I knew it was backtracking pretty fast, which was a relief.
Start by clarifying the problem constraints (e.g., array size, distinctness) and then present a backtracking solution that builds permutations incrementally. Explain the time complexity O(n * n!) and space complexity O(n) for recursion, and discuss potential optimizations like swapping elements in-place to avoid extra space.
Pro tip: Mention that for large n, generating all permutations is infeasible, so in practice you'd use lazy evaluation or itertools.permutations in Python. Also, relate it to ML tasks like hyperparameter tuning where you might need to explore permutations of parameters.
Ask about input size, whether the array can be empty, and if the output order matters. Confirm that all integers are distinct.
Explain that you'll recursively build permutations by choosing an unused element at each step. Use a boolean array or set to track used elements.
Take a small array like [1,2,3] and show how the recursion tree generates all 6 permutations. This demonstrates understanding.
State that there are n! permutations and each takes O(n) to copy, so time is O(n * n!). Space is O(n) for recursion stack and used array, plus O(n * n!) for output.
Mention in-place swapping to reduce space, handling empty array, and note that for large n, generating all permutations is impractical.
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