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Permutations – Solution & Complexity

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Permutations

1. Recognize the Pattern

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

2. Build the Algorithm

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

3. Check Edge Cases

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

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)Best Time to Buy and Sell Stock solution (easy)Binary Search solution (easy)All coding interview problems
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