<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 maxSumBST(TreeNode* root) {
        unordered_map<TreeNode*,pair<bool,pair<int,int>>>mp;
        unordered_map<TreeNode*,int>sum;
        int ans=0;
        func(root,mp,sum,ans);
        return ans;
    }
    //first=max
    //second=min;
    bool func(TreeNode*root,unordered_map<TreeNode*,pair<bool,pair<int,int>>>&mp,
    unordered_map<TreeNode*,int>&sum,int &ans){
        if(!root){
            return true;
        }
        bool l=func(root->left,mp,sum,ans);
        bool r=func(root->right,mp,sum,ans);
        //cout<<root->val<<" "<<l<<" "<<r<<endl;
        if(l&&r){
            int maxi=INT_MIN;
            int mini=INT_MAX;
            int sum1=root->val;
            sum1+=sum[root->left];
            sum1+=sum[root->right];
            bool isBST=true;
            if(root->left&&root->right){
                maxi=max(root->val,mp[root->right].second.first);
                mini=min(mp[root->left].second.second,root->val);
                //cout<<root->val<<" "<<mp[root->right].second.second<<" "<<mp[root->left].second.first<<endl;
                if(mp[root->right].second.second<=root->val||
                mp[root->left].second.first>=root->val){
                    //cout<<"entered"<<endl;
                    isBST=false;
                }
                //cout<<mp[root->right].second.second<<" a "<<mp[root->left].second.first<<" "<<root->val<<endl;
            }
            else if(root->left){
                maxi=root->val;
                mini=min(mp[root->left].second.second,root->val);
                if(mp[root->left].second.first>=root->val){
                    isBST=false;
                }
                //cout<<mp[root->left].second.first<<" b "<<root->val<<endl;
            }
            else if(root->right){
                maxi=max(root->val,mp[root->right].second.first);
                mini=root->val;
                //cout<<mp[root->right].second.second<<" c "<<root->val<<endl;
                if(mp[root->right].second.second<=root->val){
                    isBST=false;
                }
            }
            else{
                mini=root->val;
                maxi=root->val;
            }
            //cout<<root->val<<"checker"<<isBST<<endl;
            mp[root]={isBST,{maxi,mini}};
            sum[root]=sum1;
            if(isBST){
                ans=max(ans,sum1);
            }
            return isBST;
        }
        mp[root]={false,{root->val,root->val}};
        return false;
    }
};
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