Sudoku Solver
Tags: leetcode, dsa, theabbie
Published: 2022-06-15 14:00:56

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:**

![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png)

**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:

![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png)

**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.

**SOLUTION:**

    class Solution:
        def getPos(self, board, i, j):
            pos = set(map(str, range(1, 10)))
            ci, cj = i - i % 3, j - j % 3
            for a in range(3):
                for b in range(3):
                    if board[ci + a][cj + b] != "." and board[ci + a][cj + b] in pos:
                        pos.remove(board[ci + a][cj + b])
            for a in range(9):
                if board[i][a] in pos:
                    pos.remove(board[i][a])
                if board[a][j] in pos:
                    pos.remove(board[a][j])
            return pos
        
        def solve(self, board, spi):
            if spi >= len(self.spaces):
                return True
            if spi < len(self.spaces):
                i, j = self.spaces[spi]
                pos = self.getPos(board, i, j)
                for p in pos:
                    board[i][j] = p
                    currsolution = self.solve(board, spi + 1)
                    if currsolution:
                        return True
                    else:
                        board[i][j] = "."
            return False
        
        def solveSudoku(self, board: List[List[str]]) -> None:
            self.spaces = []
            for i in range(9):
                for j in range(9):
                    if board[i][j] == ".":
                        self.spaces.append((i, j))
            self.solve(board, 0)