Count nodes in a complete binary tree

A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. Given the root of a complete binary tree, implement the function count_nodes(root) that returns the total number of nodes in the tree. The TreeNode structure is defined as: class TreeNode: def __init__(self, val=0, left=None, right=None): self.val = val self.left = left self.right = right Your implementation should take advantage of the complete-tree property to run faster than a naive O(n) traversal for large trees (an O((log n)^2) approach is typical). You will be given helper function build_tree(level_list) that builds a binary tree from a level-order list (use None for missing nodes). Call count_nodes(root) with the root returned by build_tree.

Implement an efficient algorithm to count nodes in a complete binary tree (better than O(n) where possible), using tree depths and recursion.

0 <= number of nodes <= 2^31 - 1. Aim for an algorithm with time complexity O((log n)^2) and space complexity O(log n) for recursion stack.