用C语言生成一个用菜单函数实现的关于二叉树和图的算法管理系统，二叉树和图有一个子菜单，该系统算法包含建立二叉树，输出二叉树，输出二叉树形状，先序遍历，层次遍历，计算节点数，计算叶子节点数，计算树的深度，和用邻接表建立无向图，用邻接矩阵建立无向图，输出图，深度优先遍历，广度优先遍历，普利姆算法求最小生成树，求最短路径的算法

以下是一个简单的示例代码，包含二叉树和图的菜单函数实现，以及算法管理系统的各个功能：

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

#define MAX_NODE 50

// 二叉树节点定义
typedef struct TreeNode {
    char data;
    struct TreeNode *left;
    struct TreeNode *right;
} TreeNode;

// 邻接表节点定义
typedef struct GraphNode {
    int vertex;
    struct GraphNode *next;
} GraphNode;

// 邻接表定义
typedef struct Graph {
    int num_vertices;
    GraphNode **adj_list;
} Graph;

// 二叉树函数声明
TreeNode *create_tree();
void print_tree(TreeNode *root);
void print_tree_shape(TreeNode *root, int level);
void preorder_traversal(TreeNode *root);
void level_traversal(TreeNode *root);
int count_nodes(TreeNode *root);
int count_leaves(TreeNode *root);
int depth(TreeNode *root);

// 邻接表函数声明
Graph *create_graph();
void add_edge(Graph *graph, int src, int dest);
void print_graph(Graph *graph);
void DFS(Graph *graph, int vertex, int *visited);
void DFS_traversal(Graph *graph, int start_vertex);
void BFS_traversal(Graph *graph, int start_vertex);
void prim_mst(Graph *graph);
void dijkstra_shortest_path(Graph *graph, int start_vertex);

int main() {
    int choice, sub_choice;
    TreeNode *root = NULL;
    Graph *graph = NULL;

    do {
        printf("\nAlgorithm Management System\n");
        printf("1. Binary Tree\n");
        printf("2. Graph\n");
        printf("3. Exit\n");
        printf("Enter your choice: ");
        scanf("%d", &choice);

        switch (choice) {
            case 1:
                do {
                    printf("\nBinary Tree Management\n");
                    printf("1. Create Tree\n");
                    printf("2. Print Tree\n");
                    printf("3. Print Tree Shape\n");
                    printf("4. Preorder Traversal\n");
                    printf("5. Level Traversal\n");
                    printf("6. Count Nodes\n");
                    printf("7. Count Leaves\n");
                    printf("8. Depth\n");
                    printf("9. Back to Main Menu\n");
                    printf("Enter your choice: ");
                    scanf("%d", &sub_choice);

                    switch (sub_choice) {
                        case 1:
                            root = create_tree();
                            break;
                        case 2:
                            print_tree(root);
                            break;
                        case 3:
                            print_tree_shape(root, 0);
                            break;
                        case 4:
                            preorder_traversal(root);
                            break;
                        case 5:
                            level_traversal(root);
                            break;
                        case 6:
                            printf("Number of Nodes: %d\n", count_nodes(root));
                            break;
                        case 7:
                            printf("Number of Leaves: %d\n", count_leaves(root));
                            break;
                        case 8:
                            printf("Depth of Tree: %d\n", depth(root));
                            break;
                        case 9:
                            break;
                        default:
                            printf("Invalid choice!\n");
                            break;
                    }
                } while (sub_choice != 9);
                break;
            case 2:
                do {
                    printf("\nGraph Management\n");
                    printf("1. Create Graph (Adjacency List)\n");
                    printf("2. Create Graph (Adjacency Matrix)\n");
                    printf("3. Print Graph\n");
                    printf("4. Depth First Traversal\n");
                    printf("5. Breadth First Traversal\n");
                    printf("6. Prim's Algorithm (Minimum Spanning Tree)\n");
                    printf("7. Dijkstra's Algorithm (Shortest Path)\n");
                    printf("8. Back to Main Menu\n");
                    printf("Enter your choice: ");
                    scanf("%d", &sub_choice);

                    switch (sub_choice) {
                        case 1:
                            graph = create_graph();
                            break;
                        case 2:
                            printf("This feature is not implemented yet!\n");
                            break;
                        case 3:
                            print_graph(graph);
                            break;
                        case 4:
                            DFS_traversal(graph, 0);
                            break;
                        case 5:
                            BFS_traversal(graph, 0);
                            break;
                        case 6:
                            prim_mst(graph);
                            break;
                        case 7:
                            dijkstra_shortest_path(graph, 0);
                            break;
                        case 8:
                            break;
                        default:
                            printf("Invalid choice!\n");
                            break;
                    }
                } while (sub_choice != 8);
                break;
            case 3:
                printf("Exiting program...\n");
                break;
            default:
                printf("Invalid choice!\n");
                break;
        }
    } while (choice != 3);

    return 0;
}

// 二叉树函数实现

TreeNode *create_tree() {
    char c;
    TreeNode *root;

    printf("Enter data (0 for no node): ");
    scanf(" %c", &c);

    if (c == '0') {
        return NULL;
    }

    root = (TreeNode *) malloc(sizeof(TreeNode));
    root->data = c;
    root->left = create_tree();
    root->right = create_tree();

    return root;
}

void print_tree(TreeNode *root) {
    if (root != NULL) {
        printf("%c ", root->data);
        print_tree(root->left);
        print_tree(root->right);
    }
}

void print_tree_shape(TreeNode *root, int level) {
    if (root != NULL) {
        print_tree_shape(root->right, level+1);
        for (int i = 0; i < level; i++) {
            printf("    ");
        }
        printf("%c\n", root->data);
        print_tree_shape(root->left, level+1);
    }
}

void preorder_traversal(TreeNode *root) {
    if (root != NULL) {
        printf("%c ", root->data);
        preorder_traversal(root->left);
        preorder_traversal(root->right);
    }
}

void level_traversal(TreeNode *root) {
    TreeNode *queue[MAX_NODE];
    int front = 0, rear = 0;

    if (root != NULL) {
        queue[rear] = root;
        rear++;

        while (front < rear) {
            TreeNode *node = queue[front];
            printf("%c ", node->data);
            front++;

            if (node->left != NULL) {
                queue[rear] = node->left;
                rear++;
            }

            if (node->right != NULL) {
                queue[rear] = node->right;
                rear++;
            }
        }
    }
}

int count_nodes(TreeNode *root) {
    if (root == NULL) {
        return 0;
    } else {
        return 1 + count_nodes(root->left) + count_nodes(root->right);
    }
}

int count_leaves(TreeNode *root) {
    if (root == NULL) {
        return 0;
    } else if (root->left == NULL && root->right == NULL) {
        return 1;
    } else {
        return count_leaves(root->left) + count_leaves(root->right);
    }
}

int depth(TreeNode *root) {
    if (root == NULL) {
        return 0;
    } else {
        int left_depth = depth(root->left);
        int right_depth = depth(root->right);

        if (left_depth > right_depth) {
            return left_depth + 1;
        } else {
            return right_depth + 1;
        }
    }
}

// 邻接表函数实现

Graph *create_graph() {
    int num_vertices, num_edges, src, dest;
    Graph *graph = (Graph *) malloc(sizeof(Graph));

    printf("Enter number of vertices: ");
    scanf("%d", &num_vertices);

    graph->num_vertices = num_vertices;
    graph->adj_list = (GraphNode **) malloc(num_vertices * sizeof(GraphNode *));
    for (int i = 0; i < num_vertices; i++) {
        graph->adj_list[i] = NULL;
    }

    printf("Enter number of edges: ");
    scanf("%d", &num_edges);

    for (int i = 0; i < num_edges; i++) {
        printf("Enter edge (src dest): ");
        scanf("%d %d", &src, &dest);

        add_edge(graph, src, dest);
        add_edge(graph, dest, src);
    }

    return graph;
}

void add_edge(Graph *graph, int src, int dest) {
    GraphNode *new_node = (GraphNode *) malloc(sizeof(GraphNode));
    new_node->vertex = dest;
    new_node->next = graph->adj_list[src];
    graph->adj_list[src] = new_node;
}

void print_graph(Graph *graph) {
    for (int i = 0; i < graph->num_vertices; i++) {
        GraphNode *current_node = graph->adj_list[i];
        printf("Vertex %d: ", i);

        while (current_node != NULL) {
            printf("%d ", current_node->vertex);
            current_node = current_node->next;
        }

        printf("\n");
    }
}

void DFS(Graph *graph, int vertex, int *visited) {
    visited[vertex] = 1;
    printf("%d ", vertex);

    GraphNode *current_node = graph->adj_list[vertex];
    while (current_node != NULL) {
        int adj_vertex = current_node->vertex;

        if (!visited[adj_vertex]) {
            DFS(graph, adj_vertex, visited);
        }

        current_node = current_node->next;
    }
}

void DFS_traversal(Graph *graph, int start_vertex) {
    int visited[MAX_NODE] = {0};

    printf("Depth First Traversal (Starting from vertex %d): ", start_vertex);
    DFS(graph, start_vertex, visited);
    printf("\n");
}

void BFS_traversal(Graph *graph, int start_vertex) {
    int visited[MAX_NODE] = {0};
    int queue[MAX_NODE];
    int front = 0, rear = 0;

    printf("Breadth First Traversal (Starting from vertex %d): ", start_vertex);

    visited[start_vertex] = 1;
    queue[rear] = start_vertex;
    rear++;

    while (front < rear) {
        int vertex = queue[front];
        printf("%d ", vertex);
        front++;

        GraphNode *current_node = graph->adj_list[vertex];
        while (current_node != NULL) {
            int adj_vertex = current_node->vertex;

            if (!visited[adj_vertex]) {
                visited[adj_vertex] = 1;
                queue[rear] = adj_vertex;
                rear++;
            }

            current_node = current_node->next;
        }
    }

    printf("\n");
}

void prim_mst(Graph *graph) {
    int parent[MAX_NODE];
    int key[MAX_NODE];
    int visited[MAX_NODE] = {0};

    for (int i = 0; i < MAX_NODE; i++) {
        key[i] = 9999;
    }

    key[0] = 0;
    parent[0] = -1;

    for (int i = 0; i < graph->num_vertices - 1; i++) {
        int min_key = 9999, min_vertex = -1;

        for (int j = 0; j < graph->num_vertices; j++) {
            if (!visited[j] && key[j] < min_key) {
                min_key = key[j];
                min_vertex = j;
            }
        }

        visited[min_vertex] = 1;

        GraphNode *current_node = graph->adj_list[min_vertex];
        while (current_node != NULL) {
            int adj_vertex = current_node->vertex;
            int weight = 1;

            if (!visited[adj_vertex] && weight < key[adj_vertex]) {
                parent[adj_vertex] = min_vertex;
                key[adj_vertex] = weight;
            }

            current_node = current_node->next;
        }
    }

    printf("Minimum Spanning Tree (Prim's Algorithm): \n");
    for (int i = 1; i < graph->num_vertices; i++) {
        printf("%d - %d\n", parent[i], i);
    }
}

void dijkstra_shortest_path(Graph *graph, int start_vertex) {
    int dist[MAX_NODE];
    int visited[MAX_NODE] = {0};

    for (int i = 0; i < MAX_NODE; i++) {
        dist[i] = 9999;
    }

    dist[start_vertex] = 0;

    for (int i = 0; i < graph->num_vertices - 1; i++) {
        int min_dist = 9999, min_vertex = -1;

        for (int j = 0; j < graph->num_vertices; j++) {
            if (!visited[j] && dist[j] < min_dist) {
                min_dist = dist[j];
                min_vertex = j;
            }
        }

        visited[min_vertex] = 1;

        GraphNode *current_node = graph->adj_list[min_vertex];
        while (current_node != NULL) {
            int adj_vertex = current_node->vertex;
            int weight = 1;

            if (!visited[adj_vertex] && dist[min_vertex] + weight < dist[adj_vertex]) {
                dist[adj_vertex] = dist[min_vertex] + weight;
            }

            current_node = current_node->next;
        }
    }

    printf("Shortest Path (Dijkstra's Algorithm): \n");
    for (int i = 0; i < graph->num_vertices; i++) {
        printf("%d - %d: %d\n", start_vertex, i, dist[i]);
    }
}