Floyd算法求每对顶点间最短路径(有向网)
作者：互联网
递推公式：
1.Dist(0)[i][j] = weight[i][j]
2.Dist(n)[i][j] = Min( Dist(n-1)[i][j] , Dist(n-1)[i][n] + Dist(n-1)[n][j] )
Floyd函数：
1 void Floyd(AdjMatrix* G, int Dist[][MAXVEX], int Path[][MAXVEX][MAXVEX])
2 {
3 //Dist 路径长度
4 //若 Path[i][j][k]为1，则 k 是从 i 到 j 当前求得最短路径上的顶点
5 int i = 0, j = 0, k = 0, s = 0;
6 for (i = 0; i < G->vexnum; i++)
7 {
8 for (j = 0; j < G->vexnum; j++)
9 {
10 Dist[i][j] = G->arcs[i][j];
11 if (Dist[i][j] < INFINITY)
12 {
13 Path[i][j][i] = 1;
14 Path[i][j][j] = 1;
15 }
16 }
17 }
18
19 for (k = 0; k < G->vexnum; k++)
20 {
21 for (i = 0; i < G->vexnum; i++)
22 {
23 for (j = 0; j < G->vexnum; j++)
24 {
25 if ((Dist[i][k] + Dist[k][j]) < Dist[i][j])//从 i 经 k 到 j 的一条路径更短
26 {
27 Dist[i][j] = Dist[i][k] + Dist[k][j];
28 for (s = 0; s < G->vexnum; s++)
29 {
30 Path[i][j][s] = Path[i][k][s] || Path[k][j][s];
31 }
32 }
33 }
34 }
35 }
36 }
源代码：
1 #define _CRT_SECURE_NO_WARNINGS
2 #include <stdio.h>
3 #include <stdlib.h>
4 #define MAXVEX 20
5 #define INFINITY 32767
6
7 typedef struct
8 {
9 int vexnum, arcnum;
10 char vex[MAXVEX];
11 int arcs[MAXVEX][MAXVEX];
12 }AdjMatrix;
13
14
15 void Floyd(AdjMatrix* G, int Dist[][MAXVEX], int Path[][MAXVEX][MAXVEX])
16 {
17 //Dist 路径长度
18 //若 Path[i][j][k]为1，则 k 是从 i 到 j 当前求得最短路径上的顶点
19 int i = 0, j = 0, k = 0, s = 0;
20 for (i = 0; i < G->vexnum; i++)
21 {
22 for (j = 0; j < G->vexnum; j++)
23 {
24 Dist[i][j] = G->arcs[i][j];
25 if (Dist[i][j] < INFINITY)
26 {
27 Path[i][j][i] = 1;
28 Path[i][j][j] = 1;
29 }
30 }
31 }
32
33 for (k = 0; k < G->vexnum; k++)
34 {
35 for (i = 0; i < G->vexnum; i++)
36 {
37 for (j = 0; j < G->vexnum; j++)
38 {
39 if ((Dist[i][k] + Dist[k][j]) < Dist[i][j])//从 i 经 k 到 j 的一条路径更短
40 {
41 Dist[i][j] = Dist[i][k] + Dist[k][j];
42 for (s = 0; s < G->vexnum; s++)
43 {
44 Path[i][j][s] = Path[i][k][s] || Path[k][j][s];
45 }
46 }
47 }
48 }
49 }
50 }
51
52
53 int LocateVex(AdjMatrix* G, char vex)
54 {
55 int i = 0;
56 for (i = 0; i < G->vexnum; i++)
57 {
58 if (G->vex[i] == vex)
59 {
60 return i;
61 }
62 }
63 return -1;
64 }
65
66 void Create(AdjMatrix* G)
67 {
68 int weight = 0;
69 int i = 0, j = 0, k = 0;
70 char vex1 = '\0', vex2 = '\0';
71
72 printf("请输入顶点数和弧数(逗号分隔)：");
73 scanf("%d%*c%d", &G->vexnum, &G->arcnum);
74 for (i = 0; i < G->vexnum; i++)//初始化
75 {
76 for (j = 0; j < G->vexnum; j++)
77 {
78 G->arcs[i][j] = INFINITY;
79 }
80 }
81 for (i = 0; i < G->vexnum; i++)
82 {
83 printf("请输入第%d个顶点：", i + 1);
84 scanf(" %c", &G->vex[i]);
85 }
86 for (k = 0; k < G->arcnum; k++)
87 {
88 printf("请输入第%d条弧尾、头和权值(逗号分隔)：", k + 1);
89 scanf(" %c%*c%c%*c%d", &vex1, &vex2, &weight);
90 i = LocateVex(G, vex1);
91 j = LocateVex(G, vex2);
92 G->arcs[i][j] = weight;
93 }
94 }
95
96 void Print(AdjMatrix* G, int Dist[][MAXVEX], int Path[][MAXVEX][MAXVEX])
97 {
98 int i = 0, j = 0, k = 0;
99 for (i = 0; i < G->vexnum; i++)
100 {
101 for (j = 0; j < G->vexnum; j++)
102 {
103 if (i == j)
104 {
105 continue;
106 }
107 printf("%c->%c最短路径长度为%d,经过顶点：", G->vex[i], G->vex[j], Dist[i][j]);
108 for (k = 0; k < G->vexnum; k++)
109 {
110 if (Path[i][j][k])
111 {
112 printf("%c ", G->vex[k]);
113 }
114 }
115 printf("\n");
116 }
117 }
118 }
119
120 int main(void)
121 {
122 int Dist[MAXVEX][MAXVEX] = { 0 };//路径长度
123 int Path[MAXVEX][MAXVEX][MAXVEX] = { 0 };//若 Path[i][j][k]为1，则 k 是从 i 到 j 当前求得最短路径上的顶点
124 AdjMatrix G;
125 Create(&G);
126 Floyd(&G, Dist, Path);
127 Print(&G, Dist, Path);
128 system("pause");
129 return 0;
130 }
源代码
标签：vexnum,Dist,++,MAXVEX,int,算法,Floyd,Path,顶点 来源： https://www.cnblogs.com/lvhui123/p/15858900.html