Skip to main content

Maximum Sum BST in Binary Tree

Problem​

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.

Solution Approach​

Expected Time complexity: O(n)O(n)

Click - to see solution code
class Solution {
   public:
    int ans = 0;
    bool f(TreeNode *root, int &minv, int &maxv, int &s) {
        if (root == NULL) return true;

        int lmin = minv, lmax = maxv, lsum = 0;
        bool l = f(root->left, lmin, lmax, lsum);

        int rmin = minv, rmax = maxv, rsum = 0;
        bool r = f(root->right, rmin, rmax, rsum);

        if (l == false || r == false || root->val <= lmax || root->val >= rmin)
            return false;

        s += lsum + rsum + root->val;
        ans = max(ans, s);

        minv = min(lmin, root->val);
        maxv = max(rmax, root->val);
        return true;
    }

    int maxSumBST(TreeNode *root) {
        int s = 0;
        int lm = INT_MAX, rm = INT_MIN;
        f(root, lm, rm, s);
        return ans;
    }
};