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# Valid Sudoku

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.

![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png)

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`.

```java
class Solution {
    public boolean isValidSudoku(char[][] board) {
        for (int i = 0; i < 9; i++) {
            HashSet<Character> rows = new HashSet<Character>();
            HashSet<Character> columns = new HashSet<Character>();
            HashSet<Character> cube = new HashSet<Character>();
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.' && !rows.add(board[i][j]))
                    return false;
                if (board[j][i] != '.' && !columns.add(board[j][i]))
                    return false;
                int RowIndex = 3 * (i / 3);
                int ColIndex = 3 * (i % 3);
                if (board[RowIndex + j / 3][ColIndex + j % 3] != '.'
                        && !cube.add(board[RowIndex + j / 3][ColIndex + j % 3]))
                    return false;
            }
        }
        return true;
    }
}
```