.isEmpty()) {
let t = s.pop();
//记录从堆栈中出来的每个元素
console.log(t);
//节点
//直接连接。
//2.我们过滤掉已经探索过的节点。
//3.然后，我们将每个未探索的节点标记为已探索并推动它
//到堆栈。
this.edges[t].filter(n => !explored.has(n)).forEach(n => {
explored.add(n);
s.push(n);
});
}
}
topologicalSortHelper(node, explored, s) {
explored.add(node);
this.edges[node].forEach(n => {
if (!explored.has(n)) {
this.topologicalSortHelper(n, explored, s);
}
});
s.push(node);
}
topologicalSort() {
//创建一个堆栈并在其中添加我们的初始节点
let s = new Stack(this.nodes.length);
let explored = new Set();
this.nodes.forEach(node => {
if (!explored.has(node)) {
this.topologicalSortHelper(node, explored, s);
}
});
while (!s.isEmpty()) {
console.log(s.pop());
}
}
BFSShortestPath(n1, n2) {
let q = new Queue(this.nodes.length);
let explored = new Set();
let distances = { n1: 0};
q.enqueue(n1);
explored.add(n1);
while (!q.isEmpty()) {
let t = q.dequeue();
this.edges[t].filter(n => !explored.has(n)).forEach(n => {
explored.add(n);
distances[n] = distances[t] == undefined ? 1 : distances[t] + 1;
q.enqueue(n);
});
}
return distances[n2];
}
primsMST() {
//初始化将包含MST的图形
const MST = new Graph();
if (this.nodes.length === 0) {
return MST;
}
//选择第一个节点作为起始节点
let s = this.nodes[0];
//创建一个优先级队列并浏览集
let edgeQueue = new PriorityQueue(this.nodes.length * this.nodes.length);
let explored = new Set();
explored.add(s);
MST.addNode(s);
//将所有从此起始节点开始的边以权重作为优先级添加到PQ-
this.edges[s].forEach(edge => {
edgeQueue.enqueue([s, edge.node], edge.weight);
});
//选取最小的边缘并将其添加到新图形中
let currentMinEdge = edgeQueue.dequeue();
while (!edgeQueue.isEmpty()) {
//继续去除边缘，直到我们得到带有未开发节点的边缘
while (!edgeQueue.isEmpty() && explored.has(currentMinEdge.data[1])) {
currentMinEdge = edgeQueue.dequeue();
}
let nextNode = currentMinEdge.data[1];
//再次检查，因为队列可能会变空而没有退还未开发的元素
if (!explored.has(nextNode)) {
MST.addNode(nextNode);
MST.addEdge(currentMinEdge.data[0], nextNode, currentMinEdge.priority);
//再次将所有边添加到PQ-
this.edges[nextNode].forEach(edge => {
edgeQueue.enqueue([nextNode, edge.node], edge.weight);
});
//将此节点标记为exploredexplored.add(nextNode);
s = nextNode;
}
}
return MST;
}
kruskalsMST() {
//初始化将包含MST的图形
const MST = new Graph();
this.nodes.forEach(node => MST.addNode(node));
if (this.nodes.length === 0) {
return MST;
}
//创建一个优先级队列
let edgeQueue = new PriorityQueue(this.nodes.length * this.nodes.length);
//将所有边添加到队列中：
for (let node in this.edges) {
this.edges[node].forEach(edge => {
edgeQueue.enqueue([node, edge.node], edge.weight);
});
}
let uf = new UnionFind(this.nodes);
//循环直到我们探索所有节点或队列为空
while (!edgeQueue.isEmpty()) {
//使用解构获取边缘数据
let nextEdge = edgeQueue.dequeue();
let nodes = nextEdge.data;
let weight = nextEdge.priority;
if (!uf.connected(nodes[0], nodes[1])) {
MST.addEdge(nodes[0], nodes[1], weight);
uf.union(nodes[0], nodes[1]);
}
}
return MST;
}
djikstraAlgorithm(startNode) {
let distances = {};
//存储对先前节点的引用
let prev = {};
let pq = new PriorityQueue(this.nodes.length * this.nodes.length);
//以外的所有节点的距离设置为无限
distances[startNode] = 0;
pq.enqueue(startNode, 0);
this.nodes.forEach(node => {
if (node !== startNode) distances[node] = Infinity;
prev[node] = null;
});
while (!pq.isEmpty()) {
let minNode = pq.dequeue();
let currNode = minNode.data;
let weight = minNode.priority;
this.edges[currNode].forEach(neighbor => {
let alt = distances[currNode] + neighbor.weight;
if (alt < distances[neighbor.node]) {
distances[neighbor.node] = alt;
prev[neighbor.node] = currNode;
pq.enqueue(neighbor.node, distances[neighbor.node]);
}
});
}
return distances;
}
floydWarshallAlgorithm() {
let dist = {};
for (let i = 0; i < this.nodes.length; i++) {
dist[this.nodes[i]] = {};
//对于现有的边缘，将dist设置为与weight相同
this.edges[this.nodes[i]].forEach(
e => (dist[this.nodes[i]][e.node] = e.weight)
);
this.nodes.forEach(n => {
//对于所有其他节点，将其分配给infinity-
if (dist[this.nodes[i]][n] == undefined)
dist[this.nodes[i]][n] = Infinity;
//对于自身边缘，将dist分配为0-
if (this.nodes[i] === n) dist[this.nodes[i]][n] = 0;
});
}
this.nodes.forEach(i => {
this.nodes.forEach(j => {
this.nodes.forEach(k => {
//检查从i到k再从k到j是否更好
//而不是直接从i转到j。如果是，则更新
//我将j值更改为新值
if (dist[i][k] + dist[k][j] < dist[i][j])
dist[i][j] = dist[i][k] + dist[k][j];
});
});
});
return dist;
}
}
class UnionFind {
constructor(elements) {
//断开连接的组件数量
this.count = elements.length;
//跟踪连接的组件
this.parent = {};
//初始化数据结构，使所有
//元素有自己的父母
elements.forEach(e => (this.parent[e] = e));
}
union(a, b) {
let rootA = this.find(a);
let rootB = this.find(b);
//根是相同的，因此它们已经连接。
if (rootA === rootB) return;
//始终将根较小的元素作为父元素。
if (rootA < rootB) {
if (this.parent[b] != b) this.union(this.parent[b], a);
this.parent[b] = this.parent[a];
} else {
if (this.parent[a] != a) this.union(this.parent[a], b);
this.parent[a] = this.parent[b];
}
}
//返回节点的最终父级
find(a) {
while (this.parent[a] !== a) {
a = this.parent[a];
}
return a;
}
//检查2个节点的连接
connected(a, b) {
return this.find(a) === this.find(b);
}
}