Add Sudoku Solver using Backtracking algorithm

Author: harsha08-2k6

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

@@ -1,196 +1,140 @@
 package com.thealgorithms.backtracking;
 
 /**
- * Sudoku Solver using Backtracking Algorithm
+ * Sudoku Solver using Backtracking Algorithm.
  *
- * 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
+ * Solves a 9×9 Sudoku grid by filling empty cells (0) such that every row,
+ * column, and 3×3 subgrid contains all digits 1–9 exactly once.
  */
 public class SudokuSolver {
 
-  private static final int SIZE = 9;
-  private static final int SUBGRID_SIZE = 3;
-  private static final int EMPTY = 0;
-
-  /**
-   * 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++) {
-        // Find an empty cell
-        if (board[row][col] == EMPTY) {
-          // Try digits 1-9
-          for (int num = 1; num <= SIZE; num++) {
-            if (isValid(board, row, col, num)) {
-              // Place the number
-              board[row][col] = num;
-
-              // Recursively try to solve the rest
-              if (solveSudoku(board)) {
-                return true;
-              }
-
-              // Backtrack if no solution found
-              board[row][col] = EMPTY;
-            }
-          }
-          // No valid number found, backtrack
-          return false;
+    private static final int SIZE = 9;
+    private static final int SUBGRID = 3;
+    private static final int EMPTY = 0;
+
+    /**
+     * Public API: Validates the initial board and triggers the solver.
+     *
+     * @param board 9×9 Sudoku grid
+     * @return true if solvable
+     */
+    public static boolean solveSudoku(int[][] board) {
+        if (!isInitialBoardValid(board)) {
+            return false;
         }
-      }
-    }
-    // All cells filled successfully
-    return true;
-  }
-
-  /**
-   * 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) {
-    // Check row constraint
-    if (!isRowValid(board, row, num)) {
-      return false;
+        return solve(board);
     }
 
-    // Check column constraint
-    if (!isColumnValid(board, col, num)) {
-      return false;
+    /**
+     * Solves Sudoku recursively using backtracking.
+     */
+    private static boolean solve(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;
+
+                            if (solve(board)) {
+                                return true;
+                            }
+
+                            board[row][col] = EMPTY;
+                        }
+                    }
+
+                    return false;
+                }
+            }
+        }
+        return true;
     }
 
-    // Check 3×3 subgrid constraint
-    if (!isSubgridValid(board, row, col, num)) {
-      return false;
+    /**
+     * Validates initial puzzle (checks duplicates in rows/cols/subgrids).
+     */
+    public static boolean isInitialBoardValid(int[][] board) {
+        for (int row = 0; row < SIZE; row++) {
+            for (int col = 0; col < SIZE; col++) {
+
+                int num = board[row][col];
+
+                if (num != EMPTY) {
+                    board[row][col] = EMPTY;
+
+                    if (!isValid(board, row, col, num)) {
+                        board[row][col] = num;
+                        return false;
+                    }
+
+                    board[row][col] = num;
+                }
+            }
+        }
+        return true;
     }
 
-    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;
-      }
+    private static boolean isValid(int[][] board, int row, int col, int num) {
+        return isRowOk(board, row, num)
+                && isColOk(board, col, num)
+                && isSubgridOk(board, row, col, num);
     }
-    return true;
-  }
-
-  /**
-   * 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;
-      }
+
+    private static boolean isRowOk(int[][] board, int row, int num) {
+        for (int col = 0; col < SIZE; col++) {
+            if (board[row][col] == num) {
+                return false;
+            }
+        }
+        return true;
     }
-    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;
+
+    private static boolean isColOk(int[][] board, int col, int num) {
+        for (int row = 0; row < SIZE; row++) {
+            if (board[row][col] == num) {
+                return false;
+            }
         }
-      }
+        return true;
     }
-    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("|");
+
+    private static boolean isSubgridOk(int[][] board, int row, int col, int num) {
+        int startRow = row - (row % SUBGRID);
+        int startCol = col - (col % SUBGRID);
+
+        for (int i = startRow; i < startRow + SUBGRID; i++) {
+            for (int j = startCol; j < startCol + SUBGRID; j++) {
+                if (board[i][j] == num) {
+                    return false;
+                }
+            }
         }
-        System.out.print(board[row][col]);
-      }
-      System.out.println();
+        return true;
     }
-  }
-
-  /**
-   * Main method demonstrating Sudoku solver functionality.
-   *
-   * @param args command line arguments (not used)
-   */
-  public static void main(String[] args) {
-    // Example Sudoku puzzle (0 = empty cell)
-    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}
-    };
-
-    System.out.println("Sudoku Puzzle:");
-    printBoard(board);
-
-    if (solveSudoku(board)) {
-      System.out.println("\nSolved Sudoku:");
-      printBoard(board);
-    } else {
-      System.out.println("\nNo solution exists for this Sudoku puzzle.");
+
+    /**
+     * Utility: Print Sudoku grid.
+     */
+    public static void printBoard(int[][] board) {
+        for (int row = 0; row < SIZE; row++) {
+
+            if (row % SUBGRID == 0 && row != 0) {
+                System.out.println("-----------");
+            }
+
+            for (int col = 0; col < SIZE; col++) {
+
+                if (col % SUBGRID == 0 && col != 0) {
+                    System.out.print("|");
+                }
+
+                System.out.print(board[row][col]);
+            }
+            System.out.println();
+        }
     }
-  }
-}
+}