C语言弗洛伊德算法的实现

弗洛伊德算法和迪杰斯特拉算法一样，用于求两个节点之间的最短路径，过程也比迪杰斯特拉算法更为简单。以下是实现代码：

首先仍然是预定义和类型定义：

#define OK 1#define ERROR 0#define Max_Int 37262#define MVNum 100typedef int Status;typedef char VerTexType;typedef int ArcType;typedef struct{VerTexType vex[MVNum];ArcType arc[MVNum][MVNum];int vexnum, arcnum;}AMGraph;

并定义两个二维数组：

int Path[MVNum][MVNum];ArcType D[MVNum][MVNum];

创建有向图：

int LocateVex(AMGraph *G, VerTexType v){int i;for (i = 0; i < G->vexnum; i++){if (G->vex[i] == v)return i;}return -1;}Status CreateUDN(AMGraph *G){VerTexType v1, v2;ArcType w;int i, j, k;printf("输入总节点数、总边数：");scanf("%d %d", &G->vexnum, &G->arcnum);printf("输入节点的值：");fflush(stdin);for (i = 0; i < G->vexnum; i++){scanf("%c", &G->vex[i]);}for (i = 0; i < G->vexnum; i++)for (j = 0; j < G->vexnum; j++){G->arc[i][j] = Max_Int;}for (k = 0; k < G->arcnum; k++){fflush(stdin);printf("依次输入边的两个顶点以及边的权值：");scanf("%c %c %d", &v1, &v2, &w);i = LocateVex(G, v1);j = LocateVex(G, v2);G->arc[i][j] = w;}return OK;}

弗洛伊德算法：

void ShortestPath_Floyd(AMGraph G){int i, j, k;for (i = 0; i < G.vexnum;i++)for (j = 0; j < G.vexnum; j++){D[i][j] = G.arc[i][j];if (D[i][j] < Max_Int)Path[i][j] = 0;elsePath[i][j] = -1;}for (k = 0; k < G.vexnum;k++)for (i = 0; i < G.vexnum;i++)for (j = 0; j < G.vexnum; j++){if (D[i][j]>D[i][k] + D[k][j]){D[i][j] = D[i][k] + D[k][j];Path[i][j] = Path[k][j];}}}

初始化：将D[i][j]赋值为i,j边的权值，并判断其权值若不为最大值（Max_Int），则将Path[i][j]赋值为0，否则赋值为-1.

依次判断i,j下标的边的权值是否大于i、k和k、j下标边的权值之和，若大于，则说明目前记录的并非最短路径，将i、k和k、j下标边的权值之和赋值给D[i][k]，并将Path[k][j]赋值给Path[i][j]。

加入main():

int main(void){int i, j;AMGraph G;CreateUDN(&G);ShortestPath_Floyd(G);for (i = 1; i < G.vexnum; i++){if (D[0][i] == Max_Int)printf("0无法到达%c\n", G.vex[i]);elseprintf("0到%c的权值为：%d\n", G.vex[i], D[0][i]);}return 0;}