Solution: House Robber III
Explore a backtracking approach to solve the House Robber III problem where houses are nodes in a binary tree. Understand how to calculate the maximum amount of money that can be robbed without robbing two directly connected houses by evaluating subtrees. Learn to implement the solution recursively, optimizing with include and exclude root strategies, and analyze the time and space complexity of the approach.
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