Tree: Depth-First Search - House Robber III (On Tree)
What is the space complexity of the optimal DFS with two-value return solution for House Robber III on a tree with n nodes?
What is the space complexity of the optimal DFS with two-value return solution for House Robber III on a tree with n nodes?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Consider recursion stack usage
In worst case (skewed tree), recursion stack depth can be O(n).Step 2: Memoization auxiliary space
Optimal solution uses constant auxiliary space per node, no extra table needed.Final Answer:
Option B -> Option BQuick Check:
Space dominated by recursion stack depth O(n) worst case [OK]
Quick Trick: Recursion stack dominates space in skewed trees [OK]
Common Mistakes:
MISTAKES- Forgetting recursion stack space, assuming O(1)
Trap Explanation:
PITFALL- Candidates often ignore recursion stack space, underestimating total space complexity.
Interviewer Note:
CONTEXT- Tests understanding of recursion stack space in DFS
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