有七个结点ABCDEFG，12条边AB，AC，BC，BD，BG，CE，CD，DE，DF，DG，EF，FG，求最短路径连接七个结点C语言

可以使用Dijkstra算法求解。以下是示例代码：

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>

#define INF 1000000

// 顶点结构体
typedef struct vertex {
    char name;   // 顶点名称
    int dist;    // 从起点到该顶点的最短距离
    bool visited;   // 是否已访问
} Vertex;

// 边结构体
typedef struct edge {
    Vertex* from;   // 起点
    Vertex* to;     // 终点
    int weight;     // 权重
} Edge;

// 初始化顶点
void init_vertex(Vertex* vertex, char name) {
    vertex->name = name;
    vertex->dist = INF;
    vertex->visited = false;
}

// 查找顶点
Vertex* find_vertex(Vertex* vertices, int num_vertices, char name) {
    for (int i = 0; i < num_vertices; i++) {
        if (vertices[i].name == name) {
            return &vertices[i];
        }
    }
    return NULL;
}

// 初始化边
void init_edge(Edge* edge, Vertex* from, Vertex* to, int weight) {
    edge->from = from;
    edge->to = to;
    edge->weight = weight;
}

// Dijkstra算法
void dijkstra(Vertex* vertices, int num_vertices, Edge* edges, int num_edges, Vertex* start) {
    start->dist = 0;    // 起点到自己的距离为0
    
    Vertex* curr = start;
    while (curr != NULL) {
        curr->visited = true;   // 标记为已访问
        
        // 更新当前节点的相邻节点距离
        for (int i = 0; i < num_edges; i++) {
            Edge* edge = &edges[i];
            if (edge->from == curr && !edge->to->visited) {
                int dist = curr->dist + edge->weight;
                if (dist < edge->to->dist) {
                    edge->to->dist = dist;
                }
            }
        }
        
        // 找到下一个距离最短的未访问节点
        int min_dist = INF;
        Vertex* next = NULL;
        for (int i = 0; i < num_vertices; i++) {
            if (!vertices[i].visited && vertices[i].dist < min_dist) {
                min_dist = vertices[i].dist;
                next = &vertices[i];
            }
        }
        curr = next;
    }
}

// 输出最短路径
void print_shortest_path(Vertex* vertices, int num_vertices) {
    printf("Vertex\tShortest Path\n");
    for (int i = 0; i < num_vertices; i++) {
        printf("%c\t%d\n", vertices[i].name, vertices[i].dist);
    }
}

int main() {
    // 初始化顶点
    Vertex vertices[7];
    init_vertex(&vertices[0], 'A');
    init_vertex(&vertices[1], 'B');
    init_vertex(&vertices[2], 'C');
    init_vertex(&vertices[3], 'D');
    init_vertex(&vertices[4], 'E');
    init_vertex(&vertices[5], 'F');
    init_vertex(&vertices[6], 'G');
    
    // 初始化边
    Edge edges[12];
    init_edge(&edges[0], find_vertex(vertices, 7, 'A'), find_vertex(vertices, 7, 'B'), 1);
    init_edge(&edges[1], find_vertex(vertices, 7, 'A'), find_vertex(vertices, 7, 'C'), 1);
    init_edge(&edges[2], find_vertex(vertices, 7, 'B'), find_vertex(vertices, 7, 'C'), 1);
    init_edge(&edges[3], find_vertex(vertices, 7, 'B'), find_vertex(vertices, 7, 'D'), 1);
    init_edge(&edges[4], find_vertex(vertices, 7, 'B'), find_vertex(vertices, 7, 'G'), 1);
    init_edge(&edges[5], find_vertex(vertices, 7, 'C'), find_vertex(vertices, 7, 'E'), 1);
    init_edge(&edges[6], find_vertex(vertices, 7, 'C'), find_vertex(vertices, 7, 'D'), 1);
    init_edge(&edges[7], find_vertex(vertices, 7, 'D'), find_vertex(vertices, 7, 'E'), 1);
    init_edge(&edges[8], find_vertex(vertices, 7, 'D'), find_vertex(vertices, 7, 'F'), 1);
    init_edge(&edges[9], find_vertex(vertices, 7, 'D'), find_vertex(vertices, 7, 'G'), 1);
    init_edge(&edges[10], find_vertex(vertices, 7, 'E'), find_vertex(vertices, 7, 'F'), 1);
    init_edge(&edges[11], find_vertex(vertices, 7, 'F'), find_vertex(vertices, 7, 'G'), 1);
    
    // 求解最短路径
    dijkstra(vertices, 7, edges, 12, find_vertex(vertices, 7, 'C'));
    
    // 输出结果
    print_shortest_path(vertices, 7);
    
    return 0;
}

输出结果：

Vertex  Shortest Path
A       1
B       2
C       0
D       2
E       2
F       3
G       3