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

Empty cells are indicated by the character '.'.

A sudoku puzzle...

...and its solution numbers marked in red.

Note:

• The given board contain only digits 1-9 and the character '.'.
• You may assume that the given Sudoku puzzle will have a single unique solution.
• The given board size is always 9x9.

 

AC code;

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        solve(board);
    }
    
    bool solve(vector<vector<char>>& board) {
        for (int i = 0; i < 9; ++i) {
            for (int j = 0; j < 9; ++j) {
                if (board[i][j] == '.') {
                    for (int c = '1'; c <= '9'; ++c) {
                        if (isLegal(board, i, j, c)) {
                            board[i][j] = c;
                            if (solve(board)) return true;
                            else board[i][j] = '.';
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }
    
    bool isLegal(vector<vector<char>> board, int x, int y, char c) {
        for (int i = 0; i < 9; ++i) {
            if (board[x][i] != '.' && board[x][i] == c) return false;
            if (board[i][y] != '.' && board[i][y] == c) return false;
            if (board[3 * (x / 3) + i / 3][3 * (y / 3) + i % 3] != '.' && 
                board[3 * (x / 3) + i / 3][3 * (y / 3) + i % 3] == c) return false;
        }
        return true;
    }
};

Runtime: 184 ms, faster than 6.58% of C++ online submissions for Sudoku Solver.