Problem:

https://leetcode.com/problems/house-robber-iii/description/

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.

Example 2:

     3
/ \
4   5
/ \   \
1   3   1


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

Idea:

Compare grandparent + max of grandchildren(l.l + l.r + r.l + r.r) vs max of children (l + r)

Solution 1: Recursion w/o memorization

Time complexity: O(n^2)

Space complexity: O(n)

C++

Solution 2: Recursion w/ memorization

Time complexity: O(n)

Space complexity: O(n)

Solution 3: Recursion return children’s value

Python3

Related Problems:

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