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.
3 / \ 2 3 \ \ 3 1Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.
3 / \ 4 5 / \ \ 1 3 1Maximum amount of money the thief can rob = 4 + 5 = 9.
Special thanks to @dietpepsi for adding this problem and creating all test cases.