Given a Binary Tree, write a function that returns the size of the largest subtree which is also a Binary Search Tree (BST). If the complete Binary Tree is BST, then return the size of the whole tree.
Input: 5 / \ 2 4 / \ 1 3 Output: 3 The following subtree is the maximum size BST subtree 2 / \ 1 3 Input: 50 / \ 30 60 / \ / \ 5 20 45 70 / \ 65 80 Output: 5 The following subtree is the maximum size BST subtree 60 / \ 45 70 / \ 65 80
We have discussed two methods in below post.
Find the largest BST subtree in a given Binary Tree | Set 1
In this post, a different O(n) solution is discussed. This solution is simpler than the solutions discussed above and works in O(n) time.
The idea is based on method 3 of check if a binary tree is BST article.
A Tree is BST if following is true for every node x.
- The largest value in left subtree (of x) is smaller than value of x.
- The smallest value in right subtree (of x) is greater than value of x.
We traverse tree in bottom up manner. For every traversed node, we return maximum and minimum values in subtree rooted with it. If any node follows above properties and size of
Size of largest BST is 2
Time Complexity : O(n)
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- K'th Largest Element in BST when modification to BST is not allowed
- Find the largest BST subtree in a given Binary Tree | Set 1
- Maximum sub-tree sum in a Binary Tree such that the sub-tree is also a BST
- Two nodes of a BST are swapped, correct the BST | Set-2
- Convert a normal BST to Balanced BST
- Two nodes of a BST are swapped, correct the BST
- Find k-th smallest element in BST (Order Statistics in BST)
- Overview of Data Structures | Set 2 (Binary Tree, BST, Heap and Hash)
- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- A program to check if a binary tree is BST or not
- Convert a BST to a Binary Tree such that sum of all greater keys is added to every key
- Check if a Binary Tree (not BST) has duplicate values
- Build Binary Tree from BST such that it's level order traversal prints sorted data
- Floor in Binary Search Tree (BST)
- Check if a Binary Tree is BST : Simple and Efficient Approach
- Check if the Binary Tree contains a balanced BST of size K
- Count permutations of given array that generates the same Binary Search Tree (BST)
- Check if a binary tree is subtree of another binary tree | Set 1
- Check if a binary tree is subtree of another binary tree | Set 2
- Convert a Binary Tree to Threaded binary tree | Set 1 (Using Queue)