# 563 Binary Tree Tilt

## 563. Binary Tree Tilt

## 1. Question

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.

## 2. Implementation

(1) Post-order Traversal

```java
class Solution {
    public int findTilt(TreeNode root) {
        int[] tilt = new int[1];
        getSum(root, tilt);
        return tilt[0];
    }

    public int getSum(TreeNode node, int[] tilt) {
        if (node == null) {
            return 0;
        }

        int leftSum = getSum(node.left, tilt);
        int rightSum = getSum(node.right, tilt);

        tilt[0] += Math.abs(leftSum - rightSum);
        return leftSum + rightSum + node.val;
    }
}
```

## 3. Time & Space Complexity

Post-order Traversal: 时间复杂度: O(n), 空间复杂度: O(h)


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