<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>

class node {
public:
    int sum;        // Sum of values in the subtree
    int minVal;     // Minimum value in the subtree
    int maxVal;     // Maximum value in the subtree
    bool isBST;     // Whether the subtree is a BST
    node* left;     // Pointer to the left child
    node* right;    // Pointer to the right child
    
    node() {
        sum = 0;
        minVal = INT_MAX;
        maxVal = INT_MIN;
        left = NULL;
        right = NULL;
        isBST = true;
    }
};

class Solution {
public:  
    int ans; // Variable to store the maximum sum of a BST

    // Function to create a node object representing a subtree
    node* createNode(TreeNode* root) {
        if (!root) return NULL;

        node* temp = new node();
        temp->sum = root->val;
        bool isBST = true;
        
        // Process the left subtree
        if (root->left) {
            temp->left = createNode(root->left);
            if (!temp->left->isBST || temp->left->maxVal >= root->val) isBST = false;
            temp->sum += temp->left->sum;
            temp->minVal = min(temp->minVal, temp->left->minVal);
            temp->maxVal = max(temp->maxVal, temp->left->maxVal);
        }
        
        // Process the right subtree
        if (root->right) {
            temp->right = createNode(root->right);
            if (!temp->right->isBST || temp->right->minVal <= root->val) isBST = false;
            temp->sum += temp->right->sum;
            temp->minVal = min(temp->minVal, temp->right->minVal);
            temp->maxVal = max(temp->maxVal, temp->right->maxVal);
        }
        
        // Update min and max values for the current node
        temp->minVal = min(temp->minVal, root->val);
        temp->maxVal = max(temp->maxVal, root->val);
        temp->isBST = isBST;
        
        return temp;
    }

    // Function to update the maximum sum if the current subtree is a BST
    void MaxSum(node* root) {
        if (!root) return;
        if (root->isBST) ans = max(ans, root->sum);
        MaxSum(root->left);
        MaxSum(root->right);
    }
    
    int maxSumBST(TreeNode* root) {
        node* rote = createNode(root); // Create node object for the entire tree
        ans = 0; // Initialize the maximum sum
        MaxSum(rote); // Find the maximum sum of BSTs
        return ans;
    }
};
139855