# Sudoku Solver Problem

## Description

LeetCode Problem 37.

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

A sudoku solution must satisfy all of the following rules:

- Each of the digits 1-9 must occur exactly once in each row.
- Each of the digits 1-9 must occur exactly once in each column.
- 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:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22

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.

## Sample C++ Code

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33

bool check(vector<vector<char>> &board, int i, int j, char val)
{
int row = i - i%3, column = j - j%3;
for (int x=0; x<9; x++) if (board[x][j] == val) return false;
for (int y=0; y<9; y++) if (board[i][y] == val) return false;
for (int x=0; x<3; x++)
for (int y=0; y<3; y++)
if (board[row+x][column+y] == val) return false;
return true;
}
bool solveSudoku(vector<vector<char>> &board, int i, int j)
{
if (i==9) return true;
if (j==9) return solveSudoku(board, i+1, 0);
if (board[i][j] != '.') return solveSudoku(board, i, j+1);
for (char c='1'; c<='9'; c++)
{
if (check(board, i, j, c))
{
board[i][j] = c;
if (solveSudoku(board, i, j+1)) return true;
board[i][j] = '.';
}
}
return false;
}
void solveSudoku(vector<vector>& board) {
solveSudoku(board, 0, 0);
}