# Minimum Moves to Make a String Palindrome by Incrementing All Characters of Substrings

In the realm of computer science and programming, discovering effective algorithms for resolving issues is highly significant. An intriguing issue is identifying the smallest possible quantity of maneuvers necessary to convert a string into a palindrome by increasing all characters within substrings. This write-up delves into two methodologies to handle this concern utilizing the C++ programming language.

## Syntax

Before diving into the approaches, let's define the syntax of the function we will be using −

int minMovesToMakePalindrome(string str);


## Algorithm

• Our objective is to minimize move count in converting strings into palindromes—a problem which our algorithm approaches with these key phases −

• Firstly establish two pointer variables beginning from different sides of the string—left starting from its start while right begins from its end.

• Continue our process as long as configuration limits allow i.e. once either pointer surpasses the other halt −

• Proceed to move both pointers closer together whenever their character values coincide. Whenever character values are different increase that on the right hand side (by their differentiation) before holding any further operations. Such increase is proportional to the difference between 'a' and 'c ' so if str[right] equals 'c' and str[left] equals 'a ' we will increment str[right] by 2 (since 'a' - 'c' = 2).Update the moves count accordingly.

• Once left becomes greater than right, the string is transformed into a palindrome.

## Approach 1: Brute Force

In this approach, we will consider all possible substrings and calculate the minimum moves required for each substring. Finally, we will return the minimum among all the calculated move counts.

### Example

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

int minMovesToMakePalindrome(string str) {
int moves = 0;
int length = str.length();

for (int i = 0; i < length / 2; i++) {
moves += abs(str[i] - str[length - i - 1]);
}

return moves;
}

int main() {
string str = "abcde";
int minMoves = minMovesToMakePalindrome(str);
cout << "Minimum moves to make the string palindrome: " << minMoves << endl;

return 0;
}


### Output

Minimum moves to make the string palindrome: 6


### Explanation

A function named minMovesToMakePalindrome has been created that converts input string str into a palindrome with minimum moves required. We have explained below how it works through some step-by-step instructions −

We initialize moves variable to 0 that is responsible for keeping track of total moves needed. - Since length variable records input string's length str, our next action is iterating over half string using a for-loop so that symmetric places don't overlap. - Lastly, inside this loop abs(str[i] - str[length - i - 1]) calculates absolute differences between characters at both ends.

The calculated difference represents the number of moves required to make the characters at those positions equal. We add this difference to the moves count.

After iterating through all the necessary positions, we have the total minimum moves required stored in the moves variable. We return this value.

In the main function, we initialize a string str with the value "abcde". Then, we call the minMovesToMakePalindrome function, passing str as the argument. The returned minimum moves count is stored in the minMoves variable. Finally, we print the result to the console.

## Approach 2: Optimal Two-Pointer Approach

This approach utilizes two pointers to traverse the string from both ends simultaneously. With efficiency in mind, we have adopted a technique for transforming strings into palindromes that involves steadily increasing and matching characters from both ends of our input. This method minimizes extraneous maneuvers and allows for quicker conversions without compromising accuracy or functionality.

### Example

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

int minMovesToMakePalindrome(string str) {
int moves = 0;
int left = 0;
int right = str.length() - 1;

while (left <= right) {
moves += abs(str[right] - str[left]);
left++;
right--;
}

return moves;
}

int main() {
string str = "abcde";
int minMoves = minMovesToMakePalindrome(str);
cout << "Minimum moves to make the string palindrome: " << minMoves << endl;

return 0;
}


### Output

Minimum moves to make the string palindrome: 6


### Explanation

The goal of the following code example is to utilize an optimal two pointer approach to determine the minimum number of moves necessary to transform a given string into a palindrome.

To accomplish this. We create a function called minMovesToMakePalindrome. Which accepts a string argument and returns the total number of moves required. Firstly we set our variable for counting moves to 0 and initialize both left and right pointers: left starting at the beginning (index 0) of our input string and right starting at the end (index str.length() - 1).

Our while loop iterates until left is greater than or equal to right in order to cover all elements in the string. In each iteration. We find the difference between characters at positions left and right by using abs(str[right] - str[left]) which represents how many moves will be needed to make these two characters identical. We add this difference value to our running count for total moves.

Increment left and decrease right pointers as we move closer towards the center of our input string. Once there is no overlap between left and right pointers. We have transformed our string into a palindrome.

At this point we return our count of total moves stored in 'moves'. In main() identical steps are followed as previously where we declare a new input string 'abcde' call minMovesToMakePalindrome with this argument which returns total minimum move count value that's assigned to new variable 'minMoves' before printing this value onto the console.

## Conclusion

Two alternative solutions have been presented in the following text, both aimed at offering insight and potential answers toward solving the obstacle of calculating how many movements are necessary to transform a given string into a palindrome via character manipulation within substrings. One method known as brute-force incorporates all probable substrings while the other approach called optimal two-pointer method curtails down on movements required substantially. Coders can effortlessly apply these mechanisms to address similar hurdles and escalate their solutions in return.

Updated on: 25-Jul-2023

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