# Complete Tree Node Count

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

Steps to solve this problem:

1. get the height of left-most part
2. get the height of right-most part
3. when they are equal, the # of nodes = 2h -1
4. when they are not equal, recursively get # of nodes from left&right sub-trees

## Code

``````/**
* 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 = getLeftHeight(root)+1;
int right = getRightHeight(root)+1;

if(left==right){
return (2<<(left-1))-1;
}else{
return countNodes(root.left)+countNodes(root.right)+1;
}
}

public int getLeftHeight(TreeNode n){
if(n==null) return 0;

int height=0;
while(n.left!=null){
height++;
n = n.left;
}
return height;
}

public int getRightHeight(TreeNode n){
if(n==null) return 0;

int height=0;
while(n.right!=null){
height++;
n = n.right;
}
return height;
}
}
``````