1373. Maximum Sum BST in Binary Tree

Given a binary tree root, return the maximum sum of all keys of any sub-tree which is also a Binary Search Tree (BST).

Assume a BST is defined as follows:

• The left subtree of a node contains only nodes with keys less than the node’s key.
• The right subtree of a node contains only nodes with keys greater than the node’s key.
• Both the left and right subtrees must also be binary search trees.

/**
 * 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 {
    long long res = 0;
    array<long long, 3> helper(TreeNode* node) {
        if(!node->left and !node->right) {
            res = max(res, (long long) node->val);
            return {node->val, node->val, node->val};
        }
        long long mi = node->val, ma = node->val, sum = node->val;
        bool valid = true;
        if(node->left) {
            auto [lmi, lma, lsum] = helper(node->left);
            if(lma >= node->val) valid = false;
            mi = lmi;
            sum += lsum;
        }
        if(node->right) {
            auto [rmi, rma, rsum] = helper(node->right);
            if(rmi <= node->val) valid = false;
            ma = rma;
            sum += rsum;
        }
        if(valid) {
            res = max(res, sum);
            return {mi, ma, sum};
        }
        return {INT_MIN, INT_MAX, INT_MIN};
    }
public:
    int maxSumBST(TreeNode* root) {
        helper(root);
        return res;
    }
};