DNA Substring Palindrome Cost Sum

Requirements

Given a DNA string dna, calculate the combined cost of converting every substring into a palindrome.

For an individual substring:

• Inspect characters that are mirrored around the substring's center.
• Every mirrored pair with different characters contributes one required modification.
• The substring's cost is therefore its number of unequal mirrored pairs.

Return the sum of these costs for all substrings as a long value.

A suitable function signature is:

long totalPalindromeConversionCost(String dna)

Examples

Example 1

Input: dna = "ACG"
Output: 3

The length-two substrings each contribute 1, and the full substring contributes 1; all one-character substrings contribute 0.

Example 2

Input: dna = "AAA"
Output: 0

Every mirrored pair already matches in every substring.

Example 3

Input: dna = ""
Output: 0

An empty string contains no substrings with mismatched mirrored pairs.

Notes

• Use a 64-bit integer, such as long, for the returned total because the number of substrings is quadratic in the string length and the accumulated cost may become large.
• No input-size constraints are provided.
• Include coverage for empty strings, one-character strings, strings whose characters are all equal, and strings with alternating mismatches.