Add Sudoku Solver refactored to pass Build and Clang Format

Author: khalidx3

src/main/java/com/thealgorithms/backtracking/SudokuSolver.java

@@ -0,0 +1,94 @@
+package main.java.com.thealgorithms.backtracking;
+
+/**
+ * Sudoku Solver using Backtracking Algorithm
+ *
+ * Solves a 9x9 Sudoku puzzle. All methods are static and class is final to
+ * match
+ * TheAlgorithms/Java repo conventions.
+ */
+public final class SudokuSolver {
+
+      private SudokuSolver() {
+      } // Prevent instantiation
+
+      /**
+       * Solves the Sudoku puzzle using backtracking.
+       *
+       * @param sudoku 9x9 Sudoku grid, empty cells are 0
+       * @param row    current row
+       * @param col    current column
+       * @return true if solved, false otherwise
+       */
+      public static boolean sudokuSolver(int[][] sudoku, int row, int col) {
+            if (row == 9) {
+                  return true;
+            }
+
+            int nextRow = row;
+            int nextCol = col + 1;
+            if (nextCol == 9) {
+                  nextRow = row + 1;
+                  nextCol = 0;
+            }
+
+            if (sudoku[row][col] != 0) {
+                  return sudokuSolver(sudoku, nextRow, nextCol);
+            }
+
+            for (int num = 1; num <= 9; num++) {
+                  if (isSafe(sudoku, row, col, num)) {
+                        sudoku[row][col] = num;
+                        if (sudokuSolver(sudoku, nextRow, nextCol)) {
+                              return true;
+                        }
+                        sudoku[row][col] = 0; // backtrack
+                  }
+            }
+
+            return false;
+      }
+
+      /**
+       * Checks if placing num at (row, col) is safe.
+       *
+       * @param sudoku 9x9 Sudoku grid
+       * @param row    current row
+       * @param col    current column
+       * @param num    number to place
+       * @return true if safe, false otherwise
+       */
+      private static boolean isSafe(int[][] sudoku, int row, int col, int num) {
+            for (int i = 0; i < 9; i++) {
+                  if (sudoku[row][i] == num || sudoku[i][col] == num) {
+                        return false;
+                  }
+            }
+
+            int startRow = row - row % 3;
+            int startCol = col - col % 3;
+            for (int i = startRow; i < startRow + 3; i++) {
+                  for (int j = startCol; j < startCol + 3; j++) {
+                        if (sudoku[i][j] == num) {
+                              return false;
+                        }
+                  }
+            }
+
+            return true;
+      }
+
+      /**
+       * Prints the Sudoku grid.
+       *
+       * @param sudoku 9x9 Sudoku grid
+       */
+      public static void printSudoku(int[][] sudoku) {
+            for (int i = 0; i < 9; i++) {
+                  for (int j = 0; j < 9; j++) {
+                        System.out.print(sudoku[i][j] + " ");
+                  }
+                  System.out.println();
+            }
+      }
+}