medium/36. Valid Sudoku.md · hugh_sun/leetcode

**[36. Valid Sudoku](https://leetcode.com/problems/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.

![](./png/250px-Sudoku-by-L2G-20050714.svg.png)<br/>
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.

**Solution:**

Runtime: 1 ms<br/>
Memory Usage: 43 MB

```java
class Solution {
    public boolean isValidSudoku(char[][] board) {
        boolean[][] col = new boolean[9][9];
        boolean[][] box = new boolean[9][9];
        for(int i = 0; i < 9; i++) {
            boolean[] row = new boolean[9];
            for(int j = 0; j < 9; j++) {
                if(board[i][j] == '.')
                    continue;
                int val = board[i][j] - '0' - 1;
                if(row[val] || col[j][val] || box[i / 3 * 3 + j / 3][val])
                    return false;
                row[val] = true;
                col[j][val] = true;
                box[i / 3 * 3 + j / 3][val] = true;
            }
        }
        return true;
    }
}

```

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