贪心算法求哈夫曼编码

哈夫曼编码是一种可变长度编码，用于将字符转换为二进制编码。贪心算法可以用来求解哈夫曼编码。

具体步骤如下：
1. 统计每个字符出现的频率，并将它们存储在一个优先队列中。
2. 从队列中取出频率最小的两个字符，将它们合并成一个新的节点，并将这个节点的频率设置为两个字符的频率之和。
3. 将新节点插入到队列中。
4. 重复步骤2和3，直到队列中只剩下一个节点为止。
5. 从根节点开始，对树进行遍历，每当遇到一个左子节点时，将当前编码加上0，每当遇到一个右子节点时，将当前编码加上1。最终得到每个字符的哈夫曼编码。

相关问题

贪心算法求哈夫曼编码c语言

以下是使用贪心算法求哈夫曼编码的 C 语言代码示例：

#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* node = (struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
    node->left = node->right = NULL;
    node->data = data;
    node->freq = freq;
    return node;
}

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);
}

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

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;
}

这个代码实现了一个哈夫曼编码器，按照频率构建了一个哈夫曼树，并输出了每个字符的哈夫曼编码。

贪心算法求哈夫曼编码C++

哈夫曼编码是一种可变长度编码，用于无损数据压缩。贪心算法可以用来求解哈夫曼编码。具体步骤如下：

1. 统计每个字符出现的频率，并将它们存储在一个数组中。
2. 创建一个最小堆，并将所有的字符节点插入其中。每个节点包含一个字符和它的频率。
3. 从最小堆中取出两个频率最小的节点，合并它们，并将新节点插入回最小堆中。新节点的频率为两个旧节点的频率之和。
4. 重复步骤3，直到最小堆中只剩下一个节点为止。这个节点就是哈夫曼树的根节点。
5. 遍历哈夫曼树，给左子树编码为0，给右子树编码为1。从根节点开始，每当向左走一步就在编码末尾添加一个0，每当向右走一步就在编码末尾添加一个1。最终得到每个字符的哈夫曼编码。

以下是C++代码实现：

#include <iostream>
#include <queue>
#include <vector>
using namespace std;

struct Node {
    char ch;
    int freq;
    Node* left;
    Node* right;
    Node(char c, int f) : ch(c), freq(f), left(nullptr), right(nullptr) {}
};

struct Compare {
    bool operator()(Node* a, Node* b) {
        return a->freq > b->freq;
    }
};

void encode(Node* root, string code, vector<string>& codes) {
    if (!root) return;
    if (root->ch != '#') codes[root->ch] = code;
    encode(root->left, code + "0", codes);
    encode(root->right, code + "1", codes);
}

vector<string> huffman(vector<int>& freqs) {
    priority_queue<Node*, vector<Node*>, Compare> pq;
    for (int i = 0; i < freqs.size(); i++) {
        if (freqs[i] > 0) {
            pq.push(new Node(i, freqs[i]));
        }
    }
    while (pq.size() > 1) {
        Node* left = pq.top(); pq.pop();
        Node* right = pq.top(); pq.pop();
        Node* parent = new Node('#', left->freq + right->freq);
        parent->left = left;
        parent->right = right;
        pq.push(parent);
    }
    vector<string> codes(256);
    encode(pq.top(), "", codes);
    return codes;
}

int main() {
    string s = "hello world";
    vector<int> freqs(256, 0);
    for (char c : s) freqs[c]++;
    vector<string> codes = huffman(freqs);
    for (int i = 0; i < 256; i++) {
        if (freqs[i] > 0) {
            cout << (char)i << ": " << codes[i] << endl;
        }
    }
    return 0;
}