题目

编写一个程序，通过填充空格来解决数独问题。

数独的解法需遵循如下规则：

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1：

输入：board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
输出：[["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"]]
解释：输入的数独如上图所示，唯一有效的解决方案如下所示：

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 '.'
• 题目数据 保证 输入数独仅有一个解

题解

private static final List<Character> CHARACTERS = Arrays.asList('1', '2', '3', '4', '5', '6', '7', '8', '9');

public void solveSudoku(char[][] board) {
    // 找到一个位置可填写数字
    BiFunction<Integer, Integer, List<Character>> availableChars = (row, column) -> {
        List<Character> chars = new ArrayList<>(CHARACTERS);
        // 遍历指定行 移除出现的字符
        for (char ch : board[row]) {
            chars.remove((Character) ch);
        }
        // 遍历指定列 移除出现字符
        for (char[] rowChars : board) {
            chars.remove((Character) rowChars[column]);
        }
        // 遍历开始行列
        int startRow = row - row % 3, startColumn = column - column % 3;
        // 遍历行列所在3X3块 移除出现的字符
        for (int i = startRow; i < startRow + 3; i++) {
            for (int j = startColumn; j < startColumn + 3; j++) {
                chars.remove((Character) board[i][j]);
            }
        }

        // 获得可选择的字符
        return chars;
    };

    // 数字填充到数独
    BiFunction<Integer, Integer, Boolean> isValid = new BiFunction<Integer, Integer, Boolean>() {
        @Override
        public Boolean apply(Integer row, Integer column) {
            // 遍历过最后一个位置 满足条件
            if (row == 9) {
                return true;
            }
            if (board[row][column] == '.') {
                List<Character> apply = availableChars.apply(row, column);
                // 若不存在可填写数字 结束尝试
                if (apply.isEmpty()) {
                    return false;
                }
                // 拿到可用数字依次填写
                for (Character character : apply) {
                    board[row][column] = character;
                    if (this.apply(row + (column + 1) / 9, (column + 1) % 9)) {
                        return true;
                    }
                    // 回溯
                    board[row][column] = '.';
                }

                return false;
            }

            return this.apply(row + (column + 1) / 9, (column + 1) % 9);
        }
    };

    isValid.apply(0, 0);
}