What is the optimal time complexity of solving Remove adjacent duplicates recursively?

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 Remove adjacent duplicates recursively?

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 Remove adjacent duplicates recursively?

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 Remove adjacent duplicates recursively?

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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Remove adjacent duplicates recursively

Learn how to solve the 'Remove adjacent duplicates recursively' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function remove_adjacent_duplicates(s) that recursively removes all adjacent duplicate characters from the string s until no adjacent duplicates remain. In each pass, remove all pairs of consecutive identical characters, then repeat the process on the resulting string until it stabilizes. Return the final string.

Constraints

•0 <= len(s) <= 1000
•s contains only lowercase English letters

Examples

Example 1

Input

s = 'aabccba'

Output

'a'

Explanation

First pass: remove 'aa' and 'cc' -> 'bba'. Second pass: remove 'bb' -> 'a'. No more adjacent duplicates.

Example 2

Input

s = 'abcddcba'

Output

''

Explanation

Remove 'dd' -> 'abccba'. Remove 'cc' -> 'abba'. Remove 'bb' -> 'aa'. Remove 'aa' -> ''. Empty string.

Example 3

Input

s = 'abcd'

Output

'abcd'

Explanation

No adjacent duplicates exist, so the string remains unchanged.

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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