下有关霍夫曼树的说法中，错误的是( )
- A.霍夫曼树又被称为最优二叉树
- B.霍夫曼树是一种带权路径长度最短的树
- C.具有n个叶子节点的权值为W1, W2，....Wn的最优二叉树是唯一的
- D.霍夫曼树可以用来进行通信电文的编码和解码
正确答案及解析
正确答案
解析
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。哈夫曼树是带权路径长度最短的树，权值较大的结点离根较近。
霍夫曼树可以用来进行通信电文的编码和解码。利用哈夫曼树求得的用于通信的二进制编码称为哈夫曼编码。树中从根到每个叶子节点都有一条路径，对路径上的各分支约定指向左子树的分支表示“0”码，指向右子树的分支表示“1”码，取每条路径上的“0”或“1”的序列作为各个叶子节点对应的字符编码，即是哈夫曼编码。
具有n个叶子节点的权值为W1，W2， ... Wn的最优二叉树的形态不是唯一的。
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