The minimum number of characters that need to be replaced so that the strings are concatenated into a palindrome string of length K

Tracking the minimum number of characters to convert a given string into a link of palindromic substrings of length K is a common problem in the field of string control. A string that is read in the same steps and inverted is called a palindrome string. For example, "radar" or "level". This article will cover the basic concepts, methods, and potential optimization strategies for effectively solving this problem. By the conclusion of this article, readers will be able to handle similar string manipulation problems as they will have a complete understanding of the steps required

The problem will be explained in detail in the following paragraphs, and then the advantages and disadvantages of each method will be discussed. Selected methods are thoroughly examined and code examples are provided to show how to use them. We will also examine the time complexity of each method to see how effective they are under different numbers of inputs

usage instructions

• Brute-Force method

• Sliding Window Approach

The Chinese translation of

Brute-Force Approach

is:

Brute-Force Approach

The Brute-Force The approach for finding the fewest characters to be supplanted to form a string concatenation of a K-length palindromic string includes checking all possible substrings of length K within the given string. It takes after the steps: set two pointers, cleared out and right, to the begin and conclusion of the K-character substring, initialize a variable to track the least substitutions, and iterate over the string, upgrading the window with the proper pointer moving one step right each time. For each window, check in case it could be a palindrome by comparing characters from left and right, and tally the number of substitutions required on the off chance that it's not a palindrome. Keep track of the fewest replacements found so far. Proceed with this preparation until the conclusion of the string. The result will be the fewest substitutions required to realize the specified K-length palindromic substring. In any case, this approach has high time complexity, making it wasteful for huge strings.

Algorithm

• Consider each substring of length K as you iterate through the provided string.

• Verify whether each substring is a palindrome

• Count how many characters would need to be changed if it weren't already a palindrome.

• Keep as few substrings as possible that need to be replaced

• Make a palindrome by changing the characters in the minimal replacement substring.

Example

#include <iostream>
#include <string>
using namespace std;

string minimalReplacementPalindromeSubstring(const string& str, int K) {
   int n = str.length();
   string minReplacementSubstr;

   for (int i = 0; i <= n - K; i++) {
      string substr = str.substr(i, K);
      int replacements = 0;
      for (int j = 0; j < K / 2; j++) {
         if (substr[j] != substr[K - 1 - j]) {
            replacements++;
         }
      }

      if (replacements < minReplacementSubstr.length() || minReplacementSubstr.empty()) {
         minReplacementSubstr = substr;
      }
   }

   return minReplacementSubstr;
}

int main() {
   string input = "iurefhuhfrati";
   int K = 4;

   string result = minimalReplacementPalindromeSubstring(input, K);
   cout << "Minimal Replacement Substring: " << result << endl;

   return 0;
}

Output

Minimal Replacement Substring: rati

Sliding window method

The sliding window method can be used to solve problems efficiently, including subarray or substring operations. In the case of string concatenation looking for the minimum number of characters to create a palindrome string of length K, the method consists of maintaining a fixed-size window (substring) of K characters while navigating the input string

The calculation sets two pointers 'left' and 'right', initially indicating the start and end of the K character substring. It then determines the number of substitutions required to convert this substring into a palindrome. To keep track of the minimum number of replacements required, a variable 'min_replacements' is initialized.

Algorithm

• Set two pointers, left and right, pointing to the beginning and end of the main K character substring respectively.

• Determines the number of substitutions expected to convert a substring into a palindrome.

• To track the minimum number of replacements required, initialize the variable min_replacements

• Update the window by moving the right pointer one position to the right

• If the current window is a palindrome, move the right pointer

• Calculate the amount of replacements required and, if necessary, change min_replacements if the current window is not a palindrome.

• To update the window, move the left pointer one space to the right.

• Up to the string's conclusion, repeat steps 4 through 7.

• The characters of the substring should be replaced with as few substitutions as possible

Example

#include <iostream>
#include <string>
using namespace std;

int minReplacementsForPalindrome(string s, int k) {
   int left = 0, right = k - 1, min_replacements = 0;
   while (right < s.length()) {
      int i = left, j = right;
      while (i < j) {
         if (s[i] != s[j])
            min_replacements++;
         i++;
         j--;
      }
      left++;
      right++;
   }
   return min_replacements;
}

int main() {
   string input_string = "abcxyzuvw"; // Replace this with your desired input string
   int k = 3; // Replace this with the desired value of K
   int result = minReplacementsForPalindrome(input_string, k);
   cout << "Minimum replacements required: " << result << endl;
   return 0;
}

Output

Minimum replacements required: 7

Conclusion

This article explores the problem of the minimum number of characters to convert a given string into a palindrome substring of length K. It studies two basic methods to solve this problem: brute force method and sliding window method. Brute force methods consist of checking all possible substrings of length K in a given string, determining whether they are palindromes, and checking for necessary substitutions. However, this approach has high complexity and is inefficient for large strings

On the other hand, the sliding window approach optimizes this method by maintaining a fixed size window and efficiently updating the window as the input string is navigated. This article provides code testing and experience to help users more successfully understand and solve similar string processing problems.

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