数据结构之最短路径(1) [迪杰斯特拉算法]

 1 #include "stdafx.h"
 2 #include<iostream>
 3 #include<string>
 4 #define MAX_VERTEX_NUM 100
 5 #define INFINITY 65535
 6 typedef int Pathmatirx[MAX_VERTEX_NUM];//存放最短路径下标的数组
 7 typedef int ShortPathTable[MAX_VERTEX_NUM];//存放到各顶点最短路径的权值之和
 8 using namespace std;
 9 typedef struct Graph            //有向图的邻接矩阵
10 {
11     char vexs[MAX_VERTEX_NUM];  //存放顶点的数组
12     int arcs[MAX_VERTEX_NUM][MAX_VERTEX_NUM];//定义一个临界矩阵
13     int vexnum, arcnum;         //总顶点数、总边数
14 }Graph;
15 
16 int LocateVex(Graph G, char ch) //搜索
17 {
18     for (int i = 0; i < G.vexnum; i++)
19         if (G.vexs[i] == ch)
20             return i;
21     return -1;
22 }
23 
24 void CreateGraph(Graph &G)      //创建无向图
25 {
26     char c1, c2;                //弧尾、弧头
27     int i, j, weight;           //weight为权重
28     cout << "请输入总顶点数、总边数(空格隔开):";
29     cin >> G.vexnum >> G.arcnum;
30     cout << "请输入顶点信息(空格隔开):" << endl;
31     for (i = 0; i < G.vexnum; i++)  
32     {
33         cin >> G.vexs[i];
34     }
35     for (i = 0; i < G.vexnum; i++) 
36         for (j = 0; j < G.vexnum; j++)
37             G.arcs[i][j] = INFINITY;
38     cout << "请输入弧尾、弧头以及权值:" << endl;
39     for (int k = 0; k < G.arcnum; k++)
40     {
41                  cin >> c1 >> c2 >> weight;
42                  i = LocateVex(G, c1);
43                  j = LocateVex(G, c2);
44                  G.arcs[i][j] = weight;
45      }
46 }
47 
48 void ShortestPath_Dijkstra(Graph G, int v0, int prev[], int dist[])//迪杰斯特拉算法
49 {    //求有向图G的v0顶点到其余顶点v最短路径prev[v]及带权长度dist[v]，prev[v]的值为前驱顶点下标，dist[v]表示v0到v的最短路径长度之和。
50     int v , w, k, min;
51     int final[MAX_VERTEX_NUM];  //final[w]=1表示求得顶点v0至v(w)的最短路径
52     for (v = 0; v < G.vexnum; v++)//初始化数据
53     {
54         final[v] = 0;           //全部顶点初始化为未知最短路径状态
55         dist[v] = G.arcs[v0][v];//将与v0点有连线的顶点加上权值
56         prev[v] = 0;            //初始化路径数组prev为0
57     }
58     dist[v0] = 0;               //v0至v0的路径为0
59     final[v0] = 1;              //v0至v0不需要求路径
60     for (v = 1; v < G.vexnum; v++)//开始主循环，每次求得v0到某个v顶点的最短路径
61     {
62         min = INFINITY;        //当前所知离v0顶点最近的距离
63         for (w = 0; w < G.vexnum; w++)//寻找v0最近的顶点
64         {
65             if (!final[w] && dist[w] < min)
66             {
67                 k = w;
68                 min = dist[w];  //w顶点离v0顶点最近
69             }
70         }
71         final[k] = 1;           //将目前找到的最近的顶点值为1
72         for (w = 0; w < G.vexnum; w++)//修正当前最短路径及距离
73         {      //如果经过v顶点的路径比现在这条路径的长度短的话
74             if (!final[w] && (min + G.arcs[k][w] < dist[w]))
75             {   //说明找到了了更短的路径，修改dist[w]和prev[w]
76                 dist[w] = min + G.arcs[k][w];//修改路径长度
77                 prev[w] = k;
78             }
79         }
80     }
81     cout << "起始点:";          //一下就是输出函数
82     cout << G.vexs[v0]<<endl;
83     cout << "从开始点" << G.vexs[v0] << "到各点的最短距离为：" << endl;
84     for (int i = 0; i < G.vexnum; i++)
85         cout << "到" << G.vexs[i] << "的距离为：" << dist[i] << endl;
86 }
87 
88 int main()
89 {
90     Graph G;
91     int prev[MAX_VERTEX_NUM];
92     int dist[MAX_VERTEX_NUM];
93     int v0;
94     CreateGraph(G);
95     cout << "Please input v0:";
96     cin >> v0;
97     ShortestPath_Dijkstra(G, v0, prev, dist);
98 }