Largest BST | Practice | GeeksforGeeks

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Avoid using static/global variables in coding problems as your code is tested against multiple test cases and these tend to retain their previous values.
Passing the Sample/Custom Test cases in coding problems does not guarantee the correctness of code. On submission, your code is tested against multiple test cases consisting of all possible corner cases and stress constraints.

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Suggest Changes in Problem Statement:

Given a binary tree. Find the size of its largest subtree that is a Binary Search Tree. 
Note: Here Size is equal to the number of nodes in the subtree.

Example 1:

<pre>
Input:
  1
  / \
  4 4
  / \
  6 8
Output: 1
Explanation: There's no sub-tree with size
greater than 1 which forms a BST. All the
leaf Nodes are the BSTs with size equal
to 1.
</pre>

Example 2:

<pre>
Input: 6 6 3 N 2 9 3 N 8 8 2
  6
  / \
  6 3
  \ / \
  2 9 3
  \ / \
  8 8 2 
Output: 2
Explanation: The following sub-tree is a
BST of size 2: 
      2
    /    \ 
  N      8</pre>

Your Task: 
You don't need to read input or print anything. Your task is to complete the function largestBst() that takes the root node of the Binary Tree as its input and returns the size of the largest subtree which is also the BST. If the complete Binary Tree is a BST, return the size of the complete Binary Tree.

Expected Time Complexity: O(N). 
Expected Auxiliary Space: O(Height of the BST).

Constraints: 
1 ≤ Number of nodes ≤ 105 
1 ≤ Data of a node ≤ 106

Given a binary tree. Find the size of its largest subtree that is a Binary Search Tree. 
Note: Here Size is equal to the number of nodes in the subtree.

Example 1:

<pre>
Input:
  1
  / \
  4 4
  / \
  6 8
Output: 1
Explanation: There's no sub-tree with size
greater than 1 which forms a BST. All the
leaf Nodes are the BSTs with size equal
to 1.
</pre>

Example 2:

<pre>
Input: 6 6 3 N 2 9 3 N 8 8 2
  6
  / \
  6 3
  \ / \
  2 9 3
  \ / \
  8 8 2 
Output: 2
Explanation: The following sub-tree is a
BST of size 2: 
      2
    /    \ 
  N      8</pre>

Your Task: 
You don't need to read input or print anything. Your task is to complete the function largestBst() that takes the root node of the Binary Tree as its input and returns the size of the largest subtree which is also the BST. If the complete Binary Tree is a BST, return the size of the complete Binary Tree.

Expected Time Complexity: O(N). 
Expected Auxiliary Space: O(Height of the BST).

Constraints: 
1 ≤ Number of nodes ≤ 105 
1 ≤ Data of a node ≤ 106

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