20. Valid Sudoku.cpp

/*
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:

Each row must contain the digits 1-9 without repetition.
Each column must contain the digits 1-9 without repetition.
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 or '.'.
*/

class Solution
{
public:
    bool valid(vector<vector<char>> &board, int r, int c, char val)
    {
        for (int i = 0; i < 9; ++i)
            if (board[i][c] == val || board[r][i] == val)
            {
                return false;
            }

        for (int i = 0; i < 3; ++i)
        {
            for (int j = 0; j < 3; ++j)
            {
                if (board[(r / 3) * 3 + i][(c / 3) * 3 + j] == val)
                {
                    return false;
                }
            }
        }

        return true;
    }

    bool isValidSudoku(vector<vector<char>> board)
    {
        for (int i = 0; i < board.size(); ++i)
        {
            for (int j = 0; j < board[0].size(); ++j)
            {

                if (board[i][j] != '.')
                {
                    char ch = board[i][j];
                    board[i][j] = '!';

                    if (!valid(board, i, j, ch))
                    {
                        return false;
                    }

                    board[i][j] = ch;
                }
            }
        }

        return true;
    }
};