563 Binary Tree Tilt

563. Binary Tree Tilt

1. Question

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

The tilt of a tree nodeis 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:

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

2. All the tilt values won't exceed the range of 32-bit integer.

2. Implementation

(1) DFS

思路: post order traversal, 先处理左子树和右子树，分别得到左子树和右子树的和，然后计算当前node的tilt，把结果加在res里,然后返回node.val + leftSum + rightSum

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int findTilt(TreeNode root) {
        int[] res = new int[1];

        findTiltByDFS(root, res);
        return res[0];
    }

    public int findTiltByDFS(TreeNode node, int[] res) {
        if (node == null) {
            return 0;
        }

        int rightSum= findTiltByDFS(node.right, res);
        int leftSum = findTiltByDFS(node.left, res);
        res[0] += Math.abs(leftSum - rightSum);

        return node.val + leftSum + rightSum;
    }
}

3. Time & Space Complexity

DFS: 时间复杂度O(n), 空间复杂度: O(h)