House Robber III

House Robber III is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Tree Traversal Patterns (DFS & BFS) pattern, in the Recursive Postorder Traversal subpattern.

Problem statement

The thief has found himself a new place for his thievery again. There is only one entrance to this area, called 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 form a binary tree. It will automatically contact the police if two directly-linked houses were broken into on the same night.

Given the root of the binary tree, return the maximum amount of money the thief can rob without alerting the police.

Example 1:

Input: root = [3,2,3,null,3,null,1] Output: 7 Explanation: Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.

Example 2:

Input: root = [3,4,5,1,3,null,1] Output: 9 Explanation: Maximum amount of money the thief can rob = 4 + 5 = 9.

Constraints:

- The number of nodes in the tree is in the range [1, 104].

- 0 <= Node.val <= 104

Topics and companies

Topics: Dynamic Programming, Tree, Depth-First Search, Binary Tree.

Reported in interviews at Amazon, Facebook, Google.

How to practise House Robber III on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(n) time and O(h) space.

Open House Robber III in the code editor, or read the House Robber III editorial for a worked solution with its approach and complexity analysis.

Where House Robber III sits in the DSA pattern sheet

• Tree Traversal Patterns (DFS & BFS) pattern guide
• Recursive Postorder Traversal subpattern
• The full DSA patterns sheet
• All coding practice problems

Problems related to House Robber III

Other problems that use the same Recursive Postorder Traversal and Tree Traversal Patterns (DFS & BFS) techniques:

• All Nodes Distance K in Binary Tree — Medium, same subpattern
• Balanced Binary Tree — Easy, same subpattern
• Binary Tree Maximum Path Sum — Hard, same subpattern
• Binary Tree Postorder Traversal — Easy, same subpattern
• Delete Nodes And Return Forest — Medium, same subpattern
• Diameter of Binary Tree — Easy, same subpattern