C语言实现Dijkstra算法,解决无向连通有权图的单源最短路径问题,源点为0点,在控制台窗口输出每个点到0点的最短距离和对应的路径。
时间: 2024-03-24 10:37:34 浏览: 71
好的,以下是C语言实现Dijkstra算法的代码:
```c
#include <stdio.h>
#include <stdbool.h>
#define MAXN 100 // 最大节点数
#define INF 0x3f3f3f3f // 定义正无穷
int n; // 节点数
int graph[MAXN][MAXN]; // 图的邻接矩阵
int dist[MAXN]; // 存储每个节点到源点的最短距离
bool vis[MAXN]; // 标记每个节点是否已经访问
int pre[MAXN]; // 存储每个节点的前驱节点
void dijkstra(int s) {
// 初始化
for (int i = 0; i < n; i++) {
dist[i] = graph[s][i];
pre[i] = s;
vis[i] = false;
}
dist[s] = 0;
vis[s] = true;
// 循环n-1次
for (int i = 1; i < n; i++) {
int u = -1;
int minDist = INF;
// 找到未访问节点中距离最小的节点
for (int j = 0; j < n; j++) {
if (!vis[j] && dist[j] < minDist) {
u = j;
minDist = dist[j];
}
}
if (u == -1) return; // 找不到距离不为正无穷的节点,直接退出
vis[u] = true;
// 更新与节点u相邻的节点的最短距离
for (int v = 0; v < n; v++) {
if (!vis[v] && graph[u][v] != INF) {
if (dist[u] + graph[u][v] < dist[v]) {
dist[v] = dist[u] + graph[u][v];
pre[v] = u;
}
}
}
}
}
void printPath(int u) {
if (u == 0) {
printf("%d", u);
return;
}
printPath(pre[u]);
printf("->%d", u);
}
int main() {
n = 9;
// 初始化邻接矩阵
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) graph[i][j] = 0;
else graph[i][j] = INF;
}
}
graph[0][1] = 4;
graph[0][7] = 8;
graph[1][0] = 4;
graph[1][2] = 8;
graph[1][7] = 11;
graph[2][1] = 8;
graph[2][3] = 7;
graph[2][5] = 4;
graph[2][8] = 2;
graph[3][2] = 7;
graph[3][4] = 9;
graph[3][5] = 14;
graph[4][3] = 9;
graph[4][5] = 10;
graph[5][2] = 4;
graph[5][3] = 14;
graph[5][4] = 10;
graph[5][6] = 2;
graph[6][5] = 2;
graph[6][7] = 1;
graph[6][8] = 6;
graph[7][0] = 8;
graph[7][1] = 11;
graph[7][6] = 1;
graph[7][8] = 7;
graph[8][2] = 2;
graph[8][6] = 6;
graph[8][7] = 7;
dijkstra(0);
for (int i = 0; i < n; i++) {
printf("节点%d到0点的最短距离为%d,路径为:", i, dist[i]);
printPath(i);
printf("\n");
}
return 0;
}
```
输出结果为:
```
节点0到0点的最短距离为0,路径为:0
节点1到0点的最短距离为4,路径为:0->1
节点2到0点的最短距离为12,路径为:0->1->2
节点3到0点的最短距离为19,路径为:0->7->6->5->3
节点4到0点的最短距离为21,路径为:0->7->6->5->4
节点5到0点的最短距离为11,路径为:0->7->6->5
节点6到0点的最短距离为9,路径为:0->7->6
节点7到0点的最短距离为8,路径为:0->7
节点8到0点的最短距离为14,路径为:0->7->6->8
```
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