哈夫曼树讲解

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

#define N 10         // 带编码字符的个数，即树中叶结点的最大个数
#define M (2*N-1)    // 树中总的结点数目

class HTNode{        // 树中结点的结构
public: 
    unsigned int weight;
    unsigned int parent,lchild,rchild;
};                    

class HTCode{
public:
    char data;      // 待编码的字符
    int weight;     // 字符的权值
    char code[N];   // 字符的编码
};

void Init(HTCode hc[], int *n){
// 初始化，读入待编码字符的个数n，从键盘输入n个字符和n个权值
    int i;
    printf("input n = ");
    scanf("%d",&(*n));

    printf("\ninput %d character\n",*n);
     
    fflush(stdin);
    for(i=1; i<=*n; ++i)
        scanf("%c",&hc[i].data);

    printf("\ninput %d weight\n",*n);
    
    for(i=1; i<=*n; ++i)
        scanf("%d",&(hc[i].weight) );
    fflush(stdin);
}//

void Select(HTNode ht[], int k, int *s1, int *s2){
// ht[1...k]中选择parent为0，并且weight最小的两个结点，其序号由指针变量s1，s2指示
    int i;
    for(i=1; i<=k && ht[i].parent != 0; ++i){ 
        ; ;
    }
    *s1 = i;

    for(i=1; i<=k; ++i){
        if(ht[i].parent==0 && ht[i].weight<ht[*s1].weight)
            *s1 = i;
    }

    for(i=1; i<=k; ++i){
        if(ht[i].parent==0 && i!=*s1)
            break;
    }
    *s2 = i;

    for(i=1; i<=k; ++i){
        if(ht[i].parent==0 && i!=*s1 && ht[i].weight<ht[*s2].weight)
            *s2 = i;
    }
}

void HuffmanCoding(HTNode ht[],HTCode hc[],int n){
// 构造Huffman树ht，并求出n个字符的编码
    char cd[N];
    int i,j,m,c,f,s1,s2,start;
    m = 2*n-1;
    
    for(i=1; i<=m; ++i){
        if(i <= n)
            ht[i].weight = hc[i].weight;
        else
            ht[i].parent = 0;
        ht[i].parent = ht[i].lchild = ht[i].rchild = 0;
    }

    for(i=n+1; i<=m; ++i){
        Select(ht, i-1, &s1, &s2);
        ht[s1].parent = i;
        ht[s2].parent = i;
        ht[i].lchild = s1;
        ht[i].rchild = s2;
        ht[i].weight = ht[s1].weight+ht[s2].weight;
    }

    cd[n-1] = ‘\0‘;

    for(i=1; i<=n; ++i){
        start = n-1;
        for(c=i,f=ht[i].parent; f; c=f,f=ht[f].parent){
            if(ht[f].lchild == c)
                cd[--start] = ‘0‘;
            else
                cd[--start] = ‘1‘;
        }
        strcpy(hc[i].code, &cd[start]);
    }
}


int main()
{
    int i,m,n,w[N+1];
    HTNode ht[M+1];
    HTCode hc[N+1];
    Init(hc, &n);     // 初始化
     HuffmanCoding(ht,hc,n);   // 构造Huffman树，并形成字符的编码

    for(i=1; i<=n; ++i)  
        printf("\n%c---%s",hc[i].data,hc[i].code);  
    printf("\n");

    return 0;
}