拓扑排序通常用于确定一个流程,结果并不一定是唯一的。具体的套路是:
- 找入度为0的点入栈,如果没有入度为0的点,说明必然有环路。
- 依此处栈,对于每个出栈的元素,检查它的所有边集,对边集上的每个点的入度-1。
- 若某点入度变成了1,说明这个点变成了孤家寡人,应该入栈
- 第二步,直到全部元素出栈。
- 若出栈元素小于总元素数,说明必有环路。
//拓扑排序
//顶点
function Vertex(name) {
this.name =name;
this.in = 0;
}
Vertex.prototype.setFirstedge = function(edgeNode) {
this.firstEdge = edgeNode;
edgeNode.adjVex.in++;
};
Vertex.prototype.setNext = function(edgeNode){
var temp = this.firstEdge;
if(!temp){
this.firstEdge = edgeNode;
edgeNode.adjVex.in++;
return;
}else{
while(temp){
var temp1 = temp.next;
if(!temp1){
temp.next = edgeNode;
edgeNode.adjVex.in++;
break;
}else{
temp = temp.next;
}
}
}
}
//边
function EdgeNode(){
this.adjVex = arguments[0];
this.weight = arguments[1] ? arguments[1] : undefined;
}
//图
function Graph(vertexs,numEdges){
this.vertexs = vertexs;
this.numVertexs = this.vertexs.length;
this.numEdges =numEdges;
}
//需要引入栈进行计算
function Node(data) {
this.data = data;
}
function Stack(maxSize){
this.maxSize = maxSize;
this.top = -1;
this.data = new Array(maxSize);
}
Stack.prototype.push = function(node){
if(this.top == this.maxSize-1){
return 1;
}
this.top++;
this.data[this.top] = node;
return 0;
}
Stack.prototype.pop = function(){
if(this.top==-1){
return 1;
}
var r = this.data[this.top];
this.data[this.top] = undefined;
this.top--;
return r;
}
Stack.prototype.ergodic = function(){
var s = '';
for (var i = 0; i < this.data.length; i++) {
if(this.data[i]!=null){
s += this.data[i]+',';
}
}
if(s.length){
s = s.substring(0,s.length-1);
}
return s;
}
Stack.prototype.length = function(){
return this.top+1;
}
Graph.prototype.topologicalSort = function() {
var top = 0,count = 0;
var gettop,k;
var result ='';//结果
var stack = new Stack(this.numVertexs)
for (var i = 0; i < this.numVertexs; i++) {
if(this.vertexs[i].in==0){
stack.push(i);
}
}
console.info('初始化完毕(将入度为0的顶点入栈),当前堆栈'+stack.ergodic());
while(stack.length()){
console.info('当前栈:'+stack.ergodic());
gettop = stack.pop();
result += this.vertexs[gettop].name +' ';
count++;
console.info('剥离点'+this.vertexs[gettop].name);
for (var e = this.vertexs[gettop].firstEdge; e; e=e.next) {
k = this.vertexs.indexOf(e.adjVex);
if(!(--this.vertexs[k].in)){
console.info('发现'+this.vertexs[k].name+'入度仅仅为1,必须入栈剥离');
stack.push(k);
}
}
}
if(count<this.numVertexs){
console.info('发生错误,有环路存在');
return false;
}
console.info(result);
return true;
};
var v0 = new Vertex('v0');
var v1 = new Vertex('v1');
var v2 = new Vertex('v2');
var v3 = new Vertex('v3');
var v4 = new Vertex('v4');
var v5 = new Vertex('v5');
var v6 = new Vertex('v6');
var v7 = new Vertex('v7');
var v8 = new Vertex('v8');
var v9 = new Vertex('v9');
var v10 = new Vertex('v10');
var v11 = new Vertex('v11');
var v12 = new Vertex('v12');
var v13 = new Vertex('v13');
v0.setNext(new EdgeNode(v11));
v0.setNext(new EdgeNode(v5));
v0.setNext(new EdgeNode(v4));
v1.setNext(new EdgeNode(v8));
v1.setNext(new EdgeNode(v4));
v1.setNext(new EdgeNode(v2));
v2.setNext(new EdgeNode(v9));
v2.setNext(new EdgeNode(v6));
v2.setNext(new EdgeNode(v5));
v3.setNext(new EdgeNode(v13));
v3.setNext(new EdgeNode(v2));
v4.setNext(new EdgeNode(v7));
v5.setNext(new EdgeNode(v12));
v5.setNext(new EdgeNode(v8));
v6.setNext(new EdgeNode(v5));
v8.setNext(new EdgeNode(v7));
v9.setNext(new EdgeNode(v11));
v9.setNext(new EdgeNode(v10));
v10.setNext(new EdgeNode(v13));
v12.setNext(new EdgeNode(v9));
var g = new Graph([v0,v1,v2,v3,v4,v5,v6,v7,v8,v9,v10,v11,v12,v13],20);
g.topologicalSort();
OUTPUT
初始化完毕(将入度为0的顶点入栈),当前堆栈0,1,3
当前栈:0,1,3
剥离点v3
当前栈:0,1
剥离点v1
发现v2入度仅仅为1,必须入栈剥离
当前栈:0,2
剥离点v2
发现v6入度仅仅为1,必须入栈剥离
当前栈:0,6
剥离点v6
当前栈:0
剥离点v0
发现v5入度仅仅为1,必须入栈剥离
发现v4入度仅仅为1,必须入栈剥离
当前栈:5,4
剥离点v4
当前栈:5
剥离点v5
发现v12入度仅仅为1,必须入栈剥离
发现v8入度仅仅为1,必须入栈剥离
当前栈:12,8
剥离点v8
发现v7入度仅仅为1,必须入栈剥离
当前栈:12,7
剥离点v7
当前栈:12
剥离点v12
发现v9入度仅仅为1,必须入栈剥离
当前栈:9
剥离点v9
发现v11入度仅仅为1,必须入栈剥离
发现v10入度仅仅为1,必须入栈剥离
当前栈:11,10
剥离点v10
发现v13入度仅仅为1,必须入栈剥离
当前栈:11,13
剥离点v13
当前栈:11
剥离点v11
v3 v1 v2 v6 v0 v4 v5 v8 v7 v12 v9 v10 v13 v11
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