What is the optimal time complexity of solving Minimum Swaps brackets balancing?

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 Minimum Swaps brackets balancing?

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 Minimum Swaps brackets balancing?

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 Minimum Swaps brackets balancing?

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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Competitive ProgrammingEasy

Minimum Swaps brackets balancing

Learn how to solve the 'Minimum Swaps brackets balancing' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function minimum_swaps_balancing(s) that takes a string s of square brackets [ and ] containing equal numbers of opening and closing brackets, and returns the minimum number of swaps of adjacent characters needed to balance the string.

Constraints

•2 <= len(s) <= 10^5
•s contains only '[' and ']'
•Count of '[' equals count of ']'

Examples

Example 1

Input

minimum_swaps_balancing('[]][[]')

Output

Explanation

Swap index 2 and 3 -> '[][][]', which is balanced. (1 swap)

Example 2

Input

minimum_swaps_balancing(']]][[[')

Output

Explanation

We can swap adjacent brackets to make it balanced, requiring 6 swaps in total.

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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