Table of Contents

## Question

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:**

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.

## Python Solution

class Solution: def solveSudoku(self, board: List[List[str]]) -> None: """ Do not return anything, modify board in-place instead. """ for i in range(9): for j in range(9): if board[i][j]!='.': board[i][j] = int(board[i][j]) else: board[i][j] = 0 def return_empty(board): for i in range(9): for j in range(9): if board[i][j]==0: return(i,j) return None def check(board,num,pos): row,col = pos # checking row for i in range(9): if board[row][i]==num and i!=col: return False # checking col for i in range(9): if board[i][col]==num and i!=row: return False # checking for sub-grid box_x = row//3 box_y = col//3 for i in range(box_x*3,box_x*3+3): for j in range(box_y*3,box_y*3+3): if board[i][j]==num and (i,j)!=pos: return False return True def solve(board): vacant = return_empty(board) if vacant is None:return True #means all cella are filled now and we have completed the sudoku row,col = vacant for i in range(1,10): if check(board,i,vacant): board[row][col] = i if solve(board): return True board[row][col] = 0 return False solve(board) for i in range(9): l = '' for j in range(9): l+=str(board[i][j]) board[i] = l