<p>Given a <strong>binary tree</strong> <code>root</code>, return <em>the maximum sum of all keys of <strong>any</strong> sub-tree which is also a Binary Search Tree (BST)</em>.</p>

<p>Assume a BST is defined as follows:</p>

<ul>
	<li>The left subtree of a node contains only nodes with keys <strong>less than</strong> the node&#39;s key.</li>
	<li>The right subtree of a node contains only nodes with keys <strong>greater than</strong> the node&#39;s key.</li>
	<li>Both the left and right subtrees must also be binary search trees.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2020/01/30/sample_1_1709.png" style="width: 320px; height: 250px;" /></p>

<pre>
<strong>Input:</strong> root = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6]
<strong>Output:</strong> 20
<strong>Explanation:</strong> Maximum sum in a valid Binary search tree is obtained in root node with key equal to 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2020/01/30/sample_2_1709.png" style="width: 134px; height: 180px;" /></p>

<pre>
<strong>Input:</strong> root = [4,3,null,1,2]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Maximum sum in a valid Binary search tree is obtained in a single root node with key equal to 2.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> root = [-4,-2,-5]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All values are negatives. Return an empty BST.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 4 * 10<sup>4</sup>]</code>.</li>
	<li><code>-4 * 10<sup>4</sup> &lt;= Node.val &lt;= 4 * 10<sup>4</sup></code></li>
</ul>

/**
 * 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 NodeData{
//         public:
//         bool validBST;
//         int sum;
//         int maxVal;
//         int minVal;

//         NodeData(bool valid,int sum,int max, int min){
//                 validBST = valid;
//                 this->sum = sum;
//                 minVal = min;
//                 maxVal = max;
//         }
// };

class NodeData {
public:
    bool validBST;
    int sum;
    int minVal;
    int maxVal;

    NodeData() : validBST(true), sum(0), minVal(INT_MAX), maxVal(INT_MIN) {}
    NodeData(bool valid, int sum, int min, int max) {
        this->validBST = valid;
        this->sum = sum;
        this->minVal = min;
        this->maxVal = max;
    }
};

class Solution {
public:

    // NodeData* required(TreeNode* root, int& ans){
    //     if(root == NULL){
    //         NodeData* Ans2 = new NodeData(true, 0, INT_MIN, INT_MAX);
    //         return Ans2;
    //     }


    //     NodeData* leftAns = required(root->left, ans);
    //     NodeData* rightAns = required(root->right, ans);

    //     NodeData* Ans = new NodeData();

    //     // Ans->minVal = max(root->data, leftAns->maxval);
    //     // Ans->maxVal = min(root->data, rightAns->minVal);

    //     Ans->minVal = min(root->data, leftAns->minVal);
    //     Ans->maxVal = max(root->data, rightAns->maxVal);

    //     if(leftAns->validBST && rightAns->validBST){
    //         if(root->data > leftAns->maxVal && root->data < rightAns->minVal){
    //             Ans->validBST = true;
    //             Ans->sum = leftAns->sum +rightAns->sum + root->data;
    //         }else{
    //             Ans->validBST = true;
    //         }
    //     }else{
    //         Ans->validBST = false;
    //     }

    //     if(Ans->validBST){
    //         ans = max(ans, Ans->sum);
    //     }  

    //     return Ans;
    // }

    // int maxSumBST(TreeNode* root) {
    //     int ans = 0; // Initialize ans to 0

    //     required(root, ans);
    //     return ans;

    // }

        NodeData* required(TreeNode* root, int& ans) {
        if (root == NULL) {
            return new NodeData(true, 0, INT_MAX, INT_MIN);
        }

        NodeData* leftAns = required(root->left, ans);
        NodeData* rightAns = required(root->right, ans);

        NodeData* Ans = new NodeData();

        Ans->minVal = min(root->val, leftAns->minVal);
        Ans->maxVal = max(root->val, rightAns->maxVal);

        if (leftAns->validBST && rightAns->validBST) {
            if (root->val > leftAns->maxVal && root->val < rightAns->minVal) {
                Ans->validBST = true;
                Ans->sum = leftAns->sum + rightAns->sum + root->val;
            } else {
                Ans->validBST = false;
            }
        } else {
            Ans->validBST = false;
        }

        if (Ans->validBST) {
            ans = max(ans, Ans->sum);
        }

        delete leftAns;
        delete rightAns;
        
        return Ans;
    }

    int maxSumBST(TreeNode* root) {
        int ans = 0;
        required(root, ans);
        return ans;
    }
};
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