Largest BST Subtree

Given a binary tree, find the largest subtree which is a Binary Search Tree (BST), where largest means subtree with largest number of nodes in it.

Note:

A subtree must include all of its descendants.

Here’s an example:

  1.     10
  2.     / \
  3.    5  15
  4.   / \   \ 
  5.  1   8   7

The Largest BST Subtree in this case is the highlighted one.

The return value is the subtree’s size, which is 3.

Hint:

  1. You can recursively use algorithm similar to 98. Validate Binary Search Tree at each node of the tree, which will result in O(nlogn) time complexity.

Follow up:

Can you figure out ways to solve it with O(n) time complexity?