数算教材上,对于满二叉树的定义是所有节点含有0个或2个子节点的二叉树称之为满二叉树。然后早在很久以前搞noip初赛的时候,依稀记得高度为h的满二叉树是有2^h - 1个节点的二叉树。即除了最后一层所有节点的度为0以外,其余节点的度均为2(该度指的是 树上节点的度)。
经过上网搜索才发现国内的一些定义,严格意义上名词的一一对应是否合理。
wikipedia 上对于一些二叉树的定义是这样的:
A full binary tree (sometimes proper binary tree or2-tree or strictly binary tree) is a tree in which every node other than the leaves has two children. Or, perhaps more clearly, every node in a binary tree has exactly (strictly) 0 or 2 children. Sometimes a full tree is ambiguously defined as a perfect tree
A perfect binary tree is afull binary tree in which all leaves are at the same depth or samelevel, and in which every parent has two children.(This is ambiguously also called acomplete binary tree (see next).) An example of a perfect binary tree is theancestry 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).
A complete binary tree is a binary tree in which every level,except possibly the last, is completely filled, and all nodes are as far left as possible. A tree is called an almost complete binary tree or nearly complete binary tree if the exception holds, i.e. the last level is not completely filled.
那么国内的教材上对于满二叉树,如今我已经看到了两种不同的定义。不知道国外的教材会不会出现定义不一样的情况。