Binary Trees - 1

Definition: A binary tree is a rooted tree in which no vertex has more than two children

• each vertex has 0, 1, or 2 children

Definition: A binary tree is complete iff the only vertices with less than two children are in the bottom two layers

• Vertices in the bottom layer have 0 children
• Vertices in the penultimate layer have 0, 1, or 2 children
• All other vertices have 2 children
• Note that a binary tree is complete iff every layer but the bottom is fully populated with vertices

A complete binary tree with n vertices and height H satisfies:

• 2^H <= n < 2^H+1
• H <= log n < H + 1
• H == floor(log n)