Binary Tree Tilt

Problem

Given a binary tree, return the tilt of the whole tree.

The tilt of a tree node is defined as the absolute difference between the sum of all left subtree node values and the sum of all right subtree node values. Null node has tilt 0.

The tilt of the whole tree is defined as the sum of all nodes' tilt.

Example:
Input: 
         1
       /   \
      2     3
Output: 1
Explanation: 
Tilt of node 2 : 0
Tilt of node 3 : 0
Tilt of node 1 : |2-3| = 1
Tilt of binary tree : 0 + 0 + 1 = 1

Note:

The sum of node values in any subtree won't exceed the range of 32-bit integer. All the tilt values won't exceed the range of 32-bit integer.

Solution

Postorder traversal solution

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

    int res = 0;

    public int findTilt(TreeNode root) {
        postorder(root);
        return res;
    }

    private int postorder(TreeNode node) {
        if (node == null) return 0;
        int left = postorder(node.left);
        int right = postorder(node.right);
        res += Math.abs(left - right);
        return node.val + left + right;
    }
}

Analysis

This is a typical postorder traversal problem
To get the sum of all tilt, we need to calculate tilt of each node in our traversal
We must set res as global variable, because it will be updated while the process of traversal
In the helper method postorder() we are calculating the sum of subtrees
In this process, we update the total tilt res simultaneously
Once the traversal is done, we will get the total title of all subtrees

Complexity

• Time: O(n), since all nodes will be visited once
• Space: O(n), in worst case when the tree is skewed, the recursive method will be called n times