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What is the time complexity of the iterative lexicographic combinations generation algorithm for generating all combinations of size k from n elements?

medium🪤 Complexity Trap Q13 of Q15
Subsets & Combinations - Combinations (Choose K from N)
What is the time complexity of the iterative lexicographic combinations generation algorithm for generating all combinations of size k from n elements?
AO(n^k) because each element can be chosen or not
BO(k * (n choose k)) since each combination of size k is generated once and updated in O(k)
CO(\u03C3(n choose k) * k) where \u03C3 is the number of combinations generated
DO(n * k) because the outer loop runs n times and inner loop k times
Step-by-Step Solution

  1. Step 1: Identify number of combinations

    There are exactly (n choose k) combinations to generate.

  2. Step 2: Analyze per-combination cost

    Each combination is generated and updated in O(k) time due to copying and resetting elements.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Time is proportional to number of combinations times combination size [OK]
Quick Trick: Time depends on number of combinations times k [OK]
Common Mistakes:
MISTAKES
  • Confusing with exponential O(n^k) or linear O(n*k) complexities
Trap Explanation:
PITFALL
  • Option B looks similar but σ(n choose k) is redundant notation; option A is exponential guess.
Interviewer Note:
CONTEXT
  • Tests understanding of combinatorial output size and per-output cost.
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