问题 H : 算法6 - 12：自底向下的赫夫曼编码

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最新推荐文章于 2025-05-28 22:18:33 发布

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文章标签： c++ 算法图论

本文链接：https://blog.youkuaiyun.com/m0_64083326/article/details/130466743

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该代码实现了无栈非递归的方式构建哈夫曼树并求解哈夫曼编码。通过定义HuffmanNode结构体存储树节点，使用selectMin函数选取最小权值节点，然后进行合并构建哈夫曼树。最后用贪心算法遍历哈夫曼树生成编码。

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#include<bits/stdc++.h>

using namespace std;

typedef char* HuffmanCode;
const int MAXN = 110;

typedef struct {
    int parent, lchild, rchild;
    int weight;
} HuffmanNode, * HuffmanTree;

void selectMin(HuffmanTree HT, int n, int& s1, int& s2) {
    int min = INT_MAX;
    for (int i = 1; i <= n; ++i) {
        if (HT[i].parent == 0 && min > HT[i].weight) {
            min = HT[i].weight;
            s1 = i;
        }
    }

    min = INT_MAX;
    for (int i = 1; i <= n; ++i) {
        if (HT[i].parent == 0 && min > HT[i].weight && i != s1) {
            min = HT[i].weight;
            s2 = i;
        }
    }

    if (s1 > s2) {
        swap(s1, s2);
    }
}

//无栈非递归遍历哈夫曼树，求哈夫曼编码
void HuffmanCoding(HuffmanTree& HT, HuffmanCode*& HC, int w[], int n) {
    if (n <= 1) return;
    int m = 2 * n - 1;  //m是因为需要（n - 1）次合并，所以总共要有（n + n - 1）个数据要存储

    //分配n个字符编码的头指针向量[0]不用
    HT = new HuffmanNode[m + 1];

    //  初始权值存储
    for (int i = 1; i <= n; ++i) {
        HT[i].weight = w[i];
        HT[i].parent = HT[i].lchild = HT[i].rchild = 0;
    }

    //  要存储的合并后权值的初始化
    for (int i = n + 1; i <= m; ++i) {
        HT[i].parent = HT[i].lchild = HT[i].rchild = 0;
    }

    //构建哈夫曼树
    for (int i = n + 1; i <= m; ++i) {
        int s1, s2;
        selectMin(HT, i - 1, s1, s2);
        HT[i].lchild = s1;
        HT[i].rchild = s2;
        HT[s1].parent = HT[s2].parent = i;
        HT[i].weight = HT[s1].weight + HT[s2].weight;
    }

    //分配n个字符编码的头指针向量([0]不用)
    HC = new HuffmanCode[n + 1];
    char* cd = new char[n];
    int c = m;
    int cdlen = 0;
    cd[n - 1] = '\0';
    for (int i = 1; i <= m; ++i) {
        HT[i].weight = 0;//遍历哈夫曼树作结点状态标志
    }

    //  贪心算法，0表示结点左孩子右孩子都没访问，1表示结点左孩子访问了，右孩子还没访问，2表示左右孩子都访问了。
    while (c) {
        if (HT[c].weight == 0) {//向左
            HT[c].weight = 1;
            if (HT[c].lchild != 0) {
                c = HT[c].lchild;
                cd[cdlen++] = '0';
            }
            else if (HT[c].rchild == 0) {//登记叶子结点的编码
                HC[c] = new char[cdlen + 1];
                cd[cdlen] = '\0';
                strcpy(HC[c], cd);//复制编码（串）
            }
        }
        else if (HT[c].weight == 1) { //向右
            HT[c].weight = 2;
            if (HT[c].rchild != 0) {
                c = HT[c].rchild;
                cd[cdlen++] = '1';
            }
        }
        else {//HT[c].weight == 2, 退回
            c = HT[c].parent;
            --cdlen;//退回父结点，编码长度减一
        }

    }
    delete[]cd;
}

int main() {
    HuffmanTree HT;
    HuffmanCode* HC;
    int n;
    int data[MAXN];

    while (scanf("%d", &n) != EOF) {
        for (int i = 1; i <= n; ++i) {
            scanf("%d", &data[i]);
        }

        HuffmanCoding(HT, HC, data, n);
        for (int i = 1; i <= n; ++i) {
            printf("%s\n", HC[i]);
        }
        delete(HC);
        delete(HT);
    }

    return 0;
}