js图的数据结构处理----邻链表,广度优先搜索，最小路径

Posted 2020-11-19

//邻居连表
//先加入各顶点，然后加入边

//队列
var Queue = (function(){
var item = new WeakMap();
class Queue{
constructor(){
item.set(this,[]);
}
enqueue(ele){
var ls = item.get(this);
ls.push(ele);
}
dequeue(){
var ls = item.get(this);
return ls.shift();
}
size(){
var ls = item.get(this);
return ls.length;
}
front(){
var ls = item.get(this);
return ls[0];
}
isEmpty(){
var ls = item.get(this);
return !ls.length;
}
print(){
var ls = item.get(this);

for(var i = 0; i < ls.length; i++){
console.log(`${ls[i]}`);
}
}
}
return Queue;
})();

//深度优先搜索

//广度优先搜索
function Graph(){
var vertices = []; //存储所有的顶点
var adjList = {}; //存储所有顶点的相邻顶点

this.addVertex = function(v){
if(!adjList[v]){
vertices.push(v);
adjList[v] = [];
}else{
throw new Error("该顶点已经存在");
}
};
var initializeColor = function(){
var color = {};
for(var i = 0; i < vertices.length; i++){
color[vertices[i]] = ‘white‘;
}
return color;
}

this.addEdge = function(v,w){
if(adjList[v] && adjList[w]){
adjList[v].push(w);
adjList[w].push(v);

}else{
throw new Error("链接不存在的顶点");
}
};
this.toString = function(){
var s = ‘‘;
for (var i=0; i<vertices.length; i++){ //{10}
s += vertices[i] + ‘ -> ‘;
var neighbors = adjList[vertices[i]]; //{11}
for (var j=0; j<neighbors.length; j++){ //{12}
s += neighbors[j] + ‘ ‘;
}
s += ‘ ‘; //{13}
}
return s;
};
this.print = function(){
console.log(this.toString());
};

//广度优先搜索,寻找每个点
//搜索每个点的相邻点
//1、初始化，所有的顶点状态为 white，即没有遍历到
//2、通过该点，拿到相邻点的数组，遍历相邻点
//3、如果相邻点是white，则变灰。并加入队列，进入下一次的循环


this.bfs = function(v,callback){
var color = initializeColor();
queue = new Queue();
queue.enqueue(v);
while(!queue.isEmpty()){
var u = queue.dequeue();
neighbors = adjList[u];
color[u] = ‘grey‘;
for(var i = 0; i < neighbors.length; i++){
var w = neighbors[i];
if(color[w] === ‘white‘){
color[w] = ‘grey‘;
queue.enqueue(w);
}
}
color[u] = "black";
if(callback){
callback(u);
}
}
};

//广度优先算法，计算每个顶点的距离
this.BFS = function(v){
var color = initializeColor();
queue = new Queue();
queue.enqueue(v);
d = []; //距离列表
pred = []; //前溯点
for (var i=0; i<vertices.length; i++){
d[vertices[i]] = 0;
pred[vertices[i]] = null;
}
while(!queue.isEmpty()){
var u = queue.dequeue();
neighbors = adjList[u];
color[u] = ‘grey‘;
for(var i = 0; i < neighbors.length; i++){
var w = neighbors[i];
if(color[w] === ‘white‘){
color[w] = ‘grey‘;
d[w] = d[u] + 1;
pred[w] = u;
queue.enqueue(w);
}
}
color[u] = "black";

}
return {
distances: d,
predecessors: pred
}
}

this.getPath = function(u){
//打印最短路径
//回溯之前的相邻点
var shortestPath = this.BFS(u);
var fromVertex = vertices[0];
for (var i=1; i<vertices.length; i++){

var toVertex = vertices[i],
path = [];
for (var v=toVertex; v!== fromVertex;
v=shortestPath.predecessors[v]) {
path.push(v);
}
path.push(fromVertex);
var s = path.join("-");

console.log(s);
}
}

}

var graph = new Graph();
var myVertices = [‘A‘,‘B‘,‘C‘,‘D‘,‘E‘,‘F‘,‘G‘,‘H‘,‘I‘]; //{7}
for (var i=0; i<myVertices.length; i++){ //{8}
graph.addVertex(myVertices[i]);
}
graph.addEdge(‘A‘, ‘B‘); //{9}
graph.addEdge(‘A‘, ‘C‘);
graph.addEdge(‘A‘, ‘D‘);
graph.addEdge(‘C‘, ‘D‘);
graph.addEdge(‘C‘, ‘G‘);
graph.addEdge(‘D‘, ‘G‘);
graph.addEdge(‘D‘, ‘H‘);
graph.addEdge(‘B‘, ‘E‘);
graph.addEdge(‘B‘, ‘F‘);
graph.addEdge(‘E‘, ‘I‘);

graph.bfs("A",function(cnode){
console.log(cnode);
});

console.log(graph.BFS("A"));
graph.getPath(‘A‘);

/*
如果要计算加权图中的最短路径(例如城市之间最短距离)广度优先搜索未必合适。
* Dijkstra算法解决了单源最短路径问题。 Bellman-Ford算法解决了边权值为负的
单源最短路径问题。 A*搜索算法解决了求仅一对顶点间的最短路径问题，它用经验法则来加速搜
索过程。 Floyd-Warshall算法解决了求所有顶点对间的最短路径这一问题。
*
* */