What is the optimal time complexity of solving Permutations?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Permutations?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Permutations?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Permutations?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Permutations

Learn how to solve the 'Permutations' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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

Implement a function permute(nums: list) -> list.

Constraints

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

Examples

Example 1

Input

[1,2,3]

Output

[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

Explanation

All 3! = 6 permutations of [1,2,3] are generated.

Example 2

Input

[0,1]

Output

[[0,1],[1,0]]

Explanation

All 2! = 2 permutations of [0,1] are generated.

Example 3

Input

[1]

Output

[[1]]

Explanation

Only one permutation exists for a single element.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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