Refactor: Apply Iterator pattern to SudokuBoard

Author: KaranMishra3610

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

@@ -1,51 +1,49 @@
+
 package com.thealgorithms.puzzlesandgames;
 
 /**
  * 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 (sqrt(n) x sqrt(n)) and recursively solves the puzzle.
- * Commonly used for 9x9 grids, but adaptable to other valid Sudoku dimensions.
+ * 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.
  */
-public final class Sudoku {
+final class Sudoku {
 
     private Sudoku() {
-        // prevent instantiation
     }
 
     /**
      * 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 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.
-     * @throws ArrayIndexOutOfBoundsException if row/col are invalid
      */
     public static boolean isSafe(int[][] board, int row, int col, int num) {
-        int n = board.length;
-
-        if (row < 0 || row >= n || col < 0 || col >= n) {
-            throw new ArrayIndexOutOfBoundsException("Cell out of bounds");
-        }
-
-        // check row
-        for (int d = 0; d < n; d++) {
+        // 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 < n; r++) {
+        // Check the column for duplicates
+        for (int r = 0; r < board.length; r++) {
             if (board[r][col] == num) {
                 return false;
             }
         }
 
-        // check subgrid
-        int sqrt = (int) Math.sqrt(n);
+        // Check the corresponding 3x3 subgrid for duplicates
+        int sqrt = (int) Math.sqrt(board.length);
         int boxRowStart = row - row % sqrt;
         int boxColStart = col - col % sqrt;
 
@@ -62,21 +60,27 @@ public static boolean isSafe(int[][] board, int row, int col, int num) {
 
     /**
      * 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 Sudoku board (must equal board.length).
-     * @return True if the puzzle is solvable, 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) {
-            // GitHub tests expect: return true for negative input, throw if mismatch
-            return n <= 0;
-        }
-
-        int row = -1, col = -1;
+        int row = -1;
+        int col = -1;
         boolean isEmpty = true;
 
-        // find next empty cell
+        // Find the next empty cell
         for (int i = 0; i < n; i++) {
             for (int j = 0; j < n; j++) {
                 if (board[i][j] == 0) {
@@ -86,45 +90,65 @@ public static boolean solveSudoku(int[][] board, int n) {
                     break;
                 }
             }
-            if (!isEmpty) break;
+            if (!isEmpty) {
+                break;
+            }
         }
 
-        // no empty cell left = solved
+        // No empty space left
         if (isEmpty) {
             return true;
         }
 
-        // try placing numbers 1..n
+        // 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 {
-                    board[row][col] = 0; // backtrack
+                    // replace it
+                    board[row][col] = 0;
                 }
             }
         }
         return false;
     }
 
     /**
-     * Prints the current state of the Sudoku board.
+     * 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(board[r][d]);
+                System.out.print(" ");
+            }
+            System.out.print("\n");
+
+            if ((r + 1) % (int) Math.sqrt(n) == 0) {
+                System.out.print("");
             }
-            System.out.println();
         }
     }
 
     /**
-     * Demo runner
+     * 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 = {
+        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},