Binary Tree Tilt

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

Question

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.

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)
Tile 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

Answer

This sounds like DFS. So let's start trying to recurse.

Our base case is that if the root is None, we return

if not root:
    return 0

And then we want to recurse both left and right trees.

        right_sum = self.helper(root.right)
        left_sum = self.helper(root.left)

While doing this, we want to sum each side. We can do that by storing them in these variables. And then we calculate the tilt:

        tilt = abs(left_sum - right_sum)
        self.total_sum += tilt

Finally, when we have reached a leaf node we want it to return the sums of either side added to the current value.

    return left_sum + right_sum + root.val

Thus our solution is:

# 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:
    def findTilt(self, root: TreeNode) -> int:
        self.total_sum = 0
        self.helper(root)
        return self.total_sum
    
    def helper(self, root):
        if not root:
            return 0
        right_sum = self.helper(root.right)
        left_sum = self.helper(root.left)
        tilt = abs(left_sum - right_sum)
        self.total_sum += tilt
        
        return left_sum + right_sum + root.val