37. Sudoku Solver

class Solution {
    public void solveSudoku(char[][] board) {
        solveSudoku(board, 0);
    }

    private boolean solveSudoku(char[][] board, int index) {
        int m = board.length, n = board[0].length;
        if (index == m * n) {
            return true;
        }

        int i = index / n, j = index % m;
        if (board[i][j] == '.') {
            for (char k = '1'; k <= '9'; k++) {
                if (canFill(board, i, j, k)) {
                    board[i][j] = k;
                    if (solveSudoku(board, index + 1)) {
                        return true;
                    }
                    board[i][j] = '.';
                }
            }
        } else {
            return solveSudoku(board, index + 1);
        }

        return false;
    }

    private boolean canFill(char[][] board, int i, int j, char c) {
        int m = board.length, n = board[0].length;

        for (int rowIndex = 0; rowIndex < i; rowIndex++) {
            if (board[rowIndex][j] == c) {
                return false;
            }
        }
        for (int rowIndex = i + 1; rowIndex < m; rowIndex++) {
            if (board[rowIndex][j] == c) {
                return false;
            }
        }

        for (int colIndex = 0; colIndex < j; colIndex++) {
            if (board[i][colIndex] == c) {
                return false;
            }
        }
        for (int colIndex = j; colIndex < n; colIndex++) {
            if (board[i][colIndex] == c) {
                return false;
            }
        }

        int rowIndex = i / 3 * 3, colIndex = j / 3 * 3;
        for (int k = rowIndex; k < rowIndex + 3; k++) {
            for (int l = colIndex; l < colIndex + 3; l++) {
                if (k == i && l == j) {
                    continue;
                } else {
                    if (board[k][l] == c) {
                        return false;
                    }
                }
            }
        }

        return true;
    }
}

Reference

37. Sudoku Solver