An interesting property of a non-empty binary tree: n0 = n2 + 1

For any non-empty binary tree T, if n0 represents the number of leaf nodes, the number of non-leaf nodes with a N2 representation of 2, then both satisfy the relationship N0 = n2 + 1.

This is a very interesting nature, so let's prove it.

Proof: First, suppose that the two fork tree has n nodes, then how many edges will it have? The answer is N-1, because in addition to the root node, each of the remaining nodes has only one parent node, then the N nodes contribute to the N-1 edge of the tree. This is the thinking from the bottom up, and from the top down (from the root to the leaf node) thinking, easy to get each node's degrees and 0*n0 + 1*n1 + 2*n2 is the number of edges.

So we have the equation N-1 = n1 + 2*n2, replace N with N0 + n1 + n2, get N0 + n1 + n2-1 = n1 + 2*n2, so there are

N0 = n2 + 1. The proposition is to be proven.