N个节点的二叉树形状数有随高度的N-1？ [英] Number of binary tree shapes of N nodes are there with height N-1?

问题描述

如何N个节点的许多二叉树的形状有随高度的N-1？ 还有，你怎么会去感应打样？

How many binary tree shapes of N nodes are there with height N-1? Also, how would you go about proofing by induction?

高N-1与节点，二叉树n表示所有的节点都只有1名儿童，排序链状结构？因此，二叉树的数量会有所不同排列是N N数字。我在想，在正确的方向？

So binary tree of height n-1 with node n means all node will have only 1 child, sort of chain like structure? So number of binary tree will be different permutation of n numbers which is n. Am I thinking in the right direction?

推荐答案

您正在考虑在正确的方向，你已经正确改变了原来的问题很简单。然而令人奇怪的是，它是明确表示，树是二进制的时候，其实在声明中规定更严格的约束。

You are thinking in the right direction and you have correctly transformed the original problem to a simple one. However what is strange is that it is explicitly stated that the tree is "binary" when in fact the statement dictates even tighter constraint.

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