Leetcode POTD (31 August 2025) – Hard – 37

37. Sudoku Solver

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

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: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
Explanation: The input board is shown above and the only valid solution is shown below:

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit or '.'.
• It is guaranteed that the input board has only one solution.

class Solution {
public:
    bool isValid(vector<vector<char>>& board, int row, int col, char d) {
        for(int i = 0; i < 9; i++) {
            if(board[i][col] == d)
                return false;
            
            if(board[row][i] == d) {
                return false;
            }
        }

        int start_i = row/3 * 3;
        int start_j = col/3 * 3;

        for(int k = 0; k < 3; k++) {
            for(int l = 0; l < 3; l++) {
                if(board[start_i+k][start_j+l] == d) {
                    return false;
                }
            }
        }

        return true;
    }

   
    bool solve(vector<vector<char>>& board) {
        for(int i = 0; i < 9; i++) { //O(9)
            for(int j = 0; j < 9; j++) { //O(9)
                if(board[i][j] == '.') {

                    for(char d = '1'; d <= '9'; d++) { 

                        if(isValid(board, i, j, d)) {
                            board[i][j] = d;

                            if(solve(board) == true) {
                                return true;
                            }

                            board[i][j] = '.';
                        }

                    }

                    return false;
                }
            }
        }
        return true;
    }

    void solveSudoku(vector<vector<char>>& board) {
        solve(board);
    }
};

Complexity:

Space → O(1)

Time → O(9^81)