二叉树应用——哈夫曼编码

1.实验目的

（1）掌握树和二叉树的特点、逻辑结构和物理实现；

（2）掌握实际问题中二叉树的应用

（3）掌握哈夫曼树及哈夫曼编码在实际问题中的应用。

2.实验内容

设要传输的字符集D={ C, A, S, T, ; }，字符出现频率 w={ 2,4,2,3,3 }，若电文为：CAS;CAT;SAT;AT，输出该电文的哈夫曼序列。

#include<bits/stdc++.h>
using namespace std;

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

void SetHuffmanTree(HuffmanTree H, int w, int p, int lc, int rc){
    H->weight = w;
    H->parent = p;
    H->lchild = lc;
    H->rchild = rc;
}
void CreateHuffmanTree(HuffmanTree &HT, int *w, int n){
    HT = (HuffmanTree)malloc((2 * n - 1) * sizeof(HTNode));

    for(int i = 0; i < n; i++)
      SetHuffmanTree(HT + i, w[i], -1, -1, -1);

    for(int i = n; i < 2 * n - 1; i++)
    {
        int min1 = 99999, min2 = min1;
        int x1 = -1, x2 = -1;
        for(int j = 0; j < i; j++)
        {
            if(HT[j].parent == -1)
            {
                if(HT[j].weight < min1)
                {
                    min2 = min1;
                    min1 = HT[j].weight;
                    x2 = x1;
                    x1 = j;
                }
                else if(HT[j].weight < min2)
                {
                    min2 = HT[j].weight;
                    x2 = j;
                }
            }
        }

        HT[x1].parent = i;
        HT[x2].parent = i;

        SetHuffmanTree(HT + i, min1 + min2, -1, x1, x2);
    }
}
void HuffmanTreeCode(HuffmanTree HT, char *str, int n, int path, int &e){
    int i = 0;
    int child = path;
    int parent = HT[child].parent;

    while(parent != -1)
    {
        if(HT[parent].lchild == child)
          str[i++] = '0';
        else
          str[i++] = '1';
        child = parent;
        parent = HT[child].parent;
    }

    e = i;
}

int main()
{
    int e, n = 5;
    int w[5] = {2, 4, 2, 3, 3};
    char D[5] = {'C', 'A', 'S', 'T', ';'};
    char S[15] = "CAS;CAT;SAT;AT";

    HuffmanTree HT;

    CreateHuffmanTree(HT, w, n);

    char str[n];
    for(int i = 0; i < 14; i++)
      for(int j = 0; j < 5; j++)
      {
          if(D[j] == S[i])
    	  {
    		  HuffmanTreeCode(HT, str, n, j, e);
    	  	  for(int k = e - 1; k >= 0; k--)
    	        printf("%c", str[k]);
    	  }
      }

    free(HT);

    system("pause");
}