# Maximum Difference Between Node and Ancestor

## [Maximum Difference Between Node and Ancestor](https://leetcode.com/problems/maximum-difference-between-node-and-ancestor)

Given the `root` of a binary tree, find the maximum value `V` for which there exist **different** nodes `A` and `B` where `V = |A.val - B.val|` and `A` is an ancestor of `B`.

A node `A` is an ancestor of `B` if either: any child of `A` is equal to `B`, or any child of `A` is an ancestor of `B`.

**Example 1:** ![](https://assets.leetcode.com/uploads/2020/11/09/tmp-tree.jpg)

```

Input: root = [8,3,10,1,6,null,14,null,null,4,7,13]
Output: 7
Explanation: We have various ancestor-node differences, some of which are given below :
|8 - 3| = 5
|3 - 7| = 4
|8 - 1| = 7
|10 - 13| = 3
Among all possible differences, the maximum value of 7 is obtained by |8 - 1| = 7.
```

**Example 2:** ![](https://assets.leetcode.com/uploads/2020/11/09/tmp-tree-1.jpg)

```

Input: root = [1,null,2,null,0,3]
Output: 3
```

**Constraints:**

* The number of nodes in the tree is in the range `[2, 5000]`.
* `0 <= Node.val <= 105`

## Solutions

### 🧠 Cpp

```cpp
/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution
{
    int max_check_value(TreeNode* root, int val)
    {
        if(!root)
            return 0;
        auto maxs = {abs(val - root->val), max_check_value(root->left, val), max_check_value(root->right, val)};
        return *max_element(begin(maxs), end(maxs));
    }

public:
    int maxAncestorDiff(TreeNode* root)
    {
        if(!root)
            return 0;
        auto maxs =
        {
            max_check_value(root->left, root->val),
            max_check_value(root->right, root->val),
            maxAncestorDiff(root->right),
            maxAncestorDiff(root->left)
        };

        return *max_element(begin(maxs), end(maxs));
    }
};
```


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