# [Solved] 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.

## Question

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:

```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
```