最短路径问题 C语言实现
Dijkstra算法
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
![](https://images.cnblogs.com/OutliningIndicators/ExpandedBlockStart.gif)
1 /* 2 The Greedy Approach 3 The Shortest Path Problem 4 Time: 2012-11-19 17:56:57 5 Input: A weighted directed graph G = (V,E), where V = {1,2,...,n}. 6 Output: The distance from vertex 1 to every other vertex in G. 7 */ 8 #include <stdio.h> 9 #include <stdlib.h> 10 #include <limits.h> 11 #include <stdbool.h> 12 13 typedef struct graph{ 14 int **matrix; //图的邻接矩阵 15 int vertex; //图的顶点数 16 int edge; //图的边数 17 }Graph; 18 19 void CreareGraph(Graph *g){ 20 //采用邻接矩阵存储结构,构造有向图 21 int vertex, edge; 22 int i, j; 23 int begin, end, weight; 24 25 printf("Please enter the values of vertex and edge:\n"); 26 scanf("%d %d", &vertex, &edge); 27 if (vertex>0 && edge > 0){ 28 (*g).vertex = vertex; 29 (*g).edge = edge; 30 (*g).matrix = (int **)malloc(sizeof(int *) * (*g).vertex); //为图的邻接矩阵分配空间 31 if (NULL == (*g).matrix){ 32 printf("Memory allocation failed. Goodbye."); 33 exit(EXIT_FAILURE); 34 } 35 for (i=0; i<(*g).vertex; ++i){ 36 (*g).matrix[i] = (int *)malloc(sizeof(int) * (*g).vertex); 37 if (NULL == (*g).matrix[i]){ 38 printf("Memory allocation failed. Goodbye."); 39 exit(EXIT_FAILURE); 40 } 41 } 42 43 for (i=0; i<(*g).vertex; ++i) //初始化矩阵 44 for(j=0; j<(*g).vertex; ++j) 45 (*g).matrix[i][j] = INT_MAX; //将图的顶点间权值初始化为无穷大 46 printf("Please input vertexs and weights between vertexs:\n"); 47 for (i=0; i<(*g).edge; ++i){ 48 scanf("%d %d %d", &begin, &end, &weight); 49 (*g).matrix[begin][end] = weight; 50 } 51 } 52 else{ 53 printf("Illegal vertices or edge number."); 54 exit(EXIT_FAILURE); 55 } 56 } 57 58 void Dijkstra(Graph const *g, int *dist){ 59 int i, j; 60 bool *visited = NULL; 61 int min = INT_MAX; 62 int nth; 63 64 65 dist[0] = 0; 66 for (i=1; i<(*g).vertex; ++i) 67 dist[i] = (*g).matrix[0][i]; 68 /*for (i=0; i<(*g).vertex; ++i) 69 printf("%d ", dist[i]); 70 putchar('\n');*/ 71 visited = (bool *)malloc(sizeof(bool) * (*g).vertex); //记录节点是否被访问过 72 if (NULL == visited){ 73 printf("Memory allocation failed. Goodbye."); 74 exit(EXIT_FAILURE); 75 } 76 for (i=0; i<(*g).vertex; ++i) //初始化节点均未被访问过 77 visited[i] = false; 78 79 visited[0] = true; 80 for (i=1; i<(*g).vertex; ++i){ 81 for (j=1; j<(*g).vertex; ++j){ //找到最小的dist[j] 82 if (visited[j] == false && dist[j] <= min){ 83 min = dist[j]; 84 nth = j; 85 } 86 } 87 min = INT_MAX; //min被重新赋值为INT_MAX 88 visited[nth] = true; 89 for (j=1; j<(*g).vertex; ++j){ 90 if ( visited[j] == false && //如果该节点尚未被访问 91 (*g).matrix[nth][j]!=INT_MAX && //nth与j节点连通 92 dist[nth]+(*g).matrix[nth][j]<dist[j] ) //且………… 93 dist[j] = dist[nth]+(*g).matrix[nth][j]; //更新dist[j] 94 } 95 } 96 } 97 98 void ShowDist(int const *dist, int n){ 99 int i; 100 printf("The Shortest Path(form the first vertex to others):\n"); 101 for (i=0; i<n; ++i) 102 printf("%d ", dist[i]); 103 putchar('\n'); 104 } 105 106 int main(int argc, char *argv[]) 107 { 108 Graph g; 109 int *dist = NULL; 110 int n; 111 int i, j; 112 113 CreareGraph(&g); 114 /*for (i=0; i<g.vertex; ++i) 115 for (j=0; j<g.vertex; ++j) 116 if (g.matrix[i][j] != INT_MAX) 117 printf("%d ", g.matrix[i][j]); 118 putchar('\n');*/ 119 dist = (int *)malloc(sizeof(int) * g.vertex); //为存储最短路径的数组分配空间 120 if (NULL == dist){ 121 printf("Memory allocation failed. Goodbye."); 122 exit(EXIT_FAILURE); 123 } 124 Dijkstra(&g, dist); 125 n = g.vertex; 126 ShowDist(dist, n); 127 128 free(dist); 129 for (i=0; i<n; ++i) 130 free(g.matrix[i]); 131 free(g.matrix); 132 133 return 0; 134 }
在gcc 4.6.2和visual studio 2012下测试通过