largest-bst-subtree.py

# 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:

#     10
#     / \
#    5  15
#   / \   \ 
#  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:

# 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?


# V0  : DEV 

# V1

# V2
# Time:  O(n)
# Space: O(h)
class Solution(object):
    def largestBSTSubtree(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        if root is None:
            return 0

        max_size = [1]
        def largestBSTSubtreeHelper(root):
            if root.left is None and root.right is None:
                return 1, root.val, root.val

            left_size, left_min, left_max = 0, root.val, root.val
            if root.left is not None:
                left_size, left_min, left_max = largestBSTSubtreeHelper(root.left)

            right_size, right_min, right_max = 0, root.val, root.val
            if root.right is not None:
                right_size, right_min, right_max = largestBSTSubtreeHelper(root.right)

            size = 0
            if (root.left is None or left_size > 0) and \
               (root.right is None or right_size > 0) and \
               left_max <= root.val <= right_min:
                size = 1 + left_size + right_size
                max_size[0] = max(max_size[0], size)

            return size, left_min, right_max

        largestBSTSubtreeHelper(root)
        return max_size[0]