给一个IsInHeap(H, W->AdjV);的例子

这里给出一个 IsInHeap(H, W->AdjV) 的例子：

bool IsInHeap(MinHeap H, Vertex V)
{
    for (int i = 1; i <= H->Size; i++)
    {
        if (H->Data[i] == V)
            return true;
    }
    return false;
}

该函数用于判断顶点 V 是否在最小堆 H 中。遍历堆中的元素，如果找到了与 V 相等的元素，则返回 true，表示 V 存在于堆中；否则，返回 false，表示 V 不在堆中。请注意，这只是一个示例实现，具体实现可能会根据堆的具体实现方式有所不同。在实际使用时，需要根据自己的堆实现方式来编写 IsInHeap 函数。

相关问题

请以下面的代码为模版，改为堆优化的版本 bool Dijkstra(LGraph G, int dist[], int path[], Vertex S) { Vertex V = Error; AdjNode W = G->Graph[S].FirstEdge; while (W) { dist[W->AdjV] = W->Weight; path[W->AdjV] = S; W = W->Next; } dist[S] = 0; collected[S] = true; while (1) { V = FindMinDist(G, dist, collected); if (V == Error) break; else { collected[V] = true; W = G->Graph[V].FirstEdge; while (W) { if (collected[W->AdjV] == false) { if (W->Weight < 0) return false; else { if (dist[V] + W->Weight < dist[W->AdjV]) { dist[W->AdjV] = dist[V] + W->Weight; path[W->AdjV] = V; } } } W = W->Next; } } } return true; }

下面是改为堆优化版本的代码：

bool Dijkstra(LGraph G, int dist[], int path[], Vertex S)
{
Vertex V = Error;
AdjNode W = G->Graph[S].FirstEdge;
while (W)
{
dist[W->AdjV] = W->Weight;
path[W->AdjV] = S;
W = W->Next;
}
dist[S] = 0;
collected[S] = true;

MinHeap H = CreateHeap(G->Nv);
Insert(H, S, dist);

while (!IsEmpty(H))
{
V = DeleteMin(H);
collected[V] = true;

W = G->Graph[V].FirstEdge;
while (W)
{
if (collected[W->AdjV] == false)
{
if (W->Weight < 0)
return false;
else
{
if (dist[V] + W->Weight < dist[W->AdjV])
{
dist[W->AdjV] = dist[V] + W->Weight;
path[W->AdjV] = V;
if (!IsInHeap(H, W->AdjV))
Insert(H, W->AdjV, dist);
else
UpdateHeap(H, W->AdjV, dist);
}
}
}
W = W->Next;
}
}

DestroyHeap(H);
return true;
}

小根堆排序怎么实现最小生成树C语言

以下是使用小根堆排序实现 Prim 算法生成最小生成树的 C 语言代码：

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

// 定义最大节点数
#define MAX_NODES 1000

// 定义图的节点结构体
struct Node {
    int weight; // 权值
    int dest;   // 目标节点
};

// 定义小根堆结构体
struct MinHeap {
    int size;   // 当前堆的大小
    int capacity;   // 堆的容量
    int *pos;   // 存储每个节点在堆中的位置
    struct Node **array;    // 存储最小堆的数组
};

// 创建一个新的节点
struct Node* newNode(int w, int d) {
    struct Node* node = (struct Node*) malloc(sizeof(struct Node));
    node->weight = w;
    node->dest = d;

    return node;
}

// 创建一个最小堆
struct MinHeap* createMinHeap(int capacity) {
    struct MinHeap* heap = (struct MinHeap*) malloc(sizeof(struct MinHeap));
    heap->pos = (int*) malloc(sizeof(int) * capacity);
    heap->size = 0;
    heap->capacity = capacity;
    heap->array = (struct Node**) malloc(sizeof(struct Node*) * capacity);

    return heap;
}

// 交换两个节点
void swapNode(struct Node** a, struct Node** b) {
    struct Node* tmp = *a;
    *a = *b;
    *b = tmp;
}

// 维护堆的性质
void minHeapify(struct MinHeap* heap, int idx) {
    int smallest = idx;
    int left = 2 * idx + 1;
    int right = 2 * idx + 2;

    // 找到左右子节点中权值最小的节点
    if (left < heap->size && heap->array[left]->weight < heap->array[smallest]->weight) {
        smallest = left;
    }
    if (right < heap->size && heap->array[right]->weight < heap->array[smallest]->weight) {
        smallest = right;
    }

    // 如果最小的节点不是当前节点，则交换节点并继续递归维护堆性质
    if (smallest != idx) {
        struct Node* smallestNode = heap->array[smallest];
        struct Node* idxNode = heap->array[idx];

        heap->pos[smallestNode->dest] = idx;
        heap->pos[idxNode->dest] = smallest;

        swapNode(&heap->array[smallest], &heap->array[idx]);
        minHeapify(heap, smallest);
    }
}

// 判断堆是否为空
int isEmpty(struct MinHeap* heap) {
    return heap->size == 0;
}

// 从堆中取出最小节点
struct Node* extractMin(struct MinHeap* heap) {
    if (isEmpty(heap)) {
        return NULL;
    }

    struct Node* root = heap->array[0];
    struct Node* lastNode = heap->array[heap->size - 1];

    heap->array[0] = lastNode;

    heap->pos[root->dest] = heap->size - 1;
    heap->pos[lastNode->dest] = 0;

    --heap->size;
    minHeapify(heap, 0);

    return root;
}

// 将节点的权值更新为新的值
void decreaseKey(struct MinHeap* heap, int dest, int weight) {
    int i = heap->pos[dest];

    heap->array[i]->weight = weight;

    while (i && heap->array[i]->weight < heap->array[(i - 1) / 2]->weight) {
        heap->pos[heap->array[i]->dest] = (i - 1) / 2;
        heap->pos[heap->array[(i - 1) / 2]->dest] = i;
        swapNode(&heap->array[i], &heap->array[(i - 1) / 2]);

        i = (i - 1) / 2;
    }
}

// 判断节点是否在堆中
int isInHeap(struct MinHeap* heap, int dest) {
    return heap->pos[dest] < heap->size;
}

// Prim 算法生成最小生成树
void primMST(int graph[MAX_NODES][MAX_NODES], int numNodes) {
    int parent[numNodes];
    int key[numNodes];
    struct MinHeap* heap = createMinHeap(numNodes);

    // 初始化所有节点的权值为无穷大
    for (int i = 0; i < numNodes; ++i) {
        parent[i] = -1;
        key[i] = INT_MAX;
        heap->array[i] = newNode(key[i], i);
        heap->pos[i] = i;
    }

    // 将第一个节点的权值设为0，并将其插入堆中
    key[0] = 0;
    heap->array[0] = newNode(key[0], 0);
    heap->pos[0] = 0;

    // 堆中节点数为所有节点数
    heap->size = numNodes;

    // 开始生成最小生成树
    while (!isEmpty(heap)) {
        struct Node* minNode = extractMin(heap);
        int u = minNode->dest;

        // 遍历所有相邻节点
        for (int v = 0; v < numNodes; ++v) {
            // 如果当前节点与相邻节点之间存在一条边，则判断是否需要更新相邻节点的权值
            if (graph[u][v] && isInHeap(heap, v) && graph[u][v] < key[v]) {
                key[v] = graph[u][v];
                parent[v] = u;
                decreaseKey(heap, v, key[v]);
            }
        }
    }

    // 输出最小生成树的边
    for (int i = 1; i < numNodes; ++i) {
        printf("%d - %d\t%d\n", parent[i], i, graph[i][parent[i]]);
    }
}

int main() {
    int graph[MAX_NODES][MAX_NODES];
    int numNodes, numEdges;

    // 读入节点数和边数
    scanf("%d%d", &numNodes, &numEdges);

    // 初始化图的邻接矩阵
    for (int i = 0; i < numNodes; ++i) {
        for (int j = 0; j < numNodes; ++j) {
            graph[i][j] = 0;
        }
    }

    // 读入每条边的信息，将其添加到邻接矩阵中
    for (int i = 0; i < numEdges; ++i) {
        int u, v, w;
        scanf("%d%d%d", &u, &v, &w);
        graph[u][v] = graph[v][u] = w;
    }

    // 生成最小生成树
    primMST(graph, numNodes);

    return 0;
}

其中，graph 是一个邻接矩阵，存储了图中每个节点之间的边的权值信息。numNodes 是图中的节点数，numEdges 是图中的边数。函数 primMST 实现了 Prim 算法生成最小生成树的过程。在主函数中，首先读入了节点数和边数，然后将每条边的信息添加到邻接矩阵中，最后调用 primMST 函数生成最小生成树。