哈夫曼编码代码

给定n个权值作为n个叶子结点，构造一棵二叉树，若该树的带权路径长度达到最小，称这样的二叉树为最优二叉树，也称为哈夫曼树。由此得到的二进制前缀编码称为哈夫曼编码。
例如权w={5,29,7,8,14,23,3,11}，8个结点，构造的哈夫曼树如下图所示：

算法实现如下：

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

typedef char **HuffmanCode;

//在huffmanTree[1...n-1]中选择parent为0，且weight最小的两个结点，分别是s1,s2
void Select(HuffmanTree& huffmanTree, int n,int &s1,int &s2)
{
    int min = 1;
    for(int i =1;i<=n;i++){
        if(huffmanTree[i].parent==0){
            min = i;
            break;
        }
    }
    for(int i =1;i<=n;i++){
        if(huffmanTree[i].parent==0){
            if(huffmanTree[i].weight<huffmanTree[min].weight){
                min = i;
            }
        }
    }
    s1 = min;
    for(int i =1;i<=n;i++){
        if(huffmanTree[i].parent==0 && i!=s1){
            min = i;
            break;
        }
    }
    for(int i=1;i<=n;i++){
        if(huffmanTree[i].parent==0 && i!=s1){
            if(huffmanTree[i].weight<huffmanTree[min].weight){
                min = i;
            }
        }
    }
    s2 = min;
}

void HuffmanCoding(HuffmanTree &huffmanTree, HuffmanCode &huffmanCode, int *w, int n)
{
    if(n <= 1) return;
    int m = 2*n-1;//一棵有n个叶子结点的哈夫曼树共有2n-1个结点
    int s1,s2;
    huffmanTree = (HuffmanTree)malloc((m+1)*sizeof(Node));
    HuffmanTree p = huffmanTree+1;
    //初始化叶结点
    for(int i=1;i<=n;i++,w++,p++){
        *p = {*w,0,0,0};
    }
    //初始化中间结点
    for(int i=n+1;i<=m;i++,p++){
        *p={0,0,0,0};
    }
    //构建哈夫曼树
    for(int i=n+1;i<=m;i++){
        Select(huffmanTree,i-1,s1,s2);
        huffmanTree[s1].parent = i;
        huffmanTree[s2].parent = i;
        huffmanTree[i].lchild = s1;
        huffmanTree[i].rchild = s2;
        huffmanTree[i].weight = huffmanTree[s1].weight+huffmanTree[s2].weight;
    }
    //从叶子到根逆向求每个字符的哈夫曼编码
    unsigned int c,f;
    int start;
    huffmanCode = (HuffmanCode)malloc((n+1)*sizeof(char*));
    char *cd = (char *)malloc(n*sizeof(char));
    cd[n-1]= '\0';
    for(int i=1; i<=n; i++){
        start = n-1;
        for(c=i, f=huffmanTree[i].parent; f!=0; c=f,f=huffmanTree[f].parent){
            if(huffmanTree[f].lchild == c){
                cd[--start] = '0';
            }
            else{
                cd[--start] = '1';
            }
        }
        huffmanCode[i] = (char *)malloc((n-start)*sizeof(char));
        strcpy(huffmanCode[i],&cd[start]);
    }
    free(cd);
}