# Time:  O(n)
# Space: O(h)

# We are given the head node root of a binary tree,
# where additionally every node's value is either a 0 or a 1.
#
# Return the same tree where every subtree (of the given tree)
# not containing a 1 has been removed.
#
# (Recall that the subtree of a node X is X,
#  plus every node that is a descendant of X.)
#
# Example 1:
# Input: [1,null,0,0,1]
# Output: [1,null,0,null,1]
#
# Explanation:
# Only the red nodes satisfy the property "every subtree not containing a 1".
# The diagram on the right represents the answer.
#
# Example 2:
# Input: [1,0,1,0,0,0,1]
# Output: [1,null,1,null,1]
#
# Example 3:
# Input: [1,1,0,1,1,0,1,0]
# Output: [1,1,0,1,1,null,1]
#
# Note:
# - The binary tree will have at most 100 nodes.
# - The value of each node will only be 0 or 1.

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None


class Solution(object):
    def pruneTree(self, root):
        """
        :type root: TreeNode
        :rtype: TreeNode
        """
        if not root:
            return None
        root.left = self.pruneTree(root.left)
        root.right = self.pruneTree(root.right)
        if not root.left and not root.right and root.val == 0:
            return None
        return root