37. Sudoku Solver

1. Description

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.

2. Example

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:

3. 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.

4. Solutions

My Accepted Solution

Time complexity: O(9 * rows * columns)
Space complexity: O(1)

class Solution {
public:
    bool isNewLetterValid(const vector<vector<char>>& i_board, int row, int column, char letter) {
        for (int i = 0; i < 9; ++i) {
            if (i_board[row][i] == letter || i_board[i][column] == letter ||
                i_board[row / 3 * 3 + i / 3][column / 3 * 3 + i % 3] == letter) {
                return false;
            }
        }

        return true;
    }

    bool solve(vector<vector<char>>& m_board) {
        const int rows = m_board.size(), columns = m_board.front().size();

        for (int i = 0; i < rows; ++i) {
            for (int j = 0; j < columns; ++j) {
                if (m_board[i][j] == '.') {
                    for (char letter = '1'; letter <= '9'; ++letter) {
                        if (isNewLetterValid(m_board, i, j, letter)) {
                            m_board[i][j] = letter;

                            if (solve(m_board)) {
                                return true;
                            } else {
                                m_board[i][j] = '.';
                            }
                        }
                    }

                    return false;
                }
            }
        }

        return true;
    }

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