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What is the overall time complexity of generating all permutations of n distinct elements using an iterative bitmask DP approach that stores all permutations for each subset?

medium🧠 Conceptual Q5 of Q15

Bit Manipulation - Generate All Permutations Using Bitmask DP

What is the overall time complexity of generating all permutations of n distinct elements using an iterative bitmask DP approach that stores all permutations for each subset?

AO(n! * n)

BO(n * 2^n * n!)

CO(2^n * n^2)

DO(n^2 * 2^n)

Step-by-Step Solution

Solution:

Step 1: Number of subsets
There are 2^n subsets of elements.
Step 2: Number of permutations per subset
For subset size k, there are k! permutations.
Step 3: Total permutations over all subsets
Summing over k=0 to n: sum of (C(n,k) * k!) which is O(n * n!).
Step 4: DP iteration cost
For each subset and each element, we append permutations, leading to O(n * 2^n * n!) complexity.
Final Answer:
Option B -> Option B
Quick Check:
Consider factorial growth dominates, multiplied by subsets and elements [OK]

Quick Trick: Factorial times subsets times elements = O(n*2^n*n!) [OK]

Common Mistakes:

MISTAKES

Ignoring factorial growth in permutations
Assuming only 2^n complexity without permutations
Confusing with polynomial complexities

Trap Explanation:

PITFALL

Ignoring permutations count leads to underestimating complexity

Interviewer Note:

CONTEXT

Tests understanding of complexity analysis for bitmask DP permutation generation

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