Start by clarifying the problem constraints (e.g., array size, distinctness) and then explain a backtracking approach that builds permutations by swapping elements in-place. Walk through a small example to illustrate the recursion and discuss time/space complexity.
Pro tip: Mention that swapping avoids extra space for a 'used' array and that the algorithm generates permutations in-place, but be careful to swap back to maintain correctness. Also, note that for very large n, generating all permutations is impractical due to factorial time, so clarify if the interviewer expects an optimized approach for large inputs.
Ask about input size, whether the array can be modified, and if the output should be in a specific order. Confirm that all integers are distinct.
Decide between backtracking with a 'used' array or in-place swapping. Explain that swapping is more space-efficient (O(1) extra space) but modifies the input.
Describe the base case (when the current index reaches the end, add a copy of the permutation to the result) and the recursive step (swap the current element with each subsequent element, recurse, then swap back).
State that there are n! permutations, each of length n, so time complexity is O(n * n!) and space complexity is O(n) for recursion stack (plus output storage).
Walk through a small array like [1,2,3] to demonstrate how the swaps generate all permutations and ensure no duplicates are produced.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.