My purpose is to count permutations with certain properties. I first generate the permutations and then remove those that do not satisfy the desired properties. How could I improve the code to be able to enumerate more permutations? from itertools import permutations def check(seq, verbose=False): """check that the elements of the sequence equal a difference of previous elements""" n = len(seq) for k in range(1, n-1): # build a set of admissible values dk = {abs(seq-seq[j]) for i in range(0, k) for j in range(i+1, k+1) if i < j} if k > 0 and verbose: print('current index = ', k) print('current subsequence = ', seq[:k+1]) print('current admissible values = ', dk) print('next element = ', seq[k+1]) # check if the next element is in the set of admissible values if k > 0 and seq[k+1] not in dk: # return an invalid subsequence (k+2 to include the invalid element) return seq[:k+2] return seq def is_valid(seq): """check that the sequence satisfies certain properties""" n = len(seq) if n < 3: return False if len(check(seq)) == n: return True return False def filter_perms(perms): for perm in perms: if is_valid(perm): yield perm def make_perms(n): """The elements of the list are integers, where a list of length n stores all integers from 1 to n.""" for p in permutations(range(1,n-1)): yield (n,) + p + (n-1,) def enumerate_perms(n): perms = make_perms(n) return filter_perms(perms) # testing a good sequence seq=(5, 2, 3, 1, 4) check(seq, verbose=True) is_valid(seq) # True # testing a bad sequence seq=[5, 2, 1, 3, 4] check(seq, verbose=True) is_valid(seq) # False # testing permutations tuple(make_perms(5)) # testing enumeration tuple(enumerate_perms(5)) # ((5, 2, 3, 1, 4), (5, 3, 2, 1, 4)) len(tuple(enumerate_perms(14))) # 29340 Summary of discussions in the comments section: Should I use numpy arrays? Should I save the permutations to a database? Continue reading...
