Solution: House Robber III
Explore how to implement an optimized backtracking solution to the House Robber III problem in C#. Understand how to recursively calculate the maximum amount of money a thief can rob from a binary tree of houses without robbing two connected houses, ensuring no police alert. Gain insights into balancing include and exclude node values to maximize the stolen amount while maintaining efficient time and space complexities.
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