Suppose we have one 9×9 Sudoku grid. 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 (3−3) sub−boxes of the grid must contain the digits from 1−9 without repetition.
Suppose the Sudoku grid is like −
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 −
Example
class Solution(object):
def isValidSudoku(self, board):
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"]]))Input
[ ["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
True