What is the optimal time complexity of solving Print All Permutations of a String?

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 Print All Permutations of a String?

The space complexity is O(1) 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 Print All Permutations of a String?

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 Print All Permutations of a String?

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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Python BasicsEasy

Print All Permutations of a String

Learn how to solve the 'Print All Permutations of a String' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function permutations(s) that takes a string s and returns a sorted list of all unique permutations of the characters in s. Each permutation is a rearrangement of all characters. The returned list must be sorted in lexicographic (alphabetical) order.

Constraints

•1 <= len(s) <= 8
•s contains only lowercase English letters

Examples

Example 1

Input

s = 'abc'

Output

['abc', 'acb', 'bac', 'bca', 'cab', 'cba']

Explanation

All 3! = 6 rearrangements of 'a', 'b', 'c', sorted alphabetically.

Example 2

Input

s = 'ab'

Output

['ab', 'ba']

Explanation

Two characters give 2! = 2 permutations.

Example 3

Input

s = 'aab'

Output

['aab', 'aba', 'baa']

Explanation

There are only 3 unique permutations since 'a' is repeated.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

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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