What Am I Doing Wrong? Longest Repeating Character Replacement

In this post, we’ll dive into a common problem encountered in algorithmic challenges: the Longest Repeating Character Replacement. This problem is not just a test of your coding skills, but also of your understanding of optimal approaches and time complexity.

Problem Statement

Given a string s and an integer k, you are to find the length of the longest substring that can be obtained by replacing at most k characters in s with any other character. The goal is to maximize the number of repeating characters in a substring.

The Initial Approach

The initial implementation of the solution uses a sliding window approach with two pointers (l and r) to define the current substring. The code also maintains a frequency map (charFrequency) to count occurrences of characters within the window. Here’s the provided code snippet:

java class Solution { public int characterReplacement(String s, int k) { int l = 0, r = 0; Map<Character, Integer> charFrequency = new HashMap<>(); int max = 0;

    while (l < s.length() && r < s.length()) {
        int mFC = mostFrequentChar(charFrequency);
        if (r - l + 1 - mFC <= k) {
            max = Math.max(max, r - l + 1);
            charFrequency.put(s.charAt(r), charFrequency.getOrDefault(s.charAt(r), 0) + 1);
            r++;
        } else {
            charFrequency.put(s.charAt(l), charFrequency.get(s.charAt(l)) - 1);
            l++;
        }
    }
    return max;    
}

public int mostFrequentChar(Map<Character, Integer> charFrequency) {
    int val = 0;
    for (char c = 'A'; c <= 'Z'; c++)
        val = Math.max(val, charFrequency.getOrDefault(c, 0));
    return val;
}

}

What’s Going Wrong?

In this implementation, the check for the most frequent character (mFC) is performed before adding the character at the right pointer (r). This leads to an incorrect calculation of the maximum frequency within the current window since we are not considering the newly included character.

Suggested Improvements

1. Check Frequency After Addition: The frequency of the newly added character should be considered immediately after updating the frequency map. This can be achieved by moving the frequency check to after the character has been added.

2. Use a Frequency Array: Instead of using a HashMap to store character frequencies, a simple array of size 26 can be used (for uppercase English letters). This allows for O(1) access time and reduces the overhead of searching through the map.

Optimized Code

Here’s an optimized version of the solution:

java class Solution { public int characterReplacement(String s, int k) { int l = 0, maxCount = 0, maxLength = 0; int[] charCount = new int[26];

    for (int r = 0; r < s.length(); r++) {
        maxCount = Math.max(maxCount, ++charCount[s.charAt(r) - 'A']);

        while (r - l + 1 - maxCount > k) {
            charCount[s.charAt(l) - 'A']--;
            l++;
        }

        maxLength = Math.max(maxLength, r - l + 1);
    }
    return maxLength;
}

}

Time and Space Complexity

• Time Complexity: The optimized solution runs in O(n) time, where n is the length of the string s. Each character is processed at most twice (once when r moves forward and once when l moves forward).

• Space Complexity: The space complexity is O(1) since we are using a fixed-size array of length 26 to store character counts, irrespective of the input size.

Conclusion

The Longest Repeating Character Replacement problem exemplifies the importance of understanding how data structures work in conjunction with algorithms. By optimizing the frequency check and using a frequency array, we can improve both the efficiency and clarity of our solution.

Feel free to share your thoughts or any further optimizations you might consider. Happy coding!

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