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What is the time complexity of generating all permutations of n elements using bitmask DP with iterative tabulation as shown in the code snippet? Assume appending to lists is O(1) amortized.

medium🪤 Complexity Trap Q13 of Q15
Bit Manipulation - Generate All Permutations Using Bitmask DP
What is the time complexity of generating all permutations of n elements using bitmask DP with iterative tabulation as shown in the code snippet? Assume appending to lists is O(1) amortized.
AO(n!)
BO(n * n!)
CO(n^2 * 2^n)
DO(2^n * n!)
Step-by-Step Solution

  1. Step 1: Identify number of states and transitions

    There are 2^n bitmask states. Each state has up to n transitions to add an unused element.

  2. Step 2: Calculate total permutations generated

    Total permutations are n!; each permutation is built by adding elements one by one, so total operations ~ n * n!.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Time complexity is O(n * n!) due to building all permutations incrementally [OK]
Quick Trick: Generating all permutations requires at least O(n * n!) time [OK]
Common Mistakes:
MISTAKES
  • Confusing 2^n states with n! permutations
  • Ignoring the cost of building each permutation step
Trap Explanation:
PITFALL
  • Option A (O(n!)) looks plausible but misses the factor n for building permutations; option C confuses DP states with permutations.
Interviewer Note:
CONTEXT
  • Tests if candidate understands complexity of bitmask DP for permutations, not just number of states.
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