Maximize the count of 3-length palindromic subsequences where each index is a single subsequence

In this article, we will delve into an interesting issue related to string manipulation and dynamic programming in C. The problem we discuss today is "Maximize the count of a 3-length palindromic subsequence where each index part is 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 part of a single subsequence.

3 A length palindrome subsequence is a subsequence of the form "aba", where "a" and "b" are arbitrary characters.

C Solution

To solve this problem, we will calculate the frequency of each character in the string. We will then select the character that appears most frequently. We will use this character to form as many 3-length palindrome subsequences as possible. Each subsequence will consist of the selected character, any other characters, and the selected character again.

Example

Here is the C code to solve 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() {
   string str = "abcaaadcb";
   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

Test case description

Let us consider the string "abcaaadcb".

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 } .

Then find the character with the highest frequency, that is, "a", with a frequency of 4.

To maximize the number of 3-length palindrome subsequences, it forms as many subsequences as possible with the character "a". Each subsequence consists of "a", any other characters, and "a" again.

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

Therefore, the function returns 2.

in conclusion

This question shows how we can use frequency counting and selection strategies to solve complex string manipulation problems. This is an excellent question to practice and improve your C coding skills.

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