【算法導論】決策樹是滿二叉樹嗎？

今天看《算法導論》第三版中文版第八章，文中說“決策樹是一顆完全二叉樹”，再看看右邊的配圖：

我當時就懵了，學了幾年數據結構，也沒看過有這樣的完全二叉樹啊，按常理完全二叉樹應該倒數第二層是滿的，最後一層的葉子是從左到右開始排的啊，所以上圖明顯不符合完全二叉樹的定義。

後來我想，都聽說第三版的翻譯很爛，是不是翻譯出錯了，於是查看英文原文如下：

“A decision tree is a full binary tree..."一個決策樹是滿二叉樹！

再仔細想想，滿二叉樹也不對啊，滿二叉樹首先是完全二叉樹，而且滿二叉樹的最後一層是滿的，也就是說葉子都是在最後一層的。

難道是這本書出錯了？不可能吧，好歹也到了第三版，這麼多人用，如果真的出錯，也不至於到現在還沒更正啊，於是再次查看滿二叉樹(full binary tree)的定義。

中文百度百科關於”滿二叉樹“上有這麼一段話

美國以及國際上所定義的滿二叉樹，即full binary tree,和國內的定義不同，美國NIST給出的定義爲：A binary tree in which each node has exactly zero or two children. In other words, every node is either a leaf or has two children. For efficiency, any Huffman coding is a full binary tree.

滿二叉樹的任意節點，要麼度爲0，要麼度爲2.換個說法即要麼爲葉子結點，要麼同時具有左右孩子。霍夫曼樹是符合這種定義的，滿足國際上定義的滿二叉樹，但是不滿足國內的定義.

再看英文wiki上關於"Binary tree"的介紹：

• A full binary tree or proper binary tree ^[17] (sometimes 2-tree or strictly binary tree) is a tree in which every node other than the leaves has two children. Physicists define a binary tree to mean a full binary tree.^[18] 
  An ancestry chart which maps to a perfect depth-4 binary tree
  . A full tree is sometimes ambiguously defined as a perfect tree (see next).
• A perfect binary tree is a full binary tree in which all leaves have the same depth or same level, and in which every parent has two children.^[19] (This is ambiguously also called a complete binary tree (see next).) An example of a perfect binary tree is the ancestry chart of a person to a given depth, as each person has exactly two biological parents (one mother and one father); note that this reverses the usual parent/child tree convention, and these trees go in the opposite direction from usual (root at bottom).

原來是國內和國際上關於滿二叉樹的定義不一樣啊，國內認爲的滿二叉樹其實就是英文wiki上說的”perfect binary tree"，而其認爲的滿二叉樹只要滿足“一個節點要麼是葉子節點，要麼有2個子節點”，根據這個定義，《算法導論》上說決策樹是滿二叉樹也沒有錯！