Binary Tree Tilt

• LeetCode: Binary Tree Tilt

• Problem:

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

The tilt of a tree node is 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.

• 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.

• Examples:

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

• Analysis:

Traverse all node in the tree and get sum of subtree to retrieve the tilt.

• Code - Java:

class Solution {
    int result = 0;
    public int findTilt(TreeNode root) {
        helper(root);
        return result;
    }

    private int helper(TreeNode node) {
        if (node == null) {
            return 0;
        }
        int left = helper(node.left);
        int right = helper(node.right);
        result += Math.abs(left - right);
        return left + right + node.val;
    } 
}

• Code - C++:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int result = 0;
    int findTilt(TreeNode* root) {
        helper(root);
        return result;
    }

    int helper(TreeNode* node) {
        if (node == NULL) {
            return 0;
        }
        int left = helper(node->left);
        int right = helper(node->right);
        result += abs(left - right);
        return left + right + node->val;
    }    
};

• Code - Python:

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    result = 0
    def findTilt(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        self.helper(root)
        return self.result
    def helper(self, node):
        if node == None:
            return 0
        left, right = self.helper(node.left), self.helper(node.right)
        self.result += abs(left - right)
        return left + right + node.val

• Time Complexity: O(N), N is the number nodes of the input tree

• Space Complexity: O(1)