Subsets & Combinations - Largest Divisible Subset
Given an unsorted array of distinct positive integers, which approach is most suitable to find the largest subset where each element divides the next one in the subset?
Given an unsorted array of distinct positive integers, which approach is most suitable to find the largest subset where each element divides the next one in the subset?
easy💻 Programming Q1 of Q15
Step-by-Step Solution
Solution:
Step 1: Sort the array to ensure divisibility order
Sorting ensures that if a number divides another, it appears before it.Step 2: Use dynamic programming to build the largest divisible subset
Check divisibility with previous elements and build the longest chain.Final Answer:
Option C -> Option CQuick Check:
Sorting + DP is the standard approach for this problem [OK]
Quick Trick: Sort first, then use DP to find divisible chains [OK]
Common Mistakes:
MISTAKES- Assuming greedy picking smallest elements always works
- Ignoring sorting step before DP
- Trying BFS which is inefficient here
Trap Explanation:
PITFALL- Greedy or BFS approaches ignore the importance of sorting and DP for divisibility.
Interviewer Note:
CONTEXT- Tests understanding of the fundamental approach to the Largest Divisible Subset problem.
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