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Grokking the Coding Interview Patterns in C++

Solution: House Robber III

Explore how to apply backtracking to solve the House Robber III problem where houses are nodes in a binary tree. Understand how to maximize robbery amounts without triggering alarms by recursively evaluating included and excluded nodes. This lesson covers algorithm optimization and complexity analysis for efficient solutions.

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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 [1,500][1, 500].
  • 0≤0 \leq node.data ≤104\leq 10^4
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