[leetcode #563] Binary Tree Tilt

Problem

Given the root of a binary tree, return the sum of every tree node's tilt.

The tilt of a tree node is the absolute difference between the sum of all left subtree node values and all right subtree node values. If a node does not have a left child, then the sum of the left subtree node values is treated as 0. The rule is similar if there the node does not have a right child.

Example 1:

Input: root = [1,2,3]
Output: 1
Explanation: 
Tilt of node 2 : |0-0| = 0 (no children)
Tilt of node 3 : |0-0| = 0 (no children)
Tilt of node 1 : |2-3| = 1 (left subtree is just left child, so sum is 2; right subtree is just right child, so sum is 3)
Sum of every tilt : 0 + 0 + 1 = 1

Example 2:

Input: root = [4,2,9,3,5,null,7]
Output: 15
Explanation: 
Tilt of node 3 : |0-0| = 0 (no children)
Tilt of node 5 : |0-0| = 0 (no children)
Tilt of node 7 : |0-0| = 0 (no children)
Tilt of node 2 : |3-5| = 2 (left subtree is just left child, so sum is 3; right subtree is just right child, so sum is 5)
Tilt of node 9 : |0-7| = 7 (no left child, so sum is 0; right subtree is just right child, so sum is 7)
Tilt of node 4 : |(3+5+2)-(9+7)| = |10-16| = 6 (left subtree values are 3, 5, and 2, which sums to 10; right subtree values are 9 and 7, which sums to 16)
Sum of every tilt : 0 + 0 + 0 + 2 + 7 + 6 = 15

Example 3:

Input: root = [21,7,14,1,1,2,2,3,3]
Output: 9

Constraints:

・ The number of nodes in the tree is in the range [0, 10⁴].
・ -1000 <= Node.val <= 1000

Idea

직관적으로 풀어도 쉽게 풀리는 문제다. 주어진 Tree에서 왼쪽 자식 노드들의 합과 오른쪽 자식 노드들의 합 차이를 절대값으로 계산해 전부 더하면 얼마인지 구하면 된다.

우선 Tree를 탐색하면서 각 노드의 값을 해당 subtree의 합으로 설정했다.

이후 Tree를 재탐색하면서 앞에서 구한 합의 차이를 절대값으로 계산해 더한다. 왼쪽 자식 노드와 오른쪽 자식 노드를 인자로 해 재귀함수로 계속 호출하면 원하는 답을 얻을 수 있다.

Solution

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    int res = 0;

    public int findTilt(TreeNode root) {
        traverseTree(root);
        tilt(root);

        return res;
    }

    private int traverseTree(TreeNode node) {
        if (node == null) {
            return 0;
        }

        node.val += traverseTree(node.left) + traverseTree(node.right);

        return node.val;
    }

    private void tilt(TreeNode node) {
        if (node == null) {
            return;
        }

        int leftSum = node.left == null ? 0 : node.left.val;
        int rightSum = node.right == null ? 0 : node.right.val;
        res += Math.abs(leftSum-rightSum);

        tilt(node.left);
        tilt(node.right);
    }
}

Reference

https://leetcode.com/problems/binary-tree-tilt/