Improve power sum algorithm

[manishraj27]

• [x] I have read CONTRIBUTING.md.
• [x] This pull request is all my own work -- I have not plagiarized it.
• [x] All filenames are in PascalCase.
• [x] All functions and variable names follow Java naming conventions.
• [x] All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
• [x] All new code is formatted with clang-format -i --style=file path/to/your/file.java

Description

This PR enhances the PowerSum class in the backtracking package. The changes focus on improving code quality, readability, and documentation. Key improvements include:

1. Enhanced code structure and efficiency:

   • Removed class-level variables for better thread safety
   • Optimized the recursive approach to avoid unnecessary calculations
   • Simplified the overall logic for easier understanding

2. Improved readability:

   • Used more descriptive variable names (e.g., 'targetSum' instead of 'n', 'power' instead of 'x')
   • Enhanced method structure with a private recursive helper method

3. Better documentation:

   • Added comprehensive JavaDoc comments explaining the algorithm's purpose and implementation
   • Clarified the meaning of parameters, especially relating them to the original problem statement (N and X)
   • Improved inline comments for better code understanding

4. Adhered to Java best practices:

   • Improved encapsulation by making the recursive method private
   • Used Math.pow() directly instead of a custom power method

5. Maintained core functionality:

   • The algorithm still solves the same problem as before, but with improved code quality

These changes make the code more maintainable, easier to understand, and more in line with modern Java conventions. The enhanced documentation also helps future contributors and users to quickly grasp the purpose and functionality of the algorithm.

Hacktoberfest

I would like to submit this pull request as part of Hacktoberfest. I believe this contribution meets the quality standards for the event and would appreciate if it could be considered for acceptance under Hacktoberfest-Accepted label.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 88.88889% with 1 line in your changes missing coverage. Please review.

Project coverage is 58.57%. Comparing base (d437d58) to head (dc0244e).

Files with missing lines	Patch %	Lines
.../java/com/thealgorithms/backtracking/PowerSum.java	88.88%	0 Missing and 1 partial :warning:

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #5652      +/-   ##
============================================
- Coverage     58.59%   58.57%   -0.03%     
+ Complexity     3747     3746       -1     
============================================
  Files           553      553              
  Lines         15924    15918       -6     
  Branches       3029     3029              
============================================
- Hits           9331     9324       -7     
  Misses         6196     6196              
- Partials        397      398       +1     

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[manishraj27]

Thank You for accepting my PR.