# Maximize count of 3-length palindromic subsequences with each index part of a single subsequence

In this article, we are going to delve into an interesting problem related to string manipulation and dynamic programming in C++. The problem we're discussing today is "Maximize the count of 3-length palindromic subsequences with each index part of a single subsequence".

## Problem Statement

Given a string, the task is to find the maximum count of 3-length palindromic subsequences such that each index in the string is a part of a single subsequence.

A 3-length palindromic subsequence is a subsequence of the form "aba", where 'a' and 'b' are any characters.

## C++ Solution Approach

To solve this problem, we'll count the frequency of each character in the string. We'll then select the character that appears most frequently. We'll form as many 3-length palindromic subsequences as possible with this character. Each subsequence will consist of the selected character, any other character, and the selected character again.

### Example

Here's the C++ code that solves this problem −

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

int maxPalindromeSubsequences(string str) {
const int CHAR_MAX = 256;
int count[CHAR_MAX] = {0};

for (int i=0; i<str.size(); i++) {
count[str[i]]++;
}

return *max_element(count, count + CHAR_MAX) / 2;
}

int main() {
int result = maxPalindromeSubsequences(str);
cout << "The maximum count of 3-length palindromic subsequences is: " << result << endl;
return 0;
}


### Output

The maximum count of 3-length palindromic subsequences is: 2


## Explanation with a Test Case

When this string is passed to the maxPalindromeSubsequences function, it first counts the frequency of each character in the string: {'a': 4, 'b': 2, 'c': 2, 'd': 1}.

It then finds the character that appears most frequently, which is 'a' with a frequency of 4.

To maximize the count of 3-length palindromic subsequences, it forms as many subsequences as possible with the character 'a'. Each subsequence consists of 'a', any other character, and 'a' again.

Since 'a' appears 4 times, it can form 2 such subsequences, "aba" and "aca".

So, the function returns 2.

## Conclusion

This problem showcases how we can solve complex string manipulation problems using frequency counts and selection strategies. It's a fantastic problem to practice and improve your C++ coding skills.

Updated on: 18-May-2023

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