Solution: House Robber III
Explore how to solve the House Robber III problem using backtracking and recursion. This lesson guides you through optimizing the solution to find the maximum money that can be robbed from houses arranged in a binary tree, avoiding alarms by not robbing two connected houses. Understand how to calculate values including and excluding the root node, and implement an efficient approach with O(n) time and space complexity.
Statement
A thief has discovered a new neighborhood to target, where the houses can be represented as nodes in a binary tree. 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