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# 0563. Binary Tree Tilt

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

## Description

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:**

![](https://assets.leetcode.com/uploads/2020/10/20/tilt1.jpg)

```
**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:**

![](https://assets.leetcode.com/uploads/2020/10/20/tilt2.jpg)

```
**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:**

![](https://assets.leetcode.com/uploads/2020/10/20/tilt3.jpg)

```
**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`

## ac

```java
class Solution {
    int sum = 0;

    public int findTilt(TreeNode root) {
        helper(root);
        return sum;
    }

    public int helper(TreeNode node) {
        if (node == null) return 0;

        int l = helper(node.left);
        int r = helper(node.right);

        sum += Math.abs(l - r);

        return node.val + l + r;
    }
}

/*
helper function return subtree sum, calculate tilt add to result
*/
```