Count Complete Tree Nodes

Background Knowledge

A complete binary tree is a type of binary tree where every level is fully filled, except for the last level, which is filled from left to right. This means that all nodes at a given level have two children, except for the nodes at the last level, which may have zero, one, or two children. Understanding the structure of a complete binary tree is crucial to solving this problem. The given tree is represented as a level-order array, where the nodes are stored in an array in the order they are visited during a level-order traversal.

In a level-order traversal, we visit all the nodes at a given level before moving on to the next level. This is in contrast to other traversal methods, such as in-order or pre-order, which visit nodes in a specific order based on their position in the tree. The level-order array representation of a complete binary tree can be useful for solving problems that involve traversing the tree or calculating properties of the tree.

The concept of a complete binary tree is closely related to the concept of a full binary tree, where every node has either zero or two children. While a full binary tree is a special case of a complete binary tree, not all complete binary trees are full. Understanding the differences between these two types of trees can help you approach problems involving binary trees.