迪克特斯拉 Dijkstra 最短路径算法

在进行三维管线连通性分析时，需要运用到最短路径算法，主要思路为首先初始化图，然后将查询到的管点以及管线分别作为图的顶点数以及边数。

export default {

    PathMatirx: [], // 用于存储最短路径下标的数组，下标为各个顶点，值为下标顶点的前驱顶点
    ShortPathTable: [], //用于存储到各点最短路径的权值和
    G: {},
    clear: function () {
        this.G = {};
        this.PathMatirx = [];
        this.ShortPathTable = [];
    },
    //初始化图
    init: function (points, lines) {
        this.clear();
        this.MGraph(this.G);
        this.createMGraph(points, lines);
        return this.G;
    },
    path(start, end) {
        this.Dijkstra2(start);
        return this.PrintVn(start, end);
    },
    //创建图
    createMGraph: function (points, lines) {
        let G = this.G;
        G.numVertexes = points.length; //设置顶点数
        G.numEdges = lines.length; //设置边数

        //录入顶点信息
        for (let i = 0; i < G.numVertexes; i++) {
            G.vexs[i] = points[i].feature.attributes.WTDH;//'V' + i; //scanf('%s'); //ascii码转字符 //String.fromCharCode(i + 65);
        }
        // console.log(G.vexs); //打印顶点

        //无向图构建
        for (let i = 0; i < G.numVertexes; i++) {
            G.arc[i] = [];
        }
        for (let i = 0; i < G.numVertexes; i++) {
            for (let j = i; j < G.numVertexes; j++) {
                if (i === j) {
                    G.arc[i][j] = 0;
                } else {
                    G.arc[i][j] = Infinity;
                    G.arc[j][i] = Infinity;
                    for (let k = 0; k < G.numEdges; k++) {
                        let line = lines[k];
                        if ((line.feature.attributes.QDDH === G.vexs[i] && line.feature.attributes.ZDDH === G.vexs[j]) ||
                            (line.feature.attributes.QDDH === G.vexs[j] && line.feature.attributes.ZDDH === G.vexs[i])) {
                            G.arc[i][j] = parseFloat(line.feature.attributes.SHAPE_LENG || "0");
                            G.arc[j][i] = parseFloat(line.feature.attributes.SHAPE_LENG || "0");
                        }
                    }

                }
            }
        }

        //有向图构建
        // for (let i = 0; i < G.numVertexes; i++) {
        //     G.arc[i] = [];
        //     for (let j = 0; j < G.numVertexes; j++) {
        //         if (i === j) {
        //             G.arc[i][j] = 0;
        //         } else {
        //             G.arc[i][j] = Infinity;
        //             for (let k = 0; k < G.numEdges; k++) {
        //                 let line = lines[k];
        //                 if ((line.QDDH === G.vexs[i] && line.ZDDH === G.vexs[j])) {
        //                     G.arc[i][j] = line.SHAPE_Leng;
        //                 }
        //                 if ((line.QDDH === G.vexs[j] && line.ZDDH === G.vexs[i])) {
        //                     G.arc[j][i] = line.SHAPE_Leng;
        //                 }
        //             }
        //
        //         }
        //     }
        // }

        //邻接矩阵初始化
        // for (let i = 0; i < G.numVertexes; i++) {
        //     G.arc[i] = [];
        //     for (let j = 0; j < G.numVertexes; j++) {
        //         G.arc[i][j] = Arr2[i][j]; //INFINITY;
        //     }
        // }
        // console.log(G.arc); //打印邻接矩阵
    },
    // 定义图结构
    MGraph: function (G) {
        G.vexs = []; //顶点表
        G.arc = []; // 边表
        G.numVertexes = null; //图中当前的顶点数
        G.numEdges = null; //图中当前的边数
    },
    Dijkstra2: function (n) {
        let G = this.G;
        let k, min;
        let final = [];
        for (let v = 0; v < G.numVertexes; v++) {
            final[v] = 0;
            this.ShortPathTable[v] = G.arc[n][v];
            this.PathMatirx[v] = 0;
        }
        this.ShortPathTable[0] = 0;
        final[0] = 1;

        //初始化数据
        for (let v = 0; v < G.numVertexes; v++) {
            if (v === n) {
                continue
            }
            min = Infinity;
            for (let w = 0; w < G.numVertexes; w++) { //寻找离V0最近的顶点
                if (!final[w] && this.ShortPathTable[w] < min) {
                    k = w;
                    min = this.ShortPathTable[w]; //w 顶点离V0顶点更近
                }
            }
            // console.log("b " + ShortPathTable, k, min);
            final[k] = 1; //将目前找到的最近的顶点置位1
            for (let w = 0; w < G.numVertexes; w++) { //修正当前最短路径及距离
                if (!final[w] && (min + G.arc[k][w] < this.ShortPathTable[w])) { //说明找到了更短的路径，修改PathMatirx[w]和ShortPathTable[w]
                    this.ShortPathTable[w] = min + G.arc[k][w];
                    this.PathMatirx[w] = k;
                }
            }
        }

    },

    PrintVn: function (start, end) {
        let G = this.G;
        // console.log(this.ShortPathTable, this.PathMatirx);
        //打印V0-Vn最短路径
        // console.log("%s-%s 最小权值和: %d", G.vexs[start], G.vexs[end], this.ShortPathTable[end]);
        //打印最短路线
        let temp = end,
            str = '';
        let arr = [];
        arr.push(end);
        while (temp !== 0) {
            str = '->' + G.vexs[temp] + str;
            temp = this.PathMatirx[temp];
            arr.push(temp);
        }
        str = G.vexs[start] + str;
        // console.log('最短路线：' + str);
        arr.pop();
        arr.push(start);
        // console.log(arr);
        return {
            ShortPathTable: this.ShortPathTable,
            PathMatirx: this.PathMatirx,
            path: str,
            pathArr: arr,
            Graphic: this.G,
        }
    }

}