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Suppose the House Robber III problem is modified so that you can rob each node multiple times, but robbing adjacent nodes in the same step is still forbidden. Which approach best handles this variant?

hard🎤 Interviewer Follow-up Q10 of Q15
Tree: Depth-First Search - House Robber III (On Tree)
Suppose the House Robber III problem is modified so that you can rob each node multiple times, but robbing adjacent nodes in the same step is still forbidden. Which approach best handles this variant?
AUse the same optimal DFS with two-value return, ignoring multiple robbing
BApply brute force recursion enumerating all robbing sequences
CUse dynamic programming with state tracking number of times each node is robbed
DTransform the tree into a graph and apply max flow algorithms
Step-by-Step Solution
Solution:

  1. Step 1: Understand problem change

    Allowing multiple robbings per node with adjacency constraints changes problem fundamentally.

  2. Step 2: Recognize approach

    This variant resembles scheduling or resource allocation with adjacency constraints, solvable via graph max flow or matching algorithms.

  3. Step 3: Why other approaches fail

    Simple DFS or DP cannot track multiple robbings; brute force is exponential and impractical.

  4. Final Answer:

    Option D -> Option D

  5. Quick Check:

    Graph transformation and max flow handle complex constraints [OK]
Quick Trick: Multiple robbings with adjacency constraints require graph algorithms [OK]
Common Mistakes:
MISTAKES
  • Trying to extend DP without changing approach
Trap Explanation:
PITFALL
  • Candidates often try naive DP extensions ignoring problem complexity increase.
Interviewer Note:
CONTEXT
  • Tests ability to adapt approach to problem variants
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