Dijikstra算法是从一个顶点到其余各顶点的最短路径算法,解决的是有向图中最短路径问题。该算法是由荷兰计算机科学家迪杰斯特拉于1959年提出的。
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程序(去除了原文中非标准的C语言代码):
#include程序运行结果:#define INFINITY 9999#define MAX 10void dijikstra(int G[MAX][MAX], int n, int startnode);int main(){ int G[MAX][MAX], i, j, n, u; printf("\nEnter the no. of vertices:: "); scanf("%d", &n); printf("\nEnter the adjacency matrix::\n"); for(i=0;i < n;i++) for(j=0;j < n;j++) scanf("%d", &G[i][j]); printf("\nEnter the starting node:: "); scanf("%d", &u); dijikstra(G,n,u);}void dijikstra(int G[MAX][MAX], int n, int startnode){ int cost[MAX][MAX], distance[MAX], pred[MAX]; int visited[MAX], count, mindistance, nextnode, i,j; for(i=0;i < n;i++) for(j=0;j < n;j++) if(G[i][j]==0) cost[i][j]=INFINITY; else cost[i][j]=G[i][j]; for(i=0;i< n;i++) { distance[i]=cost[startnode][i]; pred[i]=startnode; visited[i]=0; } distance[startnode]=0; visited[startnode]=1; count=1; while(count < n-1) { mindistance=INFINITY; for(i=0;i < n;i++) if(distance[i] < mindistance&&!visited[i]) { mindistance=distance[i]; nextnode=i; } visited[nextnode]=1; for(i=0;i < n;i++) if(!visited[i]) if(mindistance+cost[nextnode][i] < distance[i]) { distance[i]=mindistance+cost[nextnode][i]; pred[i]=nextnode; } count++; } for(i=0;i < n;i++) if(i!=startnode) { printf("\nDistance of %d = %d", i, distance[i]); printf("\nPath = %d", i); j=i; do { j=pred[j]; printf(" <-%d", j); } while(j!=startnode); } printf("\n");}
Enter the no. of vertices:: 4Enter the adjacency matrix::0 1 1 11 0 1 01 1 0 11 0 1 0Enter the starting node:: 1Distance of 0 = 1Path = 0 <-1Distance of 2 = 1Path = 2 <-1Distance of 3 = 2Path = 3 <-0 <-1