36. 有效的数独

请你判断一个?9 x 9?的数独是否有效。只需要?根据以下规则?，验证已经填入的数字是否有效即可。

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）

注意：

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。
• 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：true

示例 2：

输入：board = 
[["8","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：false
解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

提示：

• board.length == 9
• board[i].length == 9
• board[i][j]?是一位数字（1-9）或者?'.'

方法1：

    public static boolean isValidSudoku(char[][] board) {
        String[] rows = new String[9];
        String[] columns = new String[9];
        String[] areas = new String[9];
        for (int i = 0; i < 9; i++) {
            if (rows[i] == null){
                rows[i] = "a";
            }

            for (int j = 0; j < 9; j++) {
                if (columns[j] == null){
                    columns[j] = "a";
                }
                if (rows[i].contains(board[i][j] + "")){
                    return false;
                }else if (board[i][j] != '.' && !rows[i].contains(board[i][j] + "")){
                    rows[i] += board[i][j];
                }
                if (columns[j].contains(board[i][j] + "")){
                    return false;
                }else if (board[i][j] != '.' && !columns[j].contains(board[i][j] + "")){
                    columns[j] += board[i][j];
                }
                int row = i / 3; // 0 1 2
                int column = j / 3; //0 1 2
                int area = row * 3 + column;
                if (areas[area] == null){
                    areas[area] = "a";
                }
                if (areas[area].contains(board[i][j] + "")){
                    return false;
                }else  if (board[i][j] != '.' && !areas[area].contains(board[i][j] + "")){
                    areas[area] += board[i][j];
                }
            }
        }
        return true;
    }

方法2：（0ms）

    public boolean isValidSudoku(char[][] board) {
        short[] rows = new short[9];
        short[] cols = new short[9];
        short[] squares = new short[9];
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    short value = (short)(1 << (board[i][j] - '0'));
                    int boxNum = i / 3 * 3 + j / 3;
                    if ((rows[i] & value) != 0 || (cols[j] & value) != 0 || (squares[boxNum] & value) != 0) {
                        return false;
                    }
                    rows[i] |= value;
                    cols[j] |= value;
                    squares[boxNum] |= value;
                }
            }
        }
        return true;
    }

方法3：（1ms）

    public boolean isValidSudoku(char[][] board) {
        int[] rows = new int[9];
        int[] cols = new int[9];
        int[] subboxes = new int[9];
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char c = board[i][j];
                if (c != '.') {
                    int x = (1 << (c - '1'));
                    if ((rows[i] & x) != 0) {
                        return false;
                    } else {
                        rows[i] |= x;
                    }
                    if ((cols[j] & x) != 0) {
                        return false;
                    } else {
                        cols[j] |= x;
                    }
                    if ((subboxes[i / 3 * 3 + j / 3] & x) != 0) {
                        return false;
                    } else {
                        subboxes[i / 3 * 3 + j / 3] |= x;
                    }
                }
            }
        }
        return true;
    }

方法4：（2ms）

    public boolean isValidSudoku(char[][] board) {            
        int[][] row = new int[9][9]; // 行
        int[][] columns = new int[9][9]; // 列
        int[][][] a = new int[3][3][9];
        for (int i = 0; i < 9; i++) {
            Set<Character> set = new HashSet<>();
            for (int j = 0; j < 9; j++) {
                char c = board[i][j];
                if (c != '.') {
                    row[i][c - 49]++;
                    columns[j][c - 49]++;
                    a[i / 3][j / 3][c - 49]++;
                    if (row[i][c - 49] > 1 || columns[j][c - 49] > 1 || a[i / 3][j / 3][c - 49] > 1) {
                        return false;
                    }
                }

            }
        }
        return true;
    }