"""
337. House Robber 3
The thief has found himself a new place for his thievery again. There is only one entrance to this area, called the "root." Besides the root, each house has one and only one parent house. After a tour, the smart thief realized that "all houses in this place forms a binary tree". It will automatically contact the police if two directly-linked houses were broken into on the same night.

Determine the maximum amount of money the thief can rob tonight without alerting the police.

Example 1:
     3
    / \
   2   3
    \   \ 
     3   1
Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.
"""
# 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 rob(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        return max(self.dfsRob(root))

    def dfsRob(self, root):
        if root == None:
            return [0, 0]
        else:
            left = self.dfsRob(root.left)
            right = self.dfsRob(root.right)
            res = [0, 0]
            res[0] = max(left[0], left[1]) + max(right[0], right[1])
            res[1] = root.val + left[0] + right[0]
            return res
