Huffman Tree

Huffman Tree是树的带权路径最短的树，每次都从一堆节点中选出权值最小的两个节点组合成一个新的节点，原来的节点从那堆节点中删去，新产生的节点加入到那堆节点中。

伪代码如下，利用HuffmanTree上节点数已知的特点逐个构建树上非叶子结点，然后从叶子到根去得到HuffmanCode

HUFFMAN(n, key[], huffcode[])
    leaf = Node[2*n]//一共有2*n-1个节点，零号节点不用
    priority_queue<Node*> pq
    for i = 1 to n
        leaf[i].parent = leaf[i].left = leaf[i].right = 0
        leaf[i].key = key[i]
        pq.push(&leaf[i])
    
    for i = n+1 to 2*n-1//创建n-1个非叶子节点，同时创建HuffmanTree 
        top1 = pq.pop()
        top2 = pq.pop()
        leaf[i].key = top1.key + top2.key
        leaf[i].left = top1
        leaf[i].right = top2
        leaf[i].parent = nil
        pq.push(&leaf[i])

    for i = 1 to n//从叶子到根得到每个字符的huffman编码
        p = &leaf[i]
        while p->parent != nil
            q = p->parent
            if p == q.left
                huffcode[i] = '0' + huffcode[i]
            else 
                huffcode[i] = '1' + huffcode[i]