Add Sudoku Solver using Backtracking algorithm- Implements depth-firs…

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

@@ -2,156 +2,174 @@
 
 /**
  * Sudoku Solver using Backtracking Algorithm
- * Solves a 9x9 Sudoku puzzle by filling empty cells with valid digits (1-9)
  *
- * @author Navadeep0007
+ * This class solves a partially filled 9×9 Sudoku board by finding a valid
+ * arrangement where every row, column, and 3×3 subgrid contains digits 1-9
+ * exactly once.
+ *
+ * Algorithm References:
+ * - Backtracking: https://en.wikipedia.org/wiki/Backtracking
+ * - Sudoku: https://en.wikipedia.org/wiki/Sudoku
+ *
+ * Time Complexity: O(9^(n*n)) in worst case, where n=9
+ * Space Complexity: O(n*n) for recursion stack
+ *
+ * @author TheAlgorithms
  */
-public final class SudokuSolver {
+public class SudokuSolver {
 
-    private static final int GRID_SIZE = 9;
-    private static final int SUBGRID_SIZE = 3;
-    private static final int EMPTY_CELL = 0;
+  private static final int SIZE = 9;
+  private static final int SUBGRID_SIZE = 3;
+  private static final int EMPTY = 0;
 
-    private SudokuSolver() {
-        // Utility class, prevent instantiation
-    }
+  /**
+   * Solves the given Sudoku board using backtracking. Modifies the board
+   * in-place.
+   *
+   * @param board 9×9 2D array representing the Sudoku board (0 = empty cell)
+   * @return true if a valid solution exists, false otherwise
+   */
+  public static boolean solveSudoku(int[][] board) {
+    for (int row = 0; row < SIZE; row++) {
+      for (int col = 0; col < SIZE; col++) {
+        if (board[row][col] == EMPTY) {
+          for (int num = 1; num <= SIZE; num++) {
+            if (isValid(board, row, col, num)) {
+              board[row][col] = num;
 
-    /**
-     * Solves the Sudoku puzzle using backtracking
-     *
-     * @param board 9x9 Sudoku board with 0 representing empty cells
-     * @return true if puzzle is solved, false otherwise
-     */
-    public static boolean solveSudoku(int[][] board) {
-        if (board == null || board.length != GRID_SIZE) {
-            return false;
-        }
+              if (solveSudoku(board)) {
+                return true;
+              }
 
-        for (int row = 0; row < GRID_SIZE; row++) {
-            if (board[row].length != GRID_SIZE) {
-                return false;
+              board[row][col] = EMPTY;
             }
+          }
+          return false;
         }
-
-        return solve(board);
+      }
     }
+    return true;
+  }
 
-    /**
-     * Recursive helper method to solve the Sudoku puzzle
-     *
-     * @param board the Sudoku board
-     * @return true if solution is found, false otherwise
-     */
-    private static boolean solve(int[][] board) {
-        for (int row = 0; row < GRID_SIZE; row++) {
-            for (int col = 0; col < GRID_SIZE; col++) {
-                if (board[row][col] == EMPTY_CELL) {
-                    for (int number = 1; number <= GRID_SIZE; number++) {
-                        if (isValidPlacement(board, row, col, number)) {
-                            board[row][col] = number;
+  /**
+   * Checks if placing a number at a given position is valid.
+   *
+   * @param board the Sudoku board
+   * @param row row index
+   * @param col column index
+   * @param num number to place (1-9)
+   * @return true if placement is valid
+   */
+  private static boolean isValid(int[][] board, int row, int col, int num) {
+    return isRowValid(board, row, num)
+        && isColumnValid(board, col, num)
+        && isSubgridValid(board, row, col, num);
+  }
 
-                            if (solve(board)) {
-                                return true;
-                            }
-
-                            // Backtrack
-                            board[row][col] = EMPTY_CELL;
-                        }
-                    }
-                    return false;
-                }
-            }
-        }
-        return true;
+  /**
+   * Checks if a number already exists in the given row.
+   *
+   * @param board the Sudoku board
+   * @param row row index
+   * @param num number to check
+   * @return true if number is not in row
+   */
+  private static boolean isRowValid(int[][] board, int row, int num) {
+    for (int col = 0; col < SIZE; col++) {
+      if (board[row][col] == num) {
+        return false;
+      }
     }
+    return true;
+  }
 
-    /**
-     * Checks if placing a number at given position is valid
-     *
-     * @param board the Sudoku board
-     * @param row row index
-     * @param col column index
-     * @param number number to place (1-9)
-     * @return true if placement is valid, false otherwise
-     */
-    private static boolean isValidPlacement(int[][] board, int row, int col, int number) {
-        return !isNumberInRow(board, row, number) && !isNumberInColumn(board, col, number) && !isNumberInSubgrid(board, row, col, number);
+  /**
+   * Checks if a number already exists in the given column.
+   *
+   * @param board the Sudoku board
+   * @param col column index
+   * @param num number to check
+   * @return true if number is not in column
+   */
+  private static boolean isColumnValid(int[][] board, int col, int num) {
+    for (int row = 0; row < SIZE; row++) {
+      if (board[row][col] == num) {
+        return false;
+      }
     }
+    return true;
+  }
 
-    /**
-     * Checks if number exists in the given row
-     *
-     * @param board the Sudoku board
-     * @param row row index
-     * @param number number to check
-     * @return true if number exists in row, false otherwise
-     */
-    private static boolean isNumberInRow(int[][] board, int row, int number) {
-        for (int col = 0; col < GRID_SIZE; col++) {
-            if (board[row][col] == number) {
-                return true;
-            }
+  /**
+   * Checks if a number already exists in the 3×3 subgrid.
+   *
+   * @param board the Sudoku board
+   * @param row row index
+   * @param col column index
+   * @param num number to check
+   * @return true if number is not in subgrid
+   */
+  private static boolean isSubgridValid(
+      int[][] board, int row, int col, int num) {
+    int subgridRow = row - row % SUBGRID_SIZE;
+    int subgridCol = col - col % SUBGRID_SIZE;
+
+    for (int i = subgridRow; i < subgridRow + SUBGRID_SIZE; i++) {
+      for (int j = subgridCol; j < subgridCol + SUBGRID_SIZE; j++) {
+        if (board[i][j] == num) {
+          return false;
         }
-        return false;
+      }
     }
+    return true;
+  }
 
-    /**
-     * Checks if number exists in the given column
-     *
-     * @param board the Sudoku board
-     * @param col column index
-     * @param number number to check
-     * @return true if number exists in column, false otherwise
-     */
-    private static boolean isNumberInColumn(int[][] board, int col, int number) {
-        for (int row = 0; row < GRID_SIZE; row++) {
-            if (board[row][col] == number) {
-                return true;
-            }
+  /**
+   * Prints the Sudoku board in a readable format.
+   *
+   * @param board the Sudoku board to print
+   */
+  public static void printBoard(int[][] board) {
+    for (int row = 0; row < SIZE; row++) {
+      if (row % SUBGRID_SIZE == 0 && row != 0) {
+        System.out.println("-----------");
+      }
+      for (int col = 0; col < SIZE; col++) {
+        if (col % SUBGRID_SIZE == 0 && col != 0) {
+          System.out.print("|");
         }
-        return false;
+        System.out.print(board[row][col]);
+      }
+      System.out.println();
     }
+  }
 
-    /**
-     * Checks if number exists in the 3x3 subgrid
-     *
-     * @param board the Sudoku board
-     * @param row row index
-     * @param col column index
-     * @param number number to check
-     * @return true if number exists in subgrid, false otherwise
-     */
-    private static boolean isNumberInSubgrid(int[][] board, int row, int col, int number) {
-        int subgridRowStart = row - row % SUBGRID_SIZE;
-        int subgridColStart = col - col % SUBGRID_SIZE;
+  /**
+   * Main method demonstrating Sudoku solver functionality.
+   *
+   * @param args command line arguments (not used)
+   */
+  public static void main(String[] args) {
+    int[][] board = {
+        {5, 3, 0, 0, 7, 0, 0, 0, 0},
+        {6, 0, 0, 1, 9, 5, 0, 0, 0},
+        {0, 9, 8, 0, 0, 0, 0, 6, 0},
+        {8, 0, 0, 0, 6, 0, 0, 0, 3},
+        {4, 0, 0, 8, 0, 3, 0, 0, 1},
+        {7, 0, 0, 0, 2, 0, 0, 0, 6},
+        {0, 6, 0, 0, 0, 0, 2, 8, 0},
+        {0, 0, 0, 4, 1, 9, 0, 0, 5},
+        {0, 0, 0, 0, 8, 0, 0, 7, 9}
+    };
 
-        for (int i = subgridRowStart; i < subgridRowStart + SUBGRID_SIZE; i++) {
-            for (int j = subgridColStart; j < subgridColStart + SUBGRID_SIZE; j++) {
-                if (board[i][j] == number) {
-                    return true;
-                }
-            }
-        }
-        return false;
-    }
+    System.out.println("Sudoku Puzzle:");
+    printBoard(board);
 
-    /**
-     * Prints the Sudoku board
-     *
-     * @param board the Sudoku board
-     */
-    public static void printBoard(int[][] board) {
-        for (int row = 0; row < GRID_SIZE; row++) {
-            if (row % SUBGRID_SIZE == 0 && row != 0) {
-                System.out.println("-----------");
-            }
-            for (int col = 0; col < GRID_SIZE; col++) {
-                if (col % SUBGRID_SIZE == 0 && col != 0) {
-                    System.out.print("|");
-                }
-                System.out.print(board[row][col]);
-            }
-            System.out.println();
-        }
+    if (solveSudoku(board)) {
+      System.out.println("\nSolved Sudoku:");
+      printBoard(board);
+    } else {
+      System.out.println("\nNo solution exists for this Sudoku puzzle.");
     }
-}
+  }
+}