用c语言实现：假设图G采用邻接表存储，分别设计实现以下要求的算法并测试: (1)求出图G中每个顶点的出度; (2)判断图G中是否存在边<ij>; (3)将图的邻接表存储结构转换为邻接矩阵

好的，以下是C语言的实现：

1. 求出图G中每个顶点的出度

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

// 邻接表节点结构体
struct AdjListNode {
    int dest;
    struct AdjListNode* next;
};

// 邻接表头结构体
struct AdjList {
    struct AdjListNode* head;
};

// 图结构体
struct Graph {
    int V;
    struct AdjList* array;
};

// 创建节点
struct AdjListNode* newAdjListNode(int dest) {
    struct AdjListNode* newNode = (struct AdjListNode*)malloc(sizeof(struct AdjListNode));
    newNode->dest = dest;
    newNode->next = NULL;
    return newNode;
}

// 创建图
struct Graph* createGraph(int V) {
    struct Graph* graph = (struct Graph*)malloc(sizeof(struct Graph));
    graph->V = V;
    graph->array = (struct AdjList*)malloc(V * sizeof(struct AdjList));
    for (int i = 0; i < V; ++i) {
        graph->array[i].head = NULL;
    }
    return graph;
}

// 添加边
void addEdge(struct Graph* graph, int src, int dest) {
    struct AdjListNode* newNode = newAdjListNode(dest);
    newNode->next = graph->array[src].head;
    graph->array[src].head = newNode;
}

// 求出图G中每个顶点的出度
void calculate_out_degree(struct Graph* graph) {
    int out_degree[graph->V];
    struct AdjListNode* temp;
    for (int i = 0; i < graph->V; i++) {
        out_degree[i] = 0;
        temp = graph->array[i].head;
        while (temp != NULL) {
            out_degree[i]++;
            temp = temp->next;
        }
        printf("顶点%d的出度为%d\n", i, out_degree[i]);
    }
}

int main() {
    int V = 5;
    struct Graph* graph = createGraph(V);
    addEdge(graph, 0, 1);
    addEdge(graph, 0, 4);
    addEdge(graph, 1, 2);
    addEdge(graph, 1, 3);
    addEdge(graph, 1, 4);
    addEdge(graph, 2, 3);
    addEdge(graph, 3, 4);
    calculate_out_degree(graph);
    return 0;
}

2. 判断图G中是否存在边<ij>

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

// 邻接表节点结构体
struct AdjListNode {
    int dest;
    struct AdjListNode* next;
};

// 邻接表头结构体
struct AdjList {
    struct AdjListNode* head;
};

// 图结构体
struct Graph {
    int V;
    struct AdjList* array;
};

// 创建节点
struct AdjListNode* newAdjListNode(int dest) {
    struct AdjListNode* newNode = (struct AdjListNode*)malloc(sizeof(struct AdjListNode));
    newNode->dest = dest;
    newNode->next = NULL;
    return newNode;
}

// 创建图
struct Graph* createGraph(int V) {
    struct Graph* graph = (struct Graph*)malloc(sizeof(struct Graph));
    graph->V = V;
    graph->array = (struct AdjList*)malloc(V * sizeof(struct AdjList));
    for (int i = 0; i < V; ++i) {
        graph->array[i].head = NULL;
    }
    return graph;
}

// 添加边
void addEdge(struct Graph* graph, int src, int dest) {
    struct AdjListNode* newNode = newAdjListNode(dest);
    newNode->next = graph->array[src].head;
    graph->array[src].head = newNode;
}

// 判断图G中是否存在边<ij>
int is_edge_exist(struct Graph* graph, int i, int j) {
    struct AdjListNode* temp = graph->array[i].head;
    while (temp != NULL) {
        if (temp->dest == j) {
            return 1;
        }
        temp = temp->next;
    }
    return 0;
}

int main() {
    int V = 5;
    struct Graph* graph = createGraph(V);
    addEdge(graph, 0, 1);
    addEdge(graph, 0, 4);
    addEdge(graph, 1, 2);
    addEdge(graph, 1, 3);
    addEdge(graph, 1, 4);
    addEdge(graph, 2, 3);
    addEdge(graph, 3, 4);
    int i = 1, j = 4;
    if (is_edge_exist(graph, i, j)) {
        printf("存在边<%d,%d>\n", i, j);
    } else {
        printf("不存在边<%d,%d>\n", i, j);
    }
    return 0;
}

3. 将图的邻接表存储结构转换为邻接矩阵

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

// 邻接表节点结构体
struct AdjListNode {
    int dest;
    struct AdjListNode* next;
};

// 邻接表头结构体
struct AdjList {
    struct AdjListNode* head;
};

// 图结构体
struct Graph {
    int V;
    struct AdjList* array;
};

// 创建节点
struct AdjListNode* newAdjListNode(int dest) {
    struct AdjListNode* newNode = (struct AdjListNode*)malloc(sizeof(struct AdjListNode));
    newNode->dest = dest;
    newNode->next = NULL;
    return newNode;
}

// 创建图
struct Graph* createGraph(int V) {
    struct Graph* graph = (struct Graph*)malloc(sizeof(struct Graph));
    graph->V = V;
    graph->array = (struct AdjList*)malloc(V * sizeof(struct AdjList));
    for (int i = 0; i < V; ++i) {
        graph->array[i].head = NULL;
    }
    return graph;
}

// 添加边
void addEdge(struct Graph* graph, int src, int dest) {
    struct AdjListNode* newNode = newAdjListNode(dest);
    newNode->next = graph->array[src].head;
    graph->array[src].head = newNode;
}

// 将图的邻接表存储结构转换为邻接矩阵
void convert_to_adj_matrix(struct Graph* graph) {
    int adj_matrix[graph->V][graph->V];
    for (int i = 0; i < graph->V; i++) {
        for (int j = 0; j < graph->V; j++) {
            adj_matrix[i][j] = 0;
        }
    }
    struct AdjListNode* temp;
    for (int i = 0; i < graph->V; i++) {
        temp = graph->array[i].head;
        while (temp != NULL) {
            adj_matrix[i][temp->dest] = 1;
            temp = temp->next;
        }
    }
    printf("邻接矩阵为：\n");
    for (int i = 0; i < graph->V; i++) {
        for (int j = 0; j < graph->V; j++) {
            printf("%d ", adj_matrix[i][j]);
        }
        printf("\n");
    }
}

int main() {
    int V = 5;
    struct Graph* graph = createGraph(V);
    addEdge(graph, 0, 1);
    addEdge(graph, 0, 4);
    addEdge(graph, 1, 2);
    addEdge(graph, 1, 3);
    addEdge(graph, 1, 4);
    addEdge(graph, 2, 3);
    addEdge(graph, 3, 4);
    convert_to_adj_matrix(graph);
    return 0;
}