8. Valid Sudoku

Determine if a 9 x 9 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 nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

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.

Example 1:

Input: 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”]]
Output: true

Example 2:

Input: 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”]]
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.

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit 1-9 or '.'.

Approach

• Loop through all and then maintain a visited kind of boolean array for three things -> row, col, box as there cannot be duplicates that is how we check valid sudoku
• now we mark each non . ones as visited and if it is visited before already then not valid
• to find box number we use the formula given
• Time would 9 squared space would be 27 or we could just say O(n)

class Solution {
    public boolean isValidSudoku(char[][] board) {
        boolean[][] rows = new boolean[9][9]; //rows[r][d] -> does d+1 exist in row r
        boolean[][] cols = new boolean[9][9]; //cols[r][d] -> does d+1 exist in col c
        boolean[][] boxes = new boolean[9][9]; //boxes[k][d] -> does d+1 exist in box k
 
        for (int i = 0; i < board.length; i++) {
            for (int j = 0; j < board[0].length; j++) {
                char c = board[i][j];
                if (c == '.') continue;
 
                int d = c - '1';
                int k = (i/3)*3 + j/3;
 
                if (rows[i][d] || cols[j][d] || boxes[k][d])
                    return false;
 
                rows[i][d] = true;
                cols[j][d] = true;
                boxes[k][d] = true;    
            }
        } 
 
        return true;
    }
}