# Maximum sub-tree sum in a Binary Tree such that the sub-tree is also a BST in C++

In this tutorial, we will be discussing a program to find maximum sub-tree sum in a Binary Tree such that the sub-tree is also a BST.

For this we will be provided with a binary tree. Our task is to print the sum of a sub-tree which is also a binary search tree.

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
//creating binary tree node
struct Node {
struct Node* left; struct Node* right; int data;
Node(int data) {
this->data = data;
this->left = NULL;
this->right = NULL;
}
};
struct Info {
int max;
int min;
bool isBST;
int sum;
int currmax;
};
Info MaxSumBSTUtil(struct Node* root, int& maxsum) {
if (root == NULL) return { INT_MIN, INT_MAX, true, 0, 0 };
if (root->left == NULL && root->right == NULL) {
maxsum = max(maxsum, root->data);
return { root->data, root->data, true, root->data, maxsum };
}
Info L = MaxSumBSTUtil(root->left, maxsum);
Info R = MaxSumBSTUtil(root->right, maxsum);
Info BST;
if (L.isBST && R.isBST && L.max < root->data && R.min > root->data) {
BST.max = max(root->data, max(L.max, R.max));
BST.min = min(root->data, min(L.min, R.min));
maxsum = max(maxsum, R.sum + root->data + L.sum);
BST.sum = R.sum + root->data + L.sum;
BST.currmax = maxsum;
BST.isBST = true;
return BST;
}
BST.isBST = false;
BST.currmax = maxsum;
BST.sum = R.sum + root->data + L.sum;
return BST;
}
int MaxSumBST(struct Node* root) {
int maxsum = INT_MIN;
return MaxSumBSTUtil(root, maxsum).currmax;
}
int main() {
struct Node* root = new Node(5);
root->left = new Node(14);
root->right = new Node(3);
root->left->left = new Node(6);
root->right->right = new Node(7);
root->left->left->left = new Node(9);
root->left->left->right = new Node(1);
cout << MaxSumBST(root);
return 0;
}

## Output

10