Maximum sub-tree sum in a Binary Tree such that the sub-tree is also a BST
Given a binary tree, the task is to print the maximum sum of nodes of a sub-tree which is also a Binary Search Tree.
Input : 7 / \ 12 2 / \ \ 11 13 5 / / \ 2 1 38 Output:44 BST rooted under node 5 has the maximum sum 5 / \ 1 38 Input: 5 / \ 9 2 / \ 6 3 / \ 8 7 Output: 8 Here each leaf node represents a binary search tree also a BST with sum 5 exists 2 \ 3 But the leaf node 8 has the maximum sum.
Approach: We traverse the tree in bottom-up manner. For every traversed node, we store the information of maximum and minimum of that subtree, a variable isBST to store if it is a BST, variable currmax to store the maximum sum of BST found till now, and a variable sum to store the sum of Left and Right subtree(which is also a BST) rooted under the current node.
Below is the implementation of the above approach:
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Time Complexity: O(N)
Auxiliary Space: O(N)