Valid Sudoku

Description

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 '.'.

Code

Time Complexity: $O(n^2)$, Space Complexity: $O(1)$

注意 box 的 index 計算方式：int index = 3 * ri + ci;。

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        vector<set<char>> rows(9);
        vector<set<char>> cols(9);
        vector<set<char>> box(9);
 
        for(int i = 0; i < board.size(); i++) {
            for(int j = 0; j < board[i].size(); j++) {
                char c = board[i][j];
                if(c != '.') {
                    if(rows[i].find(c) != rows[i].end()) {
                        return false;
                    } else {
                        rows[i].insert(c);
                    }
                    
                    if(cols[j].find(c) != cols[j].end()) {
                        return false;
                    } else {
                        cols[j].insert(c);
                    }
                    
                    int ri = i / 3;
                    int ci = j / 3;
                    int index = 3 * ri + ci;
                    
                    if(box[index].find(c) != box[index].end()) {
                        return false;
                    } else {
                        box[index].insert(c);
                    }
                }
            }
        }
        
        return true;
    }
};

Source

• Valid Sudoku - LeetCode