# Minimize replacement of characters to its nearest alphabet to make a string palindromic

In this article, we will discuss a fascinating algorithmic problem: "Minimize replacement of characters to its nearest alphabet to make a string palindromic." This problem is intriguing because it involves string manipulation, palindrome checking, and the concept of ASCII values for characters. Let's dive into the problem.

## Problem Statement

Given a string of characters, the task is to transform it into a palindrome with the minimum number of replacements. These replacements are made by changing a character to its nearest alphabet.

## Understanding the Problem

A palindrome is a word, phrase, number, or other sequences of characters that reads the same backward as forward. Our goal is to minimize the total number of replacements needed to transform a given string into a palindrome.

For example, consider the string "abc". To transform it into a palindrome, we can replace 'c' with 'a' which requires two replacements ('c' to 'b' and 'b' to 'a'). Hence, the minimum number of replacements is 2.

## Algorithmic Approach

To solve this problem, we'll use a two-pointer approach. Here are the steps −

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

• Compare the characters at the pointers.

• If they are equal, move the pointers inward.

• If they are not equal, replace the farther character from 'a' with the closer one and increment the count of replacements. Also, move the pointers inward.

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

### Example

Here is the C++ code that implements the above approach −

#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


## Testcase Example

Let's run an example −

Consider the string "abcde". The above program will output "Minimum replacements: 4". Here's why −

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

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

• Now, the string is a palindrome. So, the total minimum replacements are 4 + 2 = 6.

Remember, the number of replacements is calculated as the absolute difference of ASCII values of the characters.

## Conclusion

This problem is an excellent example of how simple string manipulation and two-pointer technique can solve relatively complex problems. Understanding such problems not only helps in coding interviews but also improves overall problem-solving skills.

Updated on: 18-May-2023

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