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Suppose we have one 9x9 Sudoku board. We have to check whether that is valid or now. Only the filled cells need to be validated according to the following rules −

- Each row must contain the digits from 1-9 without repetition.
- Each column must contain the digits from 1-9 without repetition.
- Each of the 9 (3x3) sub-boxes of the grid must contain the digits from 1-9 without repetition.

Suppose the Sudoku grid is like −

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 |

This is valid.

To solve this, we will follow these steps −

- for i in range 0 to 8
- create some empty dictionary called row, col and block, row_cube := 3 * (i / 3), and col_cube := 3 * (i mod 3)
- for j in range 0 to 8
- if board[i, j] is not blank and board[i, j] in row, then return false
- row[board[i, j]] := 1
- if board[j, i] is not blank and board[j, i] in col, then return false
- col[board[j, i]] := 1
- rc := row_cube + j/3 and cc := col_cube + j mod 3
- if board[rc, cc] in block and board[rc, cc] is not blank, then return false
- block[board[rc, cc]] := 1

- return true

Let us see the following implementation to get better understanding −

class Solution(object): def isValidSudoku(self, board): """ :type board: List[List[str]] :rtype: bool """ for i in range(9): row = {} column = {} block = {} row_cube = 3 * (i//3) column_cube = 3 * (i%3) for j in range(9): if board[i][j]!='.' and board[i][j] in row: return False row[board[i][j]] = 1 if board[j][i]!='.' and board[j][i] in column: return False column[board[j][i]] = 1 rc= row_cube+j//3 cc = column_cube + j%3 if board[rc][cc] in block and board[rc][cc]!='.': return False block[board[rc][cc]]=1 return True ob1 = Solution() print(ob1.isValidSudoku([ ["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"]]))

[["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"]]

true

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