19.2.3 [LeetCode 36] 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.

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.

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        for (int i = 0; i < 9; i++) {
            bool used[10] = { false };
            for (int j = 0; j < 9; j++) {
                if (board[i][j] == '.')continue;
                if (used[board[i][j]-'0'])
                    return false;
                used[board[i][j]-'0'] = true;
            }
        }
        for (int i = 0; i < 9; i++) {
            bool used[10] = { false };
            for (int j = 0; j < 9; j++) {
                if (board[j][i] == '.')continue;
                if (used[board[j][i]-'0'])
                    return false;
                used[board[j][i]-'0'] = true;
            }
        }
        int limit[9][4] = { 0,2,0,2,
                        3,5,0,2,
                        6,8,0,2,
                        0,2,3,5,
                        3,5,3,5,
                        6,8,3,5,
                        0,2,6,8,
                        3,5,6,8,
                        6,8,6,8 };
        for (int i = 0; i < 9; i++) {
            bool used[10] = { false };
            for(int j=limit[i][2];j<=limit[i][3];j++)
                for (int k = limit[i][0]; k <= limit[i][1]; k++) {
                    if (board[j][k] == '.')continue;
                    if (used[board[j][k]-'0'])
                        return false;
                    used[board[j][k]-'0'] = true;
                }
        }
        return true;
    }
};

朴素解法