Largest BST Subtree — LeetCode 333 Python Solution

The problem

Given the root of a binary tree, find the largest subtree, which is also a Binary Search Tree (BST), where the largest means subtree has the largest number of nodes. A Binary Search Tree (BST) is a tree in which all the nodes follow the below-mentioned properties: The left subtree values are less than the value of their parent (root) node's value.

Example

Input

root = [10,5,15,1,8,null,7]

Output

3

Explanation

The Largest BST Subtree in this case is the highlighted one. The return value is the subtree's size, which is 3.

Python solution

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def largestBSTSubtree(self, root: Optional[TreeNode]) -> int:
        def dfs(root):
            if root is None:
                return inf, -inf, 0
            lmi, lmx, ln = dfs(root.left)
            rmi, rmx, rn = dfs(root.right)
            nonlocal ans
            if lmx < root.val < rmi:
                ans = max(ans, ln + rn + 1)
                return min(lmi, root.val), max(rmx, root.val), ln + rn + 1
            return -inf, inf, 0

        ans = 0
        dfs(root)
        return ans

Complexity

Pattern: Tree Traversal

Choose the order — preorder, inorder, postorder, level — and the problem solves itself. LeetCode 333. Largest BST Subtree is filed here because LeetCode tags it Tree, Binary Tree and Binary Search Tree, which is the vocabulary this hub collects.

The tree traversal guide has the Python template for the pattern and the 225 LeetCode problems that use it.

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