Minimize replacement of a character to its nearest letter, making the string a palindrome

In this article, we will discuss an interesting algorithmic problem: "Minimize the replacement of characters with their nearest alphabet to make a string palindrome." This question is interesting , as it involves string manipulation, palindrome checking, and the concepts of character ASCII values. Let’s delve deeper into this issue.

Problem Statement

Given a string, the task is to convert it into a palindrome with the minimum number of substitutions. These substitutions are accomplished by changing characters to their closest alphabet.

Understanding Questions

A palindrome is a word, phrase, number, or other sequence of characters that is read backwards the same as forwards. Our goal is to minimize the total number of substitutions required to convert a given string into a palindrome.

For example, consider the string "abc". To convert it to a palindrome, we can replace "c" with "a", which requires two substitutions ("c" to "b" and "b" to "a"). Therefore, the minimum number of substitutions is 2.

Algorithm method

To solve this problem, we will use the two pointer method. Here are the steps -

• Initialize two pointers, one at the beginning of the string and the other at the end of the string.

• Compare the characters at the pointer.

• If equal, move the pointer inward.

• If they are not equal, replace characters further from 'a' with closer characters and increase the number of substitutions. Also, move the pointer inwards.

• Repeat steps 2-4 until the start pointer is not less than the end pointer.

Example

This is the C code that implements the above method -

#include<bits/stdc++.h>
using namespace std;

int makePalindrome(string str) {
   int len = str.size();
   int res = 0;
   for (int i = 0, j = len - 1; i < j; i++, j--) {
      res += abs(str[i] - str[j]);
   }
   return res;
}

int main() {
   string str="abcde";
   cout << "Minimum replacements: " << makePalindrome(str);
   return 0;
}

Output

Minimum replacements: 6

Test case example

Let’s run an example -

Consider the string "abcde". The above program will output "Minimum replacements: 4". This is why -

• Compare "a" and "e". They are not the same, so replace 'e' with 'a'. This required 4 replacements. Our string is now "abcda".

• Compare "b" and "d". They are not the same, so replace 'd' with 'b'. This requires 2 replacements. Our string is now "abcba".

• Now, the string is a palindrome. Therefore, the minimum total number of substitutions is 4 2 = 6.

Remember that the number of substitutions is calculated based on the absolute difference of the character's ASCII values.

in conclusion

This question is a good example of how simple string manipulation and two-pointer techniques can solve a relatively complex problem. Knowing these questions will not only help in coding interviews but also improve your overall problem-solving skills.

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