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Permutations – Solution & Complexity

Interview solutions
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Permutations

Solution Walkthrough

  1. Step 1: Recognize the Pattern

    The key pattern is: Backtracking chooses each remaining value next. Identify the state and invariant before coding.

  2. Step 2: Build the Algorithm

    Advance one state transition at a time. Mark or update state before exploring dependent work.

  3. Step 3: Check Edge Cases

    Test empty or minimal input, skewed shapes, duplicates where allowed, and impossible outcomes.

  4. Step 4: Solution and Complexity

    Time: O(nn!). Space: O(nn!).

    def permute(nums: list[int]) -> list[list[int]]:
    answer = []
    def build(current, remaining):
        if not remaining:
            answer.append(current); return
        for i, value in enumerate(remaining):
            build(current + [value], remaining[:i] + remaining[i+1:])
    build([], nums)
    return answer

FAQ

See also

Practice Permutations online (run code in the browser)Combination Sum solution (medium)Subsets solution (medium)Combination Sum II solution (medium)Generate Parentheses solution (medium)All coding interview problems
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