36.valid-sudoku.cpp

//  Tag: Array, Hash Table, Matrix
//  Time: O(N^2)
//  Space: O(N^2)
//  Ref: -
//  Note: -

//  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 1-9 or '.'.
//  
//  

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        int n = board.size();

        int row[9][9] = {0};
        int col[9][9] = {0};
        int zone[9][9] = {0};

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (board[i][j] == '.') {
                    continue;
                }

                int number = board[i][j] - '1';
                int k = i / 3 * 3 + j / 3;
                if (row[i][number] || col[j][number] || zone[k][number]) {
                    return false;
                }

                row[i][number] = 1;
                col[j][number] = 1;
                zone[k][number] = 1; 
            }
        }

        return true;
    }
};