Hi, here's your problem today. This problem was recently asked by Twitter:

You are given the root of a binary tree. Find and return the largest subtree of that tree, which is a valid binary search tree.

Here's a starting point:

<pre lang=py>
class TreeNode:
  def __init__(self, key):
    self.left = None
    self.right = None
    self.key = key

  def __str__(self):
    # preorder traversal
    answer = str(self.key)
    if self.left:
      answer += str(self.left)
    if self.right:
      answer += str(self.right)
    return answer

def largest_bst_subtree(root):
  # Fill this in.

#     5
#    / \
#   6   7
#  /   / \
# 2   4   9
node = TreeNode(5)
node.left = TreeNode(6)
node.right = TreeNode(7)
node.left.left = TreeNode(2)
node.right.left = TreeNode(4)
node.right.right = TreeNode(9)
print largest_bst_subtree(node)
#749
</pre>