feat: add Sudoku Solver using Backtracking

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

@@ -0,0 +1,157 @@
+package com.thealgorithms.backtracking;
+
+/**
+ * Sudoku Solver using Backtracking Algorithm
+ * Solves a 9x9 Sudoku puzzle by filling empty cells with valid digits (1-9)
+ *
+ * @author Navadeep0007
+ */
+public final class SudokuSolver {
+
+    private static final int GRID_SIZE = 9;
+    private static final int SUBGRID_SIZE = 3;
+    private static final int EMPTY_CELL = 0;
+
+    private SudokuSolver() {
+        // Utility class, prevent instantiation
+    }
+
+    /**
+     * 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;
+        }
+
+        for (int row = 0; row < GRID_SIZE; row++) {
+            if (board[row].length != GRID_SIZE) {
+                return false;
+            }
+        }
+
+        return solve(board);
+    }
+
+    /**
+     * 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;
+
+                            if (solve(board)) {
+                                return true;
+                            }
+
+                            // Backtrack
+                            board[row][col] = EMPTY_CELL;
+                        }
+                    }
+                    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 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;
+            }
+        }
+        return false;
+    }
+
+    /**
+     * 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;
+            }
+        }
+        return false;
+    }
+
+    /**
+     * 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;
+
+        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;
+    }
+
+    /**
+     * 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();
+        }
+    }
+}

src/test/java/com/thealgorithms/backtracking/SudokuSolverTest.java

@@ -0,0 +1,53 @@
+package com.thealgorithms.backtracking;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+class SudokuSolverTest {
+
+    @Test
+    void testSolveSudokuEasyPuzzle() {
+        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}};
+
+        assertTrue(SudokuSolver.solveSudoku(board));
+
+        int[][] expected = {{5, 3, 4, 6, 7, 8, 9, 1, 2}, {6, 7, 2, 1, 9, 5, 3, 4, 8}, {1, 9, 8, 3, 4, 2, 5, 6, 7}, {8, 5, 9, 7, 6, 1, 4, 2, 3}, {4, 2, 6, 8, 5, 3, 7, 9, 1}, {7, 1, 3, 9, 2, 4, 8, 5, 6}, {9, 6, 1, 5, 3, 7, 2, 8, 4}, {2, 8, 7, 4, 1, 9, 6, 3, 5}, {3, 4, 5, 2, 8, 6, 1, 7, 9}};
+
+        assertArrayEquals(expected, board);
+    }
+
+    @Test
+    void testSolveSudokuHardPuzzle() {
+        int[][] board = {{0, 0, 0, 0, 0, 0, 6, 8, 0}, {0, 0, 0, 0, 7, 3, 0, 0, 9}, {3, 0, 9, 0, 0, 0, 0, 4, 5}, {4, 9, 0, 0, 0, 0, 0, 0, 0}, {8, 0, 3, 0, 5, 0, 9, 0, 2}, {0, 0, 0, 0, 0, 0, 0, 3, 6}, {9, 6, 0, 0, 0, 0, 3, 0, 8}, {7, 0, 0, 6, 8, 0, 0, 0, 0}, {0, 2, 8, 0, 0, 0, 0, 0, 0}};
+
+        assertTrue(SudokuSolver.solveSudoku(board));
+    }
+
+    @Test
+    void testSolveSudokuAlreadySolved() {
+        int[][] board = {{5, 3, 4, 6, 7, 8, 9, 1, 2}, {6, 7, 2, 1, 9, 5, 3, 4, 8}, {1, 9, 8, 3, 4, 2, 5, 6, 7}, {8, 5, 9, 7, 6, 1, 4, 2, 3}, {4, 2, 6, 8, 5, 3, 7, 9, 1}, {7, 1, 3, 9, 2, 4, 8, 5, 6}, {9, 6, 1, 5, 3, 7, 2, 8, 4}, {2, 8, 7, 4, 1, 9, 6, 3, 5}, {3, 4, 5, 2, 8, 6, 1, 7, 9}};
+
+        assertTrue(SudokuSolver.solveSudoku(board));
+    }
+
+    @Test
+    void testSolveSudokuInvalidSize() {
+        int[][] board = {{1, 2, 3}, {4, 5, 6}};
+        assertFalse(SudokuSolver.solveSudoku(board));
+    }
+
+    @Test
+    void testSolveSudokuNullBoard() {
+        assertFalse(SudokuSolver.solveSudoku(null));
+    }
+
+    @Test
+    void testSolveSudokuEmptyBoard() {
+        int[][] board = {{0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}};
+
+        assertTrue(SudokuSolver.solveSudoku(board));
+    }
+}