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1963. Minimum Number of Swaps to Make the String Balanced

The Minimum Swaps for Balanced Brackets problem is a common challenge in coding interviews, especially in companies like FAANG. It involves transforming a string of brackets into a balanced sequence with the minimum number of swaps. In this article, we will explore an optimized approach to solving this problem using Python, focusing on improving efficiency with a linear time complexity. By the end of this guide, you'll have a deep understanding of how to minimize swaps in an unbalanced sequence of brackets.

Understanding the Problem

The problem revolves around a string consisting of opening ([) and closing (]) brackets. The task is to rearrange the brackets so that the string is balanced, with the condition that the number of swaps must be minimized.

For example:

  • Input: s = "]]][[["
  • Output: 1

In this example, a single swap between the second ] and first [ will balance the string.

Naive Approach and Its Drawbacks

One common approach involves maintaining a stack to track mismatched closing brackets and find a matching opening bracket for each closing one. While this method works, it has a high overhead because of the need to continuously push, pop, and search the stack.

Time Complexity: O(n) for traversing the string, but maintaining the stack adds unnecessary complexity to the solution.

Optimized Solution: Balance and Imbalance

To tackle this problem more efficiently, we can observe the balance between opening and closing brackets directly without using a stack. Here’s how:

  1. Balance: Keep track of the difference between the number of opening and closing brackets as you iterate through the string.
  2. Imbalance: Whenever the balance becomes negative (more closing brackets than opening ones), we record the maximum imbalance. This imbalance helps us determine how many swaps are required.

The trick here is that one swap can fix two imbalanced brackets (one closing and one opening), so the number of swaps required is half the absolute value of the maximum imbalance.


Explanation of the Code:

  1. Balance Variable: We use the balance variable to keep track of the difference between opening ([) and closing (]) brackets as we iterate through the string.
  2. Imbalance Detection: If balance becomes negative, it indicates that there are more closing brackets than opening ones. This is where we keep track of the maximum imbalance using max_imbalance.
  3. Final Swap Calculation: The number of swaps required is derived from the maximum imbalance, as one swap can fix two imbalanced brackets.

Time and Space Complexity:


  • Time Complexity: O(n), where n is the length of the string. We only need to traverse the string once, making it highly efficient.
  • Space Complexity: O(1), since we use only a few additional variables to track the balance and the maximum imbalance, regardless of the input size.

Key Takeaways:

  • The optimized approach for the Minimum Swaps for Balanced Brackets problem leverages the concept of balance and imbalance rather than using a stack.
  • By focusing on the net imbalance of closing brackets, we can determine the minimum number of swaps required to balance the string in linear time.
  • This solution has a time complexity of O(n) and a space complexity of O(1), making it ideal for large inputs.

Why This Solution Is Perfect for Coding Interviews:

This solution demonstrates a keen understanding of algorithmic optimization, which is highly valued in coding interviews. By reducing the problem’s complexity and solving it in linear time, you show the ability to write efficient and scalable code, a crucial skill for top tech companies.

Conclusion:

The Minimum Swaps for Balanced Brackets problem can be solved in a more efficient manner than the naive approach by using a balance-tracking method. This optimized solution has a time complexity of O(n), making it ideal for handling large datasets in real-world applications.

If you're preparing for coding interviews at companies like Google, Facebook, Amazon, or other FAANG companies, mastering problems like this will give you an edge.

FAQ:

  1. Can this solution be applied to other types of problems? Yes, the balance-tracking approach is versatile and can be adapted to other parenthesis or bracket-related problems in algorithms.

  2. How can I practice this problem? You can find similar problems on platforms like LeetCode, Codeforces, or HackerRank under the category of "balanced parentheses" or "string manipulation" problems.

     

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