36. Valid Sudoku

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36. Valid Sudoku

Description

Determine if a9 x 9 Sudoku board is valid.Only the filled cells need to be validatedaccording to the following rules:

  • Each row must contain the digits1-9 without repetition.
  • Each column must contain the digits1-9without repetition.
  • Each of the nine3 x 3 sub-boxes of the grid must contain the digits1-9without 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:

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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:

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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 '.'.

Hints/Notes

  • 2024/12/19
  • The key is to find mapping to box
  • No solution from 0x3F

Solution

Language: C++

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class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        bool cols[9][9]{}, rows[9][9]{}, boxes[9][9]{};
        for (int i = 0; i < board.size(); i++) {
            for (int j = 0; j < board.size(); j++) {
                if (board[i][j] == '.') {
                    continue;
                }
                int box = (i / 3) * 3 + j / 3;
                int idx = board[i][j] - '1';
                if (cols[i][idx] || rows[j][idx] || boxes[box][idx]) {
                    return false;
                }
                cols[i][idx] = rows[j][idx] = boxes[box][idx] = true;
            }
        }
        return true;
    }
};