编写用邻接矩阵表示有向带权网时，图的基本操作的实现函数，主要包括： 1初始化邻接矩阵表示的有向带权图 2 建立邻接矩阵表示的有向带权图(即通过输入图的每条边建立图的邻接矩阵) 3 出邻接矩阵表示的有向带权图(即输出图的每条边)。4编写求最短路径的DijKstra算法函数 void Dijkstra( adjmatrix GA,int dist[],edgenode *path[], int i, int n)，该算法求从顶点i到其余顶点的最短 路径与最短路径长度，并分别存于数组path和dist中。(可选) 5 编写打印输出从源点到每个顶点的最短路径及长度的函数 void PrintPath(int dist[], edgenode *path[],int n)。(可选) 同时建立一个验证操作实现的主函数main)进行测试。数据结构，使用c++语言

好的，以下是实现函数的代码：

#include <iostream>
#include <vector>
#include <limits.h>

#define MAX_VERTEX_NUM 100

using namespace std;

typedef struct {
    int weight;
} edgenode; // 边的信息结构体

typedef struct {
    int vertex[MAX_VERTEX_NUM];
    edgenode edge[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
    int num_vertex, num_edge;
} adjmatrix; // 邻接矩阵

void InitAdjMatrix(adjmatrix& GA) {
    GA.num_vertex = 0;
    GA.num_edge = 0;
    for (int i = 0; i < MAX_VERTEX_NUM; i++) {
        for (int j = 0; j < MAX_VERTEX_NUM; j++) {
            GA.vertex[i] = 0;
            GA.edge[i][j].weight = INT_MAX;
        }
    }
}

void CreateAdjMatrix(adjmatrix& GA) {
    cout << "请输入顶点数和边数：";
    cin >> GA.num_vertex >> GA.num_edge;
    cout << "请按照\"起点 终点 权重\"的格式输入每条边的信息：" << endl;
    for (int i = 0; i < GA.num_edge; i++) {
        int u, v, w;
        cin >> u >> v >> w;
        GA.edge[u][v].weight = w;
    }
}

void PrintAdjMatrix(adjmatrix GA) {
    cout << "图的邻接矩阵为：" << endl;
    for (int i = 0; i < GA.num_vertex; i++) {
        for (int j = 0; j < GA.num_vertex; j++) {
            if (GA.edge[i][j].weight != INT_MAX) {
                cout << GA.edge[i][j].weight << " ";
            } else {
                cout << "∞ ";
            }
        }
        cout << endl;
    }
}

void Dijkstra(adjmatrix GA, int dist[], edgenode* path[], int start, int n) {
    bool visited[MAX_VERTEX_NUM] = {false};
    for (int i = 0; i < n; i++) {
        dist[i] = GA.edge[start][i].weight;
        if (dist[i] != INT_MAX) {
            path[i] = new edgenode;
            path[i]->weight = GA.edge[start][i].weight;
        } else {
            path[i] = NULL;
        }
    }
    visited[start] = true;
    for (int i = 1; i < n; i++) {
        int min_dist = INT_MAX;
        int u = start;
        for (int j = 0; j < n; j++) {
            if (!visited[j] && dist[j] < min_dist) {
                min_dist = dist[j];
                u = j;
            }
        }
        visited[u] = true;
        for (int v = 0; v < n; v++) {
            if (!visited[v] && GA.edge[u][v].weight != INT_MAX && dist[u] + GA.edge[u][v].weight < dist[v]) {
                dist[v] = dist[u] + GA.edge[u][v].weight;
                if (path[v] != NULL) {
                    delete path[v];
                }
                path[v] = new edgenode;
                path[v]->weight = GA.edge[u][v].weight;
            }
        }
    }
}

void PrintPath(int dist[], edgenode* path[], int start, int n) {
    cout << "从源点" << start << "到各个顶点的最短路径为：" << endl;
    for (int i = 0; i < n; i++) {
        if (i != start) {
            cout << start << " -> " << i << " 的最短路径为：";
            if (dist[i] == INT_MAX) {
                cout << "不存在" << endl;
            } else {
                cout << start << " ";
                edgenode* p = path[i];
                while (p != NULL) {
                    cout << "-> " << i << " ";
                    p = path[p - GA.edge[0]];
                }
                cout << "路径长度为：" << dist[i] << endl;
            }
        }
    }
}

int main() {
    adjmatrix GA;
    InitAdjMatrix(GA);
    CreateAdjMatrix(GA);
    PrintAdjMatrix(GA);

    int dist[MAX_VERTEX_NUM];
    edgenode* path[MAX_VERTEX_NUM];
    Dijkstra(GA, dist, path, 0, GA.num_vertex);
    PrintPath(dist, path, 0, GA.num_vertex);

    for (int i = 0; i < GA.num_vertex; i++) {
        if (path[i] != NULL) {
            delete path[i];
        }
    }

    return 0;
}

主函数中我们先初始化邻接矩阵，然后通过用户输入建立有向带权图的邻接矩阵，接着输出邻接矩阵。最后我们调用Dijkstra算法求出源点0到各个顶点的最短路径和最短路径长度，并输出验证。