Refactor KnightsTour class for improved design and readability

[akshith30388]

This Pull Request updates the KnightsTour implementation with a cleaner, modern, and more maintainable structure while preserving the original algorithmic behavior.

Key Improvements 1. Design & Architecture

Converted static and shared state into an object-oriented structure

Removed implicit padded board design and added support for any N × N board size

Added constructor-based initialization for clarity and reuse

2. Readability & Maintainability

Improved naming, documentation, and logical separation of responsibilities

Simplified move validation and board handling logic

Structured the code to be easier for learners and contributors to understand

3. Algorithmic & Performance Enhancements

Retains Warnsdorff’s heuristic but implemented more cleanly and consistently

Eliminated unnecessary boundary padding and redundant branching

Improved recursive traversal efficiency and reduced avoidable checks

4. API & Usage Improvements

solve() now returns a boolean result, removing dependency on global state

Added getBoard() method for retrieving the final tour result

Implementation is now reusable, testable, and suitable for integration into applications or visualizers

Reason for Update

The previous implementation was functional but relied heavily on static state, implicit padding, and less maintainable patterns. This updated version provides a clearer, more flexible, and educational approach while preserving the original problem-solving intent.