用C语言编写普利姆算法邻接表的代码

下面是用C语言编写普利姆算法邻接表的代码：

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

#define MAX_VERTICES 100

typedef struct node {
    int vertex;
    int weight;
    struct node* next;
} Node;

typedef struct graph {
    Node* vertices[MAX_VERTICES];
    int num_vertices;
} Graph;

typedef struct heap {
    int* vertex_list;
    int* weight_list;
    int size;
    int capacity;
} Heap;

Graph* createGraph(int num_vertices) {
    Graph* graph = (Graph*)malloc(sizeof(Graph));
    graph->num_vertices = num_vertices;
    for (int i = 0; i < num_vertices; i++) {
        graph->vertices[i] = NULL;
    }
    return graph;
}

void addEdge(Graph* graph, int src, int dest, int weight) {
    Node* node = (Node*)malloc(sizeof(Node));
    node->vertex = dest;
    node->weight = weight;
    node->next = graph->vertices[src];
    graph->vertices[src] = node;

    node = (Node*)malloc(sizeof(Node));
    node->vertex = src;
    node->weight = weight;
    node->next = graph->vertices[dest];
    graph->vertices[dest] = node;
}

Heap* createHeap(int capacity) {
    Heap* heap = (Heap*)malloc(sizeof(Heap));
    heap->vertex_list = (int*)malloc(sizeof(int) * capacity);
    heap->weight_list = (int*)malloc(sizeof(int) * capacity);
    heap->size = 0;
    heap->capacity = capacity;
    return heap;
}

void swap(int* a, int* b) {
    int temp = *a;
    *a = *b;
    *b = temp;
}

void heapify(Heap* heap, int i) {
    int smallest = i;
    int left = 2 * i + 1;
    int right = 2 * i + 2;
    if (left < heap->size && heap->weight_list[left] < heap->weight_list[smallest]) {
        smallest = left;
    }
    if (right < heap->size && heap->weight_list[right] < heap->weight_list[smallest]) {
        smallest = right;
    }
    if (smallest != i) {
        swap(&heap->vertex_list[smallest], &heap->vertex_list[i]);
        swap(&heap->weight_list[smallest], &heap->weight_list[i]);
        heapify(heap, smallest);
    }
}

void insert(Heap* heap, int vertex, int weight) {
    if (heap->size == heap->capacity) {
        return;
    }
    heap->vertex_list[heap->size] = vertex;
    heap->weight_list[heap->size] = weight;
    int i = heap->size;
    while (i > 0 && heap->weight_list[i] < heap->weight_list[(i - 1) / 2]) {
        swap(&heap->vertex_list[i], &heap->vertex_list[(i - 1) / 2]);
        swap(&heap->weight_list[i], &heap->weight_list[(i - 1) / 2]);
        i = (i - 1) / 2;
    }
    heap->size++;
}

int extractMin(Heap* heap) {
    if (heap->size == 0) {
        return -1;
    }
    int min_vertex = heap->vertex_list[0];
    heap->vertex_list[0] = heap->vertex_list[heap->size - 1];
    heap->weight_list[0] = heap->weight_list[heap->size - 1];
    heap->size--;
    heapify(heap, 0);
    return min_vertex;
}

int isInHeap(Heap* heap, int vertex) {
    for (int i = 0; i < heap->size; i++) {
        if (heap->vertex_list[i] == vertex) {
            return 1;
        }
    }
    return 0;
}

int prim(Graph* graph) {
    int key[MAX_VERTICES];
    int inMST[MAX_VERTICES];
    int parent[MAX_VERTICES];
    Heap* heap = createHeap(graph->num_vertices);
    for (int i = 0; i < graph->num_vertices; i++) {
        key[i] = INT_MAX;
        inMST[i] = 0;
        parent[i] = -1;
    }
    insert(heap, 0, 0);
    key[0] = 0;
    while (heap->size > 0) {
        int u = extractMin(heap);
        inMST[u] = 1;
        Node* node = graph->vertices[u];
        while (node != NULL) {
            int v = node->vertex;
            int weight = node->weight;
            if (!inMST[v] && weight < key[v]) {
                key[v] = weight;
                parent[v] = u;
                if (isInHeap(heap, v)) {
                    for (int i = 0; i < heap->size; i++) {
                        if (heap->vertex_list[i] == v) {
                            heap->weight_list[i] = weight;
                            break;
                        }
                    }
                } else {
                    insert(heap, v, weight);
                }
            }
            node = node->next;
        }
    }
    int total_weight = 0;
    for (int i = 1; i < graph->num_vertices; i++) {
        total_weight += key[i];
    }
    return total_weight;
}

int main() {
    Graph* graph = createGraph(5);
    addEdge(graph, 0, 1, 2);
    addEdge(graph, 0, 3, 6);
    addEdge(graph, 1, 2, 3);
    addEdge(graph, 1, 3, 8);
    addEdge(graph, 1, 4, 5);
    addEdge(graph, 2, 4, 7);
    addEdge(graph, 3, 4, 9);
    int total_weight = prim(graph);
    printf("Minimum Spanning Tree Weight: %d\n", total_weight);
    return 0;
}

在上述代码中，我们首先定义了 `Node` 结构体和 `Graph` 结构体，用于表示图的邻接表表示法。然后，我们定义了 `Heap` 结构体，用于实现最小堆。接下来，我们实现了 `createGraph` 和 `addEdge` 函数，用于创建图和添加边。然后，我们实现了 `createHeap` 函数和堆操作函数，包括 `swap`、`heapify`、`insert`、`extractMin` 和 `isInHeap`。最后，我们实现了主函数 `prim`，用于执行普利姆算法，并返回最小生成树的权重。在主函数中，我们首先初始化 `key`、`inMST` 和 `parent` 数组，然后将起始顶点加入堆中。接下来，我们在堆中取出权重最小的顶点，并将其标记为已访问。然后，我们遍历与该顶点相邻的所有顶点，并更新它们的权重和父节点。如果该顶点不在堆中，则将其加入堆中；否则，更新其权重。最后，我们计算最小生成树的权重并返回。

以上代码仅供参考，实际使用时可能需要进行一定的修改。