Count Complete Tree Nodes

Description

Given the root of a complete binary tree, return the number of the nodes in the tree.

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

Design an algorithm that runs in less than O(n) time complexity.

 

Example 1:

Input: root = [1,2,3,4,5,6]
Output: 6

Example 2:

Input: root = []
Output: 0

Example 3:

Input: root = [1]
Output: 1

 

Constraints:

• The number of nodes in the tree is in the range [0, 5 * 104].
• 0 <= Node.val <= 5 * 104
• The tree is guaranteed to be complete.

Solution(javascript)

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number}
 */
var countNodes = function(root) {
     return treeNodes(root);
 
     function treeNodes(node){
         if(!node){
             return 0;
         }else{
             var leftDepth = 0;
             var rightDepth = 0;
             var leftChild = node.left;
             while(leftChild){
                 leftDepth++;
                 leftChild = leftChild.left;
             }
             var rightChild = node.right;
             while(rightChild){
                 rightDepth++;
                 rightChild = rightChild.right;
             }
             if(leftDepth === rightDepth){
                 return Math.pow(2, leftDepth + 1) - 1;
             }else{
                 return treeNodes(node.left) + treeNodes(node.right) + 1;
             }
         }
     }
};