I am trying to enumerate the number of valid sudokus of a given size. I have a function that takes a sudoku transformed into a list as input and checks to see if it is a valid sudoku or not. My original method was just to write nested for loops to check every single combination of a list. For a 2 x 2 sudoku, my code looks something like this:
def enumerate2x2():
cnt = 0
for i1 in range(1,3):
for i2 in range(1,3):
for i3 in range(1,3):
for i4 in range(1,3):
if checkValidSudoku([i1, i2, i3, i4]):
cnt += 1
print(cnt)
This code just generates every possible combination of a 4-element list (that's how many squares are in a 2x2 sudoku) with each element in the list being either a 1 or a 2. It then checks each combination.
However, when trying this on a 5x5 sudoku i ran into a problem as python only allows you to have 20 nested loops, so I want to generalize this ugly method into something that will work with any size sudoku. Any help would be appreciated.
The Python product intrinsic function, just importing the itertools module, is what you need:
import itertools
sudoku = list(itertools.product(range(1,3), repeat=4))
for x in range(len(sudoku)):
print sudoku[x]
that simply calculate all the cartesian products, you were looking for, here below the output:
(1, 1, 1, 1)
(1, 1, 1, 2)
(1, 1, 2, 1)
(1, 1, 2, 2)
(1, 2, 1, 1)
(1, 2, 1, 2)
(1, 2, 2, 1)
(1, 2, 2, 2)
(2, 1, 1, 1)
(2, 1, 1, 2)
(2, 1, 2, 1)
(2, 1, 2, 2)
(2, 2, 1, 1)
(2, 2, 1, 2)
(2, 2, 2, 1)
(2, 2, 2, 2)
it seems no combination is now missing, isn't it? Have a look at this other question Combinations with repetition in python, where order MATTERS for more details on alternative implementation too.