用c语言写一个输出关键路径 功能描述：根据创建的有向图及权重，调用TopologicalSort函数应用栈结构输出关键路径。 输出格式printf("Criticalpath: <%d,%d> length: %d\n", 开始节点数组index下标, 下一节点数组index下标, 权重);

好的，以下是用C语言编写输出关键路径的示例代码：

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

#define MAX_VERTEX_NUM 20
#define INFINITY 65535

typedef struct {
    int arc[MAX_VERTEX_NUM][MAX_VERTEX_NUM]; // 邻接矩阵
    int indegree[MAX_VERTEX_NUM]; // 入度
    int ve[MAX_VERTEX_NUM]; // 事件最早发生时间
    int vl[MAX_VERTEX_NUM]; // 事件最迟发生时间
    int path[MAX_VERTEX_NUM][MAX_VERTEX_NUM]; // 路径
    int vertex_num; // 顶点数
    int arc_num; // 弧数
} Graph;

typedef struct {
    int data[MAX_VERTEX_NUM];
    int top;
} Stack;

// 初始化栈
void InitStack(Stack *stack) {
    stack->top = -1;
}

// 判断栈是否为空
bool StackIsEmpty(Stack *stack) {
    return stack->top == -1;
}

// 判断栈是否已满
bool StackIsFull(Stack *stack) {
    return stack->top == MAX_VERTEX_NUM - 1;
}

// 入栈
void Push(Stack *stack, int data) {
    if (StackIsFull(stack)) {
        printf("Stack is full.\n");
        exit(1);
    }
    stack->data[++stack->top] = data;
}

// 出栈
int Pop(Stack *stack) {
    if (StackIsEmpty(stack)) {
        printf("Stack is empty.\n");
        exit(1);
    }
    return stack->data[stack->top--];
}

// 拓扑排序
bool TopologicalSort(Graph *graph, Stack *stack) {
    int i, j, k, count = 0;
    InitStack(stack);
    for (i = 0; i < graph->vertex_num; i++) {
        if (graph->indegree[i] == 0) {
            Push(stack, i);
        }
    }
    while (!StackIsEmpty(stack)) {
        j = Pop(stack);
        printf("%d ", j);
        count++;
        for (k = 0; k < graph->vertex_num; k++) {
            if (graph->arc[j][k] != INFINITY) {
                if (--graph->indegree[k] == 0) {
                    Push(stack, k);
                }
                if (graph->ve[j] + graph->arc[j][k] > graph->ve[k]) {
                    graph->ve[k] = graph->ve[j] + graph->arc[j][k];
                }
            }
        }
    }
    if (count < graph->vertex_num) {
        return false;
    } else {
        return true;
    }
}

// 关键路径
void CriticalPath(Graph *graph) {
    int i, j, k, e, l;
    Stack stack;
    bool result;
    result = TopologicalSort(graph, &stack);
    if (!result) {
        printf("The graph has a circle.\n");
        exit(1);
    }
    for (i = 0; i < graph->vertex_num; i++) {
        graph->vl[i] = graph->ve[graph->vertex_num - 1];
    }
    while (!StackIsEmpty(&stack)) {
        j = Pop(&stack);
        for (k = 0; k < graph->vertex_num; k++) {
            if (graph->arc[j][k] != INFINITY) {
                if (graph->vl[k] - graph->arc[j][k] < graph->vl[j]) {
                    graph->vl[j] = graph->vl[k] - graph->arc[j][k];
                }
            }
        }
    }
    for (i = 0; i < graph->vertex_num; i++) {
        for (j = 0; j < graph->vertex_num; j++) {
            graph->path[i][j] = -1;
        }
    }
    for (i = 0; i < graph->vertex_num; i++) {
        for (j = 0; j < graph->vertex_num; j++) {
            if (graph->arc[i][j] != INFINITY) {
                e = graph->ve[i];
                l = graph->vl[j] - graph->arc[i][j];
                if (e == l) {
                    printf("Criticalpath: <%d,%d> length: %d\n", i, j, graph->arc[i][j]);
                }
            }
        }
    }
}

int main() {
    Graph graph;
    int i, j, k, m, n, w;
    printf("Please input the vertex number and the arc number: ");
    scanf("%d %d", &graph.vertex_num, &graph.arc_num);
    for (i = 0; i < graph.vertex_num; i++) {
        for (j = 0; j < graph.vertex_num; j++) {
            graph.arc[i][j] = INFINITY;
        }
    }
    for (k = 0; k < graph.arc_num; k++) {
        printf("Please input the start vertex, the next vertex and the weight: ");
        scanf("%d %d %d", &m, &n, &w);
        graph.arc[m][n] = w;
        graph.indegree[n]++;
    }
    CriticalPath(&graph);
    return 0;
}

这个程序通过邻接矩阵来存储有向图，使用拓扑排序来求出每个事件的最早发生时间和最晚发生时间，然后求出关键路径。其中，INFINITY 表示两个顶点之间没有连边。