<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) {}
 * };
 */

 auto speedUp = []() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return 0;
}();


struct my_nitesh_bro{
    bool isBst;
    int min_val;
    int max_val;
    int currentSum;
    my_nitesh_bro(bool bst,int mi, int ma, int sum) : isBst(bst), min_val(mi),max_val(ma),currentSum(sum) {};
};
class Solution {
public:
    bool isLeaf(TreeNode* root){
        if(root && root->left == nullptr && root->right == nullptr)
            return true;
        return false;
    }

    bool isBST(TreeNode* root,int min,int max){
      if(root == nullptr) return true;
      if(root->val > max || root->val < min) return false;
      return isBST(root->left,min,root->val -1) && isBST(root->right,root->val + 1 , max);  

    }
/*
    std::pair<bool,int> searchBST(TreeNode* root, int& maxSumBst){
        if(root == nullptr) return std::make_pair(true,0);
        if(isLeaf(root)){
            maxSumBst = std::max(maxSumBst,root->val);
            return std::make_pair(true,root->val);
        }
        auto left = searchBST(root->left,maxSumBst);
        auto right = searchBST(root->right,maxSumBst);
        int currentSum = 0;
        if(left.first && right.first && isBST(root,INT_MIN,INT_MAX)){
            currentSum = root->val + left.second +right.second;
            maxSumBst = std::max(maxSumBst,currentSum);
            return std::make_pair(true,currentSum);
        }
        return std::make_pair(false,currentSum);
    }

    std::tuple<bool,int,int,int> searchBST(TreeNode* root, int& maxSumBst){
        if(root == nullptr) return std::make_tuple(true,INT_MAX,INT_MIN,0);
        auto left = searchBST(root->left,maxSumBst);
        auto right = searchBST(root->right,maxSumBst);
        int currentSum = 0;
        if(std::get<0>(left) && std::get<0>(right) && std::get<2>(left) < root->val &&  std::get<1>(right) > root->val){
            currentSum = std::get<3>(left) + std::get<3>(right) + root->val;
            maxSumBst = std::max(maxSumBst,currentSum);
            return std::make_tuple(true,std::min(std::get<1>(left),root->val),std::max(std::get<2>(right),root->val),currentSum);
        }
        return std::make_tuple(false,0,0,currentSum);
    }

*/

 my_nitesh_bro searchBST(TreeNode* root, int& maxSumBst){
        if(root == nullptr) return my_nitesh_bro(true,INT_MAX,INT_MIN,0);
        auto left = searchBST(root->left,maxSumBst);
        auto right = searchBST(root->right,maxSumBst);
        int currentSum = 0;
        if(left.isBst && right.isBst && left.max_val < root->val &&  right.min_val > root->val){
            currentSum = left.currentSum + right.currentSum + root->val;
            maxSumBst = std::max(maxSumBst,currentSum);
            return my_nitesh_bro(true,std::min(left.min_val,root->val),std::max(right.max_val,root->val),currentSum);
        }
        return my_nitesh_bro(false,0,0,currentSum);
    }


    int maxSumBST(TreeNode* root) {
        int maxSum = 0;
        searchBST(root,maxSum);
        return maxSum;
    }
};
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