Find orthogonal solutions for hypersudoku

hypersudoku.py

#!/usr/bin/env python3

from collections import defaultdict
from itertools import combinations, permutations
from math import isqrt
from subprocess import check_call


def inner(n):
    return range(1, n+1)


def outer(n):
    return range(1, n*n, n)


def hyperbox(n):
    for x in inner(n):
        for y in inner(n):
            yield range(x, x+(n*n), x), range(y, y+(n*n), n)


def hyperrow(n):
    for x in outer(n):
        for y in inner(n):
            yield range(x, x+n), range(y, y+(n*n), n)


def hypercolumn(n):
    for x in inner(n):
        for y in outer(n):
            yield range(x, x+(n*n), n), range(y, y+n)


def mkregions(f, n):
    for r, c in f(n):
        yield '-c=extraregion:R{}C{}'.format(
            ','.join(str(x) for x in r),
            ','.join(str(x) for x in c)
    )


def hyper(n):
    yield from mkregions(hyperrow, n)
    yield from mkregions(hypercolumn, n)


def t2s(s):
    return ''.join(str(d) for d in s)


def ravel(*solutions):
    sstrings = list(t2s(s) for s in solutions)
    for n in range(0, 81, 9):
        print('    '.join(s[n:n+9] for s in sstrings))
    print()


given='123......456......789............................................................'
n = isqrt(isqrt(len(given)))

args = [
    './SudokuSolverConsole',
    '-g='+given.strip(),
    #'-b 4', # no solutions!
    '-n', '-o=result.txt'
]

args.append('-c=djg') # equivalent to hyperbox

args.extend(list(hyper(n)))

print(args)

check_call(args)

with open('result.txt', 'r') as f:
    solutions = set()
    for line in f:
        sln = tuple(int(c) for c in line.strip())
        solutions.add(sln)


orthogonal = defaultdict(set)

for s1, s2 in combinations(solutions, 2):
    combined = set(zip(s1,s2))
    if len(combined) == 81:
        orthogonal[s1].add(s1)
        orthogonal[s1].add(s2)
        orthogonal[s2].add(s1)
        orthogonal[s2].add(s2)


seen = []


print('And now the final result...')
print()

for k, v in orthogonal.items():
    if v in seen:
        continue
#    ravel(*v)
    for sln in v:
        print(t2s(sln))
    print()
    seen.append(v)