void init_heap(MinHeap *heap,int capacity) { heap->data=(Edge*)malloc(sizeof(Edge)*capacity); heap->size=0; heap->capacity=capacity; } void push_heap(MinHeap *heap,Edge e) { int i; i=++heap->size; while(i>1&&heap->data[i/2].w>e.w) { heap->data[i]

这是一个最小堆（MinHeap）的实现，用于存储边（Edge）并进行堆排序（heap sort）。

函数 init_heap 用于初始化一个最小堆，其中 heap->data 用于存储边，heap->size 表示当前堆的大小，heap->capacity 是堆的容量。

函数 push_heap 用于向最小堆中添加一条边 e，先将边插入到堆的最后一个位置，然后进行堆调整，将边上浮到其正确的位置。

在 while 循环中，每次将 i 指向当前节点的父节点，如果父节点的权值大于要插入的边的权值，就将父节点下沉到当前节点的位置，继续向上比较，直到当前节点的权值小于等于其父节点的权值或者已经到达堆顶。最后将要插入的边插入到 i 指向的位置即可。

这个最小堆的实现可以用于解决最小生成树（Minimum Spanning Tree）问题，例如 Prim 算法和 Kruskal 算法。

相关问题

用c代码解释堆

下面是使用 C 语言实现一个小根堆的例子，实现了堆的插入和弹出操作：

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

#define HEAP_SIZE 100

typedef struct {
    int *arr;   // 堆的数组
    int size;   // 堆中元素的个数
    int capacity;   // 堆的容量
} MinHeap;

// 初始化堆
void init_heap(MinHeap *heap, int capacity) {
    heap->arr = (int *)malloc(sizeof(int) * capacity);
    heap->size = 0;
    heap->capacity = capacity;
}

// 插入元素
void push(MinHeap *heap, int val) {
    if (heap->size >= heap->capacity) {
        return;
    }
    heap->arr[heap->size] = val;
    int idx = heap->size;
    while (idx > 0) {
        int parent_idx = (idx - 1) / 2;
        if (heap->arr[parent_idx] > heap->arr[idx]) {
            int tmp = heap->arr[parent_idx];
            heap->arr[parent_idx] = heap->arr[idx];
            heap->arr[idx] = tmp;
            idx = parent_idx;
        } else {
            break;
        }
    }
    heap->size++;
}

// 弹出堆顶元素
int pop(MinHeap *heap) {
    if (heap->size == 0) {
        return -1;
    }
    int root = heap->arr[0];
    heap->size--;
    heap->arr[0] = heap->arr[heap->size];
    int idx = 0;
    while (idx < heap->size) {
        int left_idx = idx * 2 + 1;
        int right_idx = idx * 2 + 2;
        int min_idx = idx;
        if (left_idx < heap->size && heap->arr[left_idx] < heap->arr[min_idx]) {
            min_idx = left_idx;
        }
        if (right_idx < heap->size && heap->arr[right_idx] < heap->arr[min_idx]) {
            min_idx = right_idx;
        }
        if (min_idx != idx) {
            int tmp = heap->arr[min_idx];
            heap->arr[min_idx] = heap->arr[idx];
            heap->arr[idx] = tmp;
            idx = min_idx;
        } else {
            break;
        }
    }
    return root;
}

int main() {
    MinHeap heap;
    init_heap(&heap, HEAP_SIZE);
    push(&heap, 3);
    push(&heap, 1);
    push(&heap, 4);
    push(&heap, 2);
    push(&heap, 5);
    while (heap.size > 0) {
        printf("%d ", pop(&heap));
    }
    return 0;
}

这里使用结构体来表示堆，包含堆的数组、元素个数和容量。插入时将元素添加到数组尾部，然后将元素与其父节点进行比较，如果父节点较大则交换两个节点，直到满足小根堆的性质。

弹出时将堆顶元素取出，将数组最后一个元素放到堆顶，然后将堆顶元素与其左右子节点中较小的那个进行比较，如果子节点较小则交换两个节点，直到满足小根堆的性质。

霍夫曼编码译码器c++

以下是一个简单的霍夫曼编码译码器的C代码示例：

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

#define MAX_TREE_HT 100

struct MinHeapNode {
    char data;
    unsigned freq;
    struct MinHeapNode *left, *right;
};

struct MinHeap {
    unsigned size;
    unsigned capacity;
    struct MinHeapNode **array;
};

struct MinHeapNode *newNode(char data, unsigned freq) {
    struct MinHeapNode *temp = (struct MinHeapNode *)malloc(sizeof(struct MinHeapNode));
    temp->left = temp->right = NULL;
    temp->data = data;
    temp->freq = freq;
    return temp;
}

struct MinHeap *createMinHeap(unsigned capacity) {
    struct MinHeap *minHeap = (struct MinHeap *)malloc(sizeof(struct MinHeap));
    minHeap->size = 0;
    minHeap->capacity = capacity;
    minHeap->array = (struct MinHeapNode **)malloc(minHeap->capacity * sizeof(struct MinHeapNode *));
    return minHeap;
}

void swapMinHeapNode(struct MinHeapNode **a, struct MinHeapNode **b) {
    struct MinHeapNode *t = *a;
    *a = *b;
    *b = t;
}

void minHeapify(struct MinHeap *minHeap, int idx) {
    int smallest = idx;
    int left = 2 * idx + 1;
    int right = 2 * idx + 2;

    if (left < minHeap->size && minHeap->array[left]->freq < minHeap->array[smallest]->freq)
        smallest = left;

    if (right < minHeap->size && minHeap->array[right]->freq < minHeap->array[smallest]->freq)
        smallest = right;

    if (smallest != idx) {
        swapMinHeapNode(&minHeap->array[smallest], &minHeap->array[idx]);
        minHeapify(minHeap, smallest);
    }
}

int isSizeOne(struct MinHeap *minHeap) {
    return (minHeap->size == 1);
}

struct MinHeapNode *extractMin(struct MinHeap *minHeap) {
    struct MinHeapNode *temp = minHeap->array[0];
    minHeap->array[0] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeapify(minHeap, 0);
    return temp;
}

void insertMinHeap(struct MinHeap *minHeap, struct MinHeapNode *minHeapNode) {
    ++minHeap->size;
    int i = minHeap->size - 1;

    while (i && minHeapNode->freq < minHeap->array[(i - 1) / 2]->freq) {
        minHeap->array[i] = minHeap->array[(i - 1) / 2];
        i = (i - 1) / 2;
    }

    minHeap->array[i] = minHeapNode;
}

void buildMinHeap(struct MinHeap *minHeap) {
    int n = minHeap->size - 1;
    int i;

    for (i = (n - 1) / 2; i >= 0; --i)
        minHeapify(minHeap, i);
}

void printArr(int arr[], int n) {
    int i;
    for (i = 0; i < n; ++i)
        printf("%d", arr[i]);
    printf("\n");
}

int isLeaf(struct MinHeapNode *root) {
    return !(root->left) && !(root->right);
}

struct MinHeap *createAndBuildMinHeap(char data[], int freq[], int size) {
    struct MinHeap *minHeap = createMinHeap(size);

    for (int i = 0; i < size; ++i)
        minHeap->array[i] = newNode(data[i], freq[i]);

    minHeap->size = size;
    buildMinHeap(minHeap);

    return minHeap;
}

struct MinHeapNode *buildHuffmanTree(char data[], int freq[], int size) {
    struct MinHeapNode *left, *right, *top;
    struct MinHeap *minHeap = createAndBuildMinHeap(data, freq, size);

    while (!isSizeOne(minHeap)) {
        left = extractMin(minHeap);
        right = extractMin(minHeap);
        top = newNode('$', left->freq + right->freq);
        top->left = left;
        top->right = right;
        insertMinHeap(minHeap, top);
    }

    return extractMin(minHeap);
}

void printCodes(struct MinHeapNode *root, int arr[], int top) {
    if (root->left) {
        arr[top] = 0;
        printCodes(root->left, arr, top + 1);
    }

    if (root->right) {
        arr[top] = 1;
        printCodes(root->right, arr, top + 1);
    }

    if (isLeaf(root)) {
        printf("%c: ", root->data);
        printArr(arr, top);
    }
}

void HuffmanCodes(char data[], int freq[], int size) {
    struct MinHeapNode *root = buildHuffmanTree(data, freq, size);
    int arr[MAX_TREE_HT], top = 0;
    printCodes(root, arr, top);
}

int main() {
    char arr[] = {'a', 'b', 'c', 'd', 'e', 'f'};
    int freq[] = {5, 9, 12, 13, 16, 45};
    int size = sizeof(arr) / sizeof(arr[0]);
    HuffmanCodes(arr, freq, size);
    return 0;
}

这个示例程序使用了Min Heap、霍夫曼树和深度优先搜索的概念来实现霍夫曼编码和解码。它可以生成给定字符集和频率的霍夫曼编码，并将其打印出来。该程序可以根据需要进行修改，以满足不同的编解码要求。