m0337.py

"""House Robber III
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:

Input: [3,2,3,null,3,null,1]

     3
    / \
   2   3
    \   \
     3   1

Output: 7

Explanation: Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.

Example 2:

Input: [3,4,5,1,3,null,1]

     3
    / \
   4   5
  / \   \
 1   3   1

Output: 9

Explanation: Maximum amount of money the thief can rob = 4 + 5 = 9.
"""