最短路径问题 C语言实现

Dijkstra算法

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  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