# 563. Binary Tree Tilt

## Easy

***

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`

Solution

```python
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    result = 0
    def findTilt(self, root: Optional[TreeNode]) -> int:
        result = 0
        def recursion(root):
            nonlocal result
            if root is None:
                return 0
            left = recursion(root.left)
            right = recursion(root.right)
            root.sum = abs(left-right)
            result += root.sum
            return root.val + left + right
        recursion(root)
        return result
```