有效的数独

判断一个 9x9 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。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。


上图是一个部分填充的有效的数独。

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1:

输入:
[
  ["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:
[
  ["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。
说明:

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。
给定数独序列只包含数字 1-9 和字符 '.' 。
给定数独永远是 9x9 形式的。

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/valid-sudoku
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

class Solution {
    public boolean isValidSudoku(char[][] board) {
        int len = board.length;

        for (int i = 0; i < len; i++) {
            boolean flag = validRowAndCol(board, i, i);
            if (!flag) return false;
        }

        for (int i = 0; i < len; i = i + 3) {
            for (int j = 0; j < len; j = j + 3) {
                boolean flag = validSquare(board, i, j);
                if (!flag) return false;
            }
        }

        return true;
    }

    public boolean validRowAndCol(char[][] board, int y, int x) {
        int len = board.length;
        Set<Character> rowSet = new HashSet<>();
        int count = 0;
        for (int i = 0; i < len; i++) {
            if (board[i][x] != '.') {
                count++;
                rowSet.add(board[i][x]);
            }
        }
        if (count != rowSet.size()) return false;
        count = 0;
        Set<Character> colSet = new HashSet<>();
        for (int i = 0; i < len; i++) {
            if (board[y][i] != '.') {
                count++;
                colSet.add(board[y][i]);
            }
        }
        if (count != colSet.size()) return false;
        return true;
    }

    public boolean validSquare(char[][] board, int y, int x) {
        int count = 0;
        Set<Character> set = new HashSet<>();
        for (int i = y; i < y + 3; i++) {
            for (int j = x; j < x + 3; j++) {
                if (board[i][j] != '.') {
                    count++;
                    set.add(board[i][j]);
                }
            }
        }
        if (set.size() != count) return false;
        return true;
    }
}

优雅的写法

class Solution {
    public boolean isValidSudoku(char[][] board) {
        // 记录某行，某位数字是否已经被摆放
        boolean[][] row = new boolean[9][9];
        // 记录某列，某位数字是否已经被摆放
        boolean[][] col = new boolean[9][9];
        // 记录某 3x3 宫格内，某位数字是否已经被摆放
        boolean[][] block = new boolean[9][9];

        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    int num = board[i][j] - '1';
                    int blockIndex = i / 3 * 3 + j / 3;
                    if (row[i][num] || col[j][num] || block[blockIndex][num]) {
                        return false;
                    } else {
                        row[i][num] = true;
                        col[j][num] = true;
                        block[blockIndex][num] = true;
                    }
                }
            }
        }
        return true;
    }
}

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