Count Complete Tree Nodes

Description

Given a complete binary tree, count the number of nodes.

Note:

Definition of a complete binary tree from Wikipedia:
In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2^h nodes inclusive at the last level h.

Example:

Input: 
    1
   / \
  2   3
 / \  /
4  5 6
Output: 6

Solution(javascript)

const countNodes = function (root) {
  const height = (node) => {
    if (!node) {
      return 0
    }
    return 1 + height(node.left)
  }
  const aux = (node) => {
    if (!node) {
      return 0
    }
    const leftHeight = height(node.left)
    const rightHeight = height(node.right)
    return leftHeight === rightHeight ? (2 ** leftHeight) + aux(node.right)
      : (2 ** rightHeight) + aux(node.left)
  }
  return aux(root)
}