Subsets & Combinations - Combinations (Choose K from N)
What is the time complexity of generating all combinations of size k from n elements using backtracking with pruning?
What is the time complexity of generating all combinations of size k from n elements using backtracking with pruning?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Count total combinations
Number of combinations is \u210B(n, k) = n choose k.Step 2: Account for work per combination
Each combination requires copying k elements, so total time is O(\u210B(n, k) * k).Final Answer:
Option D -> Option DQuick Check:
Backtracking enumerates all combinations, each of size k [OK]
Quick Trick: Time proportional to number of combinations times k [OK]
Common Mistakes:
MISTAKES- Confusing with n^k exponential
- Ignoring cost to copy combinations
Trap Explanation:
PITFALL- Candidates often mistake exponential permutations for combinations complexity.
Interviewer Note:
CONTEXT- Tests understanding of backtracking time complexity for combinations.
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