How many different binary trees can be constructed from three nodes?

Five different binary trees can be constructed from three nodes.

Introduction to relevant knowledge points:

What is a binary tree?

Binary tree is an important type of tree structure. The data structures abstracted from many practical problems are often in the form of binary trees. Even ordinary trees can be easily converted into binary trees. Moreover, the storage structure and algorithm of binary trees are relatively simple, so binary trees are particularly important.

Characteristics of binary trees:

Each node can only have two subtrees at most, and they can be divided into left and right.

A binary tree is a set of n finite elements. The set is either empty or consists of one element called the root and two disjoint elements, called the left subtree and the right subtree respectively. It is composed of a binary tree and is an ordered tree. When the set is empty, the binary tree is called an empty binary tree. In a binary tree, an element is also called a node.

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