/***
 * Write a program to solve a Sudoku puzzle by filling the empty cells.
 *
 * Empty cells are indicated by the character '.'.
 *
 * You may assume that there will be only one unique solution.
 */
public class Solution {
    public boolean solveSudoku(char[][] board) {
        for (int i = 0; i < 9; ++i)
            for (int j = 0; j < 9; ++j) {
                if(board[i][j] != '.') 
                    continue;
                for (int k = 0; k < 9; ++k) {
                    board[i][j] = '1' + k;
                    if (isValid(board, i, j) && solveSudoku(board))
                        return true;
                    board[i][j] = '.';
                }
                return false;
            }
        return true;
    }
    private boolean isValid(char[][] board, int x, int y) {
        int i, j;
        for (i = 0; i < 9; i++) 
            if (i != x && board[i][y] == board[x][y])
                return false;
        for (j = 0; j < 9; j++)
            if (j != y && board[x][j] == board[x][y])
                return false;
        for (i = 3 * (x / 3); i < 3 * (x / 3 + 1); i++)
            for (j = 3 * (y / 3); j < 3 * (y / 3 + 1); j++) {
                if ((i != x || j != y) && board[i][j] == board[x][y])
                    return false;
            }
        return true;
    }
}

add SudokuSolver.java