哈夫曼编码 贪心算法 c语言实现

哈夫曼编码是一种广泛用于数据文件压缩的编码方法，其压缩率通常在20%～90%之间。它利用字符在文件中出现的频率表来建立一个用0，1串表示各字符的最优表示方式。哈夫曼编码实质上是利用最优二叉树原理，求最优前缀码的长度，即平均码长或文件总长最小的前缀编码。哈夫曼编码的实现过程可以使用贪心算法，即每次选择频率最小的两个字符进行合并，直到所有字符都被合并为止。C语言实现哈夫曼编码可以使用结构体来表示哈夫曼树节点，使用指针来实现树的构建和遍历，具体实现可以参考相关的C语言教材或者网上的代码示例。

相关问题

用贪心算法解哈夫曼编码问题c语言代码实现

在C语言中，贪心算法可以用来构建哈夫曼树并生成哈夫曼编码，这是通过每次选择两棵权值最小的树合并成新的树，并将这两棵树的权值作为新树的权值来实现的。以下是一个简单的C语言代码示例：

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

// 结点结构体
typedef struct {
    int weight; // 权值
    char symbol; // 符号
    struct Node* left, *right; // 左右子节点
} Node;

// 创建新结点
Node* newNode(int weight, char symbol) {
    Node* node = (Node*)malloc(sizeof(Node));
    node->weight = weight;
    node->symbol = symbol;
    node->left = node->right = NULL;
    return node;
}

// 贪心合并函数
Node* mergeTrees(Node* t1, Node* t2) {
    if (!t1 || !t2)
        return t1 ? t1 : t2;
    if (t1->weight < t2->weight) {
        t1->right = mergeTrees(t1->right, t2);
        return t1;
    } else {
        t2->left = mergeTrees(t1, t2->left);
        return t2;
    }
}

// 构建哈夫曼树
Node* buildHuffmanTree(int weights[], int n) {
    Node** heap = (Node**)malloc(n * sizeof(Node*));
    for (int i = 0; i < n; ++i) {
        heap[i] = newNode(weights[i], i + 'A');
    }

    while (heap[0]) {
        int minIndex1 = 0, minIndex2 = 0;
        for (int i = 1; i < n; ++i) {
            if (heap[minIndex1]->weight > heap[i]->weight) {
                minIndex1 = i;
            }
        }
        for (int j = 1; j < n; ++j) {
            if (heap[j] != heap[minIndex1] && heap[j]->weight < heap[minIndex2]->weight) {
                minIndex2 = j;
            }
        }

        Node* temp = mergeTrees(heap[minIndex1], heap[minIndex2]);
        heap[minIndex1] = heap[minIndex2] = NULL;
        heap[n++] = temp;
    }

    return heap[0];
}

// 打印哈夫曼编码
void printCodes(Node* root, int symbolToCode[]) {
    if (!root)
        return;
    if (!root->left && !root->right)
        symbolToCode[root->symbol - 'A'] = '0';
    else {
        printCodes(root->left, symbolToCode);
        printCodes(root->right, symbolToCode);
    }
}

int main() {
    int weights[] = {5, 3, 4, 6}; // 示例权重数组
    int n = sizeof(weights) / sizeof(weights[0]);

    Node* huffTree = buildHuffmanTree(weights, n);
    int symbolToCode[26] = {0};

    printf("Huffman Tree:\n");
    printCodes(huffTree, symbolToCode);

    return 0;
}

这个代码首先创建了一个堆，然后不断从堆中取出两个权值最小的结点合并，直到只剩下一个结点。最后，它会递归地生成每个字符的哈夫曼编码。

贪心算法哈夫曼编码C语言

哈夫曼编码是一种基于贪心算法的压缩算法，其核心思想是将出现频率较高的字符用较短的编码表示，而出现频率较低的字符用较长的编码表示。以下是哈夫曼编码的C语言实现：

#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;
}

以上代码实现了哈夫曼编码的生成过程，包括建立哈夫曼树、生成编码等步骤。