## 题目描述

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.

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.

## 解法一

### 思路

``````def sum_and_tilt(root):
...
sum_left, tilt_left = sum_and_tilt(root.left)
sum_right, tilt_right = sum_and_tilt(root.right)
# TODO
return sum,tilt``````

### 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):
def findTilt(self, root):
"""
:type root: TreeNode
:rtype: int
"""

def sum_and_tilt(root):
if not root:
return 0, 0
sum_left, tilt_left = sum_and_tilt(root.left)
sum_right, tilt_right = sum_and_tilt(root.right)
return sum_left + sum_right + root.val, abs(sum_left - sum_right) + tilt_left + tilt_right

sum_tree, tilt_tree = sum_and_tilt(root)
return tilt_tree``````

### Java

``````/**
* 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) {
class Util {
int tilt;

int sum(TreeNode root) {
if (root == null) {
return 0;
}
int sumLeft = sum(root.left);
int sumRight = sum(root.right);
tilt += Math.abs(sumLeft - sumRight);
return sumLeft + sumRight + root.val;
}
}
Util util = new Util();
util.sum(root);
return util.tilt;
}
}``````

### 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 findTilt(TreeNode *root) {
class Util {
public:
int tilt = 0;

int sum(TreeNode *root) {
if (root == nullptr) {
return 0;
}
int sumLeft = sum(root->left);
int sumRight = sum(root->right);
tilt += abs(sumLeft - sumRight);
return sumLeft + sumRight + root->val;
}
};
Util util;
util.sum(root);
return util.tilt;
}
};``````