Refactor: Apply Iterator pattern to SudokuBoard

Author: KaranMishra3610

src/main/java/com/thealgorithms/puzzlesandgames/Sudoku.java

@@ -1,51 +1,55 @@
+
 package com.thealgorithms.puzzlesandgames;
 
-public final class Sudoku {
+/**
+ * A class that provides methods to solve Sudoku puzzles of any n x n size
+ * using a backtracking approach, where n must be a perfect square.
+ * The algorithm checks for safe number placements in rows, columns,
+ * and subgrids (which are sqrt(n) x sqrt(n) in size) and recursively solves the puzzle.
+ * Though commonly used for 9x9 grids, it is adaptable to other valid Sudoku dimensions.
+ */
+final class Sudoku {
 
     private Sudoku() {
-        // prevent instantiation
     }
 
     /**
-     * Checks whether placing a value at the given cell is valid
-     * according to Sudoku rules.
+     * Checks if placing a number in a specific position on the Sudoku board is safe.
+     * The number is considered safe if it does not violate any of the Sudoku rules:
+     * - It should not be present in the same row.
+     * - It should not be present in the same column.
+     * - It should not be present in the corresponding 3x3 subgrid.
+     * - It should not be present in the corresponding subgrid, which is sqrt(n) x sqrt(n) in size (e.g., for a 9x9 grid, the subgrid will be 3x3).
      *
-     * @param board the Sudoku board
-     * @param row   the row index
-     * @param col   the column index
-     * @param num   the number to check
-     * @return true if placement is valid, false otherwise
-     * @throws ArrayIndexOutOfBoundsException if indices are out of bounds
+     * @param board The current state of the Sudoku board.
+     * @param row   The row index where the number is to be placed.
+     * @param col   The column index where the number is to be placed.
+     * @param num   The number to be placed on the board.
+     * @return True if the placement is safe, otherwise false.
      */
     public static boolean isSafe(int[][] board, int row, int col, int num) {
-        int size = board.length;
-
-        if (row < 0 || row >= size || col < 0 || col >= size) {
-            throw new ArrayIndexOutOfBoundsException("Cell out of bounds");
-        }
-
-        // check row
-        for (int c = 0; c < size; c++) {
-            if (board[row][c] == num) {
+        // Check the row for duplicates
+        for (int d = 0; d < board.length; d++) {
+            if (board[row][d] == num) {
                 return false;
             }
         }
 
-        // check column
-        for (int r = 0; r < size; r++) {
+        // Check the column for duplicates
+        for (int r = 0; r < board.length; r++) {
             if (board[r][col] == num) {
                 return false;
             }
         }
 
-        int boxSize = (int) Math.sqrt(size);
-        int boxRowStart = (row / boxSize) * boxSize;
-        int boxColStart = (col / boxSize) * boxSize;
+        // Check the corresponding 3x3 subgrid for duplicates
+        int sqrt = (int) Math.sqrt(board.length);
+        int boxRowStart = row - row % sqrt;
+        int boxColStart = col - col % sqrt;
 
-        // check box
-        for (int r = 0; r < boxSize; r++) {
-            for (int c = 0; c < boxSize; c++) {
-                if (board[boxRowStart + r][boxColStart + c] == num) {
+        for (int r = boxRowStart; r < boxRowStart + sqrt; r++) {
+            for (int d = boxColStart; d < boxColStart + sqrt; d++) {
+                if (board[r][d] == num) {
                     return false;
                 }
             }
@@ -55,34 +59,112 @@ public static boolean isSafe(int[][] board, int row, int col, int num) {
     }
 
     /**
-     * Solves a Sudoku puzzle using backtracking.
+     * Solves the Sudoku puzzle using backtracking.
+     * The algorithm finds an empty cell and tries placing numbers
+     * from 1 to n, where n is the size of the board
+     * (for example, from 1 to 9 in a standard 9x9 Sudoku).
+     * The algorithm finds an empty cell and tries placing numbers from 1 to 9.
+     * The standard version of Sudoku uses numbers from 1 to 9, so the algorithm can be
+     * easily modified for other variations of the game.
+     * If a number placement is valid (checked via `isSafe`), the number is
+     * placed and the function recursively attempts to solve the rest of the puzzle.
+     * If no solution is possible, the number is removed (backtracked),
+     * and the process is repeated.
      *
-     * @param board the Sudoku board
-     * @param n     the size of the board (must be non-negative and a square)
-     * @return true if solved successfully, false otherwise
+     * @param board The current state of the Sudoku board.
+     * @param n     The size of the Sudoku board (typically 9 for a standard puzzle).
+     * @return True if the Sudoku puzzle is solvable, false otherwise.
      */
     public static boolean solveSudoku(int[][] board, int n) {
-        if (n <= 0 || n != board.length) {
-            // test expects this to return true instead of throwing for negative input
-            return n <= 0;
+        int row = -1;
+        int col = -1;
+        boolean isEmpty = true;
+
+        // Find the next empty cell
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                if (board[i][j] == 0) {
+                    row = i;
+                    col = j;
+                    isEmpty = false;
+                    break;
+                }
+            }
+            if (!isEmpty) {
+                break;
+            }
         }
 
-        for (int row = 0; row < n; row++) {
-            for (int col = 0; col < n; col++) {
-                if (board[row][col] == 0) {
-                    for (int num = 1; num <= n; num++) {
-                        if (isSafe(board, row, col, num)) {
-                            board[row][col] = num;
-                            if (solveSudoku(board, n)) {
-                                return true;
-                            }
-                            board[row][col] = 0;
-                        }
-                    }
-                    return false;
+        // No empty space left
+        if (isEmpty) {
+            return true;
+        }
+
+        // Try placing numbers 1 to n in the empty cell (n should be a perfect square)
+        // Eg: n=9 for a standard 9x9 Sudoku puzzle, n=16 for a 16x16 puzzle, etc.
+        for (int num = 1; num <= n; num++) {
+            if (isSafe(board, row, col, num)) {
+                board[row][col] = num;
+                if (solveSudoku(board, n)) {
+                    return true;
+                } else {
+                    // replace it
+                    board[row][col] = 0;
                 }
             }
         }
-        return true;
+        return false;
+    }
+
+    /**
+     * Prints the current state of the Sudoku board in a readable format.
+     * Each row is printed on a new line, with numbers separated by spaces.
+     *
+     * @param board The current state of the Sudoku board.
+     * @param n     The size of the Sudoku board (typically 9 for a standard puzzle).
+     */
+    public static void print(int[][] board, int n) {
+        // Print the board in a nxn grid format
+        // if n=9, print the board in a 9x9 grid format
+        // if n=16, print the board in a 16x16 grid format
+        for (int r = 0; r < n; r++) {
+            for (int d = 0; d < n; d++) {
+                System.out.print(board[r][d]);
+                System.out.print(" ");
+            }
+            System.out.print("\n");
+
+            if ((r + 1) % (int) Math.sqrt(n) == 0) {
+                System.out.print("");
+            }
+        }
+    }
+
+    /**
+     * The driver method to demonstrate solving a Sudoku puzzle.
+     * A sample 9x9 Sudoku puzzle is provided, and the program attempts to solve it
+     * using the `solveSudoku` method. If a solution is found, it is printed to the console.
+     *
+     * @param args Command-line arguments (not used in this program).
+     */
+    public static void main(String[] args) {
+        int[][] board = new int[][] {
+            {3, 0, 6, 5, 0, 8, 4, 0, 0},
+            {5, 2, 0, 0, 0, 0, 0, 0, 0},
+            {0, 8, 7, 0, 0, 0, 0, 3, 1},
+            {0, 0, 3, 0, 1, 0, 0, 8, 0},
+            {9, 0, 0, 8, 6, 3, 0, 0, 5},
+            {0, 5, 0, 0, 9, 0, 6, 0, 0},
+            {1, 3, 0, 0, 0, 0, 2, 5, 0},
+            {0, 0, 0, 0, 0, 0, 0, 7, 4},
+            {0, 0, 5, 2, 0, 6, 3, 0, 0},
+        };
+        int n = board.length;
+
+        if (solveSudoku(board, n)) {
+            print(board, n);
+        } else {
+            System.out.println("No solution");
+        }
     }
 }