Binary Tree Heights and Leaves For any binary tree with L leaves and height H
Binary Tree Properties Property 1: A binary tree with N > 0 nodes has exactly N-1 edges. Proof: Every node, except the root, receives exactly one edge from its parent.
Binary Tree Properties Property 2: If T is a binary tree of height h≥0, T has at least h+1 and at most 2 h+1 - 1 nodes. Proof: Since T is of height h, T has h+1 levels. There must be at least one node on each level. So the number of nodes is at least h+1. Each level j has at most 2 j nodes. Thus, the number of nodes is at most 2 h+1 – 1.