Solution: House Robber III
Explore how to apply backtracking to solve the House Robber III problem on a binary tree. Understand how to recursively compute maximum robbery amounts by including or excluding parent nodes, ensuring the thief avoids alerting the police through adjacent robberies. This lesson equips you with a method to optimize problem-solving in tree-based challenges with time complexity O(n).
Statement
A thief has discovered a new neighborhood to target, where the houses can be represented as nodes in a binary tree, and the money in the house is the data of the respective node. The thief can enter the neighborhood from a house represented as root of the binary tree. Each house has only one parent house. The thief knows that if he robs two houses that are directly connected, the police will be notified. The thief wants to know the maximum amount of money he can steal from the houses without getting caught by the police. The thief needs your help determining the maximum amount of money he can rob without alerting the police.
Constraints:
- The number of nodes in the tree is in the range