How do you approach Permutations?

Use backtracking to generate permutations.

What is the time complexity of Permutations?

Time complexity: O(n * n!). Space complexity: O(n) for recursion stack.

What are common mistakes on Permutations?

Pushing the working array into the results without copying it, so every entry aliases the same array. Forgetting to undo the choice after the recursive call returns. Deduplicating at the end instead of pruning at the branch - the difference between passing and timing out.

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Permutations

MediumAlgorithms

Description

Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order.

Example 1

Input: nums = [1,2,3]

Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

Example 2

Input: nums = [0,1]

Output: [[0,1],[1,0]]

Example 3

Input: nums = [1]

Output: [[1]]

Constraints

- 1 <= nums.length <= 6 - -10 <= nums[i] <= 10 - All the integers of nums are unique.

Permutations: approach, complexity and pitfalls

A medium backtracking problem, graded against 5 test cases (2 of them hidden).

The pattern: Backtracking

Systematic exploration of all candidates, abandoning partial ones that cannot work.

Reach for it when you see: "All permutations/combinations/subsets", or constraint puzzles like N-Queens and Sudoku.

If you are stuck

Show the 3-step hint ladder

Use backtracking to generate permutations.
At each step, choose an element that hasn't been used yet.
Use a set or boolean array to track which elements are already in the current permutation.

The optimal approach

Show the approach: Backtracking

Build permutations by choosing unused elements at each position. Backtrack after adding each element.

Time: O(n * n!)
Space: O(n) for recursion stack

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

What the tests check

Read off this problem's own test suite, so these are the cases a submission actually has to survive.

Single element. A one-element case is included. Two-pointer and window solutions frequently return the wrong thing when the two indices start out equal.
Zero. Zero appears in the input, which is the value most likely to break a truthiness check used in place of an explicit comparison.

Common Backtracking mistakes

These apply to the pattern as a whole, not just this problem.

Pushing the working array into the results without copying it, so every entry aliases the same array.
Forgetting to undo the choice after the recursive call returns.
Deduplicating at the end instead of pruning at the branch - the difference between passing and timing out.