Improve power sum algorithm (#5652)

* Update directory

* Improve PowerSum algorithm implementation and documentation

This commit 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

* updated PowerSum

* Refactor PowerSum algorithm implementation and documentation

* Refactor PowerSum algorithm implementation and documentation

* Refactor code formatting and remove unnecessary line in PowerSum.java

* Refactor code formatting and add newline at end of file in .clang-format

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Co-authored-by: manishraj27 <manishraj27@users.noreply.github.com>
Co-authored-by: Bama Charan Chhandogi <b.c.chhandogi@gmail.com>