Description

This PR adds a Sudoku Solver implementation using the Backtracking algorithm as requested in issue#6929.

Changes

• AddedSudokuSolver.java insrc/main/java/com/thealgorithms/backtracking/

  • Implements backtracking algorithm to solve 9×9 Sudoku puzzles
  • IncludesisValid() method to verify Sudoku constraints (row, column, 3×3 subgrid)
  • IncludessolveSudoku() method with recursive backtracking logic
  • IncludesprintBoard() helper method for formatted output
  • Provides example usage inmain() method

• AddedSudokuSolverTest.java insrc/test/java/com/thealgorithms/backtracking/

  • Tests solvable Sudoku puzzle with expected solution verification
  • Tests unsolvable Sudoku puzzle (invalid constraints)
  • Tests already solved Sudoku
  • Tests empty Sudoku board
  • Tests difficult Sudoku puzzle with fewer clues

Algorithm Details

• Approach: Depth-first search with backtracking
• Time Complexity: O(9^m) where m is the number of empty cells
• Space Complexity: O(m) for the recursion stack
• Reference:https://en.wikipedia.org/wiki/Sudoku_solving_algorithms#Backtracking

Testing

✅ All new tests pass:mvn test -Dtest=SudokuSolverTest
✅ Verified with multiple Sudoku puzzles
✅ Code follows repository formatting standards
✅ Includes proper documentation and comments

Checklist

• I have readCONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized it.
• All filenames are in PascalCase.
• All functions and variable names follow Java naming conventions.
• All new algorithms have a URL