Count Complete Tree Nodes

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

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 2h nodes inclusive at the last level h.

Solution

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int countNodes(TreeNode root) {
        if (root == null) {
            return 0;
        }

        int left = left(root.left);
        int right = right(root.right);
        if (left == right) {
                       return (1 << (left + 1)) - 1;

        } else {
            return countNodes(root.left) + countNodes(root.right) + 1;
        }
    }

    private int left(TreeNode node) {
        int height = 0;
        while (node != null) {
            height++;
            node = node.left;
        }

        return height;
    }

    private int right(TreeNode node) {
        int height = 0;
        while (node != null) {
            height++;
            node = node.right;
        }

        return height;
    }


}