<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 Solution {
public:
    int ans;
    map<TreeNode* ,int> mn;
    map<TreeNode* ,int> mx;

    int getMin(TreeNode* root){
        if(!root) return INT_MAX;
        int left  = getMin(root->left);
        int right  = getMin(root->right);
        int ans = min({left,right,root->val});
        mn[root] = ans;
        return min(ans,root->val);
    }
    int getMax(TreeNode* root){
        if(!root) return INT_MIN;
        int left  = getMax(root->left);
        int right  = getMax(root->right);
        int ans = max({left,right,root->val});
        mx[root] = ans;
        return max(ans,root->val);
    }

    pair<int,int> solve(TreeNode* root){
        if(!root) return {1,0};
        if(!root->left && !root->right){
            ans = max(ans,root->val);
            return {1,root->val};
        }
        int val = root->val;
        int left = INT_MIN;
        int right = INT_MAX;
        if(root->left){
            left = mx[root->left];
        }
        if(root->right){
            right = mn[root->right];
        }
        bool isBst = 1;
        if(left >= root->val) isBst = 0;
        if(right <= root->val) isBst = 0;

        auto l = solve(root->left);
        auto r = solve(root->right);
        // cout<<root->val<<" "<<l.second<<" "<<r.second<<endl;
        isBst = isBst & l.first & r.first;
        
        // cout<<root->val<<" "<<left<<" "<<right<<" "<<isBst<<" "<<l.second + r.second + root->val<<endl;
        if(isBst && l.first && r.first){
            ans = max(ans,l.second + r.second + root->val);
            return {1,l.second + r.second + root->val};
        }
        return {0,0};
    }


    int maxSumBST(TreeNode* root) {
        ans = 0;
        getMin(root);
        getMax(root);
        solve(root);
        return ans;
    }  
};


/*
if(!root) return {1,0};
        if(!root->left && !root->right){
            ans = max(ans,root->val);
            return {1,root->val,root->val,root->val};
        }
        vector<int> l = {1,0,INT_MAX,INT_MIN};
        vector<int> r = {1,0,INT_MAX,INT_MIN};
        bool isBst = true;
        if(root->left && root->left->val >= root->val){
            isBst = 0;
        }
        if(root->right && root->right->val <= root->val){
            isBst = 0;
        }

        bool leftBst = true,rightBst = true;

        if(root->left){
            l = solve(root->left);
            if(l[2] >= root->val || l[3] >= root->val){
                leftBst = 0;
            }
        }
        if(root->right){
            r = solve(root->right);
            if(l[2] <= root->val || l[3] <= root->val){
                rightBst = 0;
            }
        }
        // cout<<root->val<<" { "<<l.first<<" , "<<l.second<<" } "<<"{ "<<r.first<<" , "<<r.second<<" }"<<endl;
        if(isBst && leftBst && rightBst){
            int sum = root->val + l[1] + r[1];
            ans = max(ans,sum);
            return {1,sum,min({root->val,l[2],r[2]}),max({root->val,l[3],r[3]})};
        }
        else return {0,0,INT_MAX,INT_MIN};
*/
199368