def generate_permutation(size):
"""
Input should be SET_SIZE
Special cases are 2 and 3, where a random shuffling of integers
are used as the permutation.
Else loop works as follows:
- Finds primes uses Sieve of Eratosthenes until sum of generated
primes (subcycle_length) exceeds size.
- Removes last number if subcycle_length is bigger than size.
- Uses subcycle_length to pull permutations out of the shuffled
list of integers.
"""
shuffled_nums = [(i + 1) for i in range(size)]
shuffle(shuffled_nums)
if (size == 2 or size == 3):
return Permutation.cycle(*shuffled_nums)
else:
bool_vals = [True for i in range(2, size)]
subcycle_lengths = []
j = 0
while(sum(subcycle_lengths) < size and j < size - 2):
if (bool_vals[j] == True):
cur_val = 2
while ((j + 2) * cur_val < size):
bool_vals[((j + 2) * cur_val) - 2] = False
cur_val += 1
subcycle_lengths.append(j + 2)
j += 1
if (sum(subcycle_lengths) > size):
subcycle_lengths.pop()
perm = Permutation.cycle()
start = 0
for num in subcycle_lengths:
perm *= Permutation.cycle(*shuffled_nums[start:start + num])
start += num
return perm
def test_bad_cycle(cyc):
with pytest.raises(ValueError):
Permutation.cycle(*cyc)
import pytest
from permutation import Permutation
EQUIV_CLASSES = [
[
Permutation(),
Permutation(1),
Permutation(1, 2),
Permutation(1, 2, 3, 4, 5),
Permutation.cycle(),
Permutation.from_cycles(),
Permutation.from_cycles(()),
],
[
Permutation(2, 1),
Permutation(2, 1, 3, 4, 5),
Permutation.cycle(1, 2),
Permutation.cycle(2, 1),
Permutation.from_cycles((1, 2)),
Permutation.from_cycles((2, 1)),
],
[
Permutation(2, 3, 1),
Permutation(2, 3, 1, 4, 5),
Permutation.cycle(1, 2, 3),
Permutation.cycle(2, 3, 1),
Permutation.cycle(3, 1, 2),
Permutation.from_cycles((1, 2, 3)),
Permutation.from_cycles((2, 3, 1)),
Permutation.from_cycles((3, 1, 2)),
],
def test_cycle(cyc, p):
assert Permutation.cycle(*cyc) == p
