Introduction

The Longest Repeating Character Replacement problem involves finding the length of the longest substring that can become entirely repeating after replacing at most k characters.

Given:

  • a string s
  • an integer k

the task is to:

  • replace at most k characters
  • make all characters in substring identical
  • return maximum possible substring length

This problem is an important application of:

 Sliding Window Technique

This problem helps in understanding:

  • frequency tracking
  • dynamic window resizing
  • optimization logic
  • substring processing

Example

Input:s = "AABABBA"k = 1

Output:
4

Explanation:
Replace one 'B' with 'A':
"AABA"
Length = 4

Input:
s = "AAAA"
k = 2

Output:
4

Explanation:
String already contains same repeating characters.

Constraints

1 <= s.length <= 10^50 <= k <= s.length

s contains uppercase English letters

Approach 1 : Brute Force

Explanation

The simplest way to solve this problem is:

  1. Generate all substrings
  2. Count character frequencies
  3. Check how many replacements are needed
  4. Track maximum valid substring

This approach works but checking all substrings increases time complexity.

Steps

  1. Generate all substrings.
  2. Count character frequencies.
  3. Find highest frequency character.
  4. Calculate replacements needed.
  5. If replacements ≤ k:
    • update maximum length

Dry Run

Input:s = "AABABBA"k = 1

Check substring:
"AABA"

Highest frequency:
A → 3
Length = 4

Replacements needed:
4 - 3 = 1
Valid substring
Maximum length = 4

Brute Force Code

Complexity Analysis

Time Complexity: O(n²)Explanation:All substrings are generated and checked.

Space Complexity: O(n)
Explanation:
Extra hashmap is used for frequencies.


Approach 2 : Optimized Solution (Sliding Window)

Explanation

The optimized solution uses the Sliding Window Technique.

The idea is:

  1. Expand window using right pointer
  2. Track maximum frequency character
  3. If replacements needed exceed k:
    • shrink window
  4. Track maximum valid window size

Key formula:

 Window Length - Highest Frequency <= k

This means:

  • remaining characters can be replaced

Steps

  1. Initialize:
    • left = 0
    • right = 0
  2. Store frequencies.
  3. Track highest frequency.
  4. Shrink invalid window.
  5. Update maximum length.

Dry Run

Input:s = "AABABBA"
k = 1

Window:
"AABA"

Highest frequency:
A → 3
Length = 4

Changes needed:
4 - 3 = 1
Valid window
Maximum length = 4

Optimized Code

Complexity Analysis

Time Complexity: O(n)Explanation:Each character is processed at most once.

Space Complexity: O(n)
Explanation:
Extra hashmap is used for frequencies.

Edge Cases

  1. String contains same characters
  2. k = 0
  3. String length = 1
  4. Large replacement value
  5. Entire string becomes valid

Why This Problem is Important

This problem helps in understanding:

  1. Sliding Window Technique
  2. Frequency tracking
  3. Window optimization
  4. Dynamic resizing
  5. Replacement logic

It is one of the most important advanced sliding window interview problems.

Real-World Applications

Sliding window optimization concepts are used in:

  1. Data streaming
  2. Pattern recognition
  3. Text analytics
  4. Real-time monitoring
  5. Signal processing

Common Mistakes

  1. Incorrect frequency tracking
  2. Wrong window shrinking condition
  3. Improper max frequency handling
  4. Incorrect replacement formula

Interview Tips

Interviewers often expect:

  1. Sliding Window optimization
  2. O(n) solution explanation
  3. Correct replacement logic

Always explain why:

 Window Length - Max Frequency

represents replacements needed.

Related Questions

  1. Longest Substring Without Repeating Characters
  2. Minimum Window Substring
  3. Frequency Count
  4. Valid Anagram
  5. Subarray Sum = K

Final Takeaway

The Longest Repeating Character Replacement problem is a fundamental advanced sliding window problem that teaches dynamic window optimization and frequency-tracking techniques. Understanding this problem builds a strong foundation for advanced substring and sliding window interview problems.