Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the 9 3x3
    sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
  ["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"]
]
Output:
 
 true

Example 2:

Input:
[
  ["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"]
]
Output:
 
 false
Explanation: Same as Example 1, except with the 5 in the top left corner being 
    modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Note:

• A Sudoku board (partially filled) could be valid but is not necessarily solvable.
• Only the filled cells need to be validated according to the mentioned rules.
• The given board contain only digits 1-9 and the character '.'.
• The given board size is always 9x9.

這個題的意思是判斷目前已知的九宮格中是否符合規則，使用一個HashMap或者是Set即可解決。

1）

class Solution {
    public boolean isValidSudoku(char[][] board) {
        Set seen = new HashSet();
        for (int i=0; i<9; ++i) {
            for (int j=0; j<9; ++j) {
                if (board[i][j] != '.') {
                    String b = "(" + board[i][j] + ")";
                    if (!seen.add(b + i) || !seen.add(j + b) || !seen.add(i/3 + b + j/3))
                        return false;
                }
            }
        }
        return true;
    }
}

時間複雜度O（n2）

2）

class Solution {
    public boolean isValidSudoku(char[][] board) {
    for(int i = 0; i < board.length; i++) {
        if (!isRowValid(board, i) || !isColumnValid(board, i)) {
            return false;
    }		
    } 
    for (int i = 0; i < board.length; i+=3) {
        for(int j = 0; j < board.length; j+=3) {
            if (!isSquareValid(board,i, j)) {
                return false;
            }
        }
    }
    return true;
    }

    public boolean isSquareValid(char[][] board, int iStart, int jStart) {
        Set<Integer> set = new HashSet<>();
        for (int i = iStart; i < iStart + 3; i++) {
            for (int j = jStart; j < jStart + 3; j++) {
            if (board[i][j] != '.' && !set.add(board[i][j] - '.')) {
                return false;
            }
            }
        }
        return true;
    }

    public boolean isRowValid(char[][] board, int index) {
        Set<Integer> set = new HashSet<>();
        for(int i = 0; i < board.length; i++) {
            if (board[index][i] != '.' && !set.add(board[index][i] - '.')) {
                return false;
            }
        }
        return true;
    }
    public boolean isColumnValid(char[][] board, int index) {
        Set<Integer> set = new HashSet<>();
        for(int i = 0; i < board.length; i++) {
            if (board[i][index] != '.' && !set.add(board[i][index] - '.')) {
                return false;
            }
        }
        return true;

    }

}