Subsets & Combinations - Largest Divisible Subset
Given the dp array [1, 2, 3, 2, 4] and prev array [-1, 0, 1, 0, 2] after processing a sorted input array, which of the following input arrays could produce this state?
Given the dp array [1, 2, 3, 2, 4] and prev array [-1, 0, 1, 0, 2] after processing a sorted input array, which of the following input arrays could produce this state?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze dp and prev meaning
dp[i] is length of largest divisible subset ending at i; prev[i] points to previous index in chain.Step 2: Match arrays to input
dp[4]=4 with prev[4]=2 means nums[4] divisible by nums[2]; dp[2]=3 with prev[2]=1 means chain 1->2->4; input must be sorted and divisible accordingly.Step 3: Verify options
[1, 2, 4, 3, 8]: sorted is [1, 2, 3, 4, 8], matches dp and prev relations.Final Answer:
Option B -> Option BQuick Check:
dp and prev arrays consistent with [1, 2, 4, 3, 8] input [OK]
Quick Trick: dp and prev arrays encode chain structure [OK]
Common Mistakes:
MISTAKES- Ignoring sorting or misinterpreting prev pointers
Trap Explanation:
PITFALL- Candidates often fail to reverse engineer dp and prev arrays correctly.
Interviewer Note:
CONTEXT- Tests deep understanding of DP state and reconstruction.
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