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# issue 6
# http://www-graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation
from bitarray import bitarray
from bitarray.util import zeros, ba2int, int2ba
def all_perm(n, k, endian=None):
"""all_perm(n, k, endian=None) -> iterator
Return an iterator over all bitarrays of length `n` and
population count `k` in lexicographical order.
"""
if n < 0:
raise ValueError("length must be >= 0")
# error check inputs and handle edge cases
if k <= 0 or k > n:
if k == 0:
yield zeros(n, endian)
return
raise ValueError("k must be in range 0 <= k <= n, got %s" % k)
v = (1 << k) - 1
while True:
try:
yield int2ba(v, length=n, endian=endian)
except OverflowError:
return
t = (v | (v - 1)) + 1
v = t | ((((t & -t) // (v & -v)) >> 1) - 1)
def next_perm(__a):
"""next_perm(a, /) -> bitarray
Return the next lexicographical permutation of bitarray `a`. The length
and population count of the result is that of `a`. The integer
value (`ba2int()`) of the next permutation will always increase, except
when the cycle is completed. In that case, the lowest lexicographical
permutation will be returned.
"""
v = ba2int(__a)
if v == 0:
return __a
t = (v | (v - 1)) + 1
v = t | ((((t & -t) // (v & -v)) >> 1) - 1)
try:
return int2ba(v, length=len(__a), endian=__a.endian)
except OverflowError:
return __a[::-1]
# ---------------------------------------------------------------------------
import unittest
from math import comb
from random import choice, getrandbits, randrange
from itertools import pairwise
from bitarray import frozenbitarray
from bitarray.util import random_k
class PermTests(unittest.TestCase):
def test_errors(self):
N = next_perm
self.assertRaises(TypeError, N)
self.assertRaises(TypeError, N, bitarray('1'), 1)
self.assertRaises(TypeError, N, '1')
self.assertRaises(ValueError, N, bitarray())
A = all_perm
self.assertRaises(TypeError, A)
self.assertRaises(TypeError, A, 4)
self.assertRaises(TypeError, next, A("4", 2))
self.assertRaises(TypeError, next, A(1, "0.5"))
self.assertRaises(TypeError, A, 1, p=1)
self.assertRaises(TypeError, next, A(11, 5.5))
self.assertRaises(ValueError, next, A(-1, 0))
for k in -1, 11: # k is not 0 <= k <= n
self.assertRaises(ValueError, next, A(10, k))
self.assertRaises(ValueError, next, A(10, 7, 'foo'))
self.assertRaises(ValueError, next, A(10, 7, endian='foo'))
def test_zeros_ones(self):
for n in range(1, 30):
endian = choice(["little", "big"])
v = getrandbits(1)
lst = list(all_perm(n, v * n, endian))
self.assertEqual(len(lst), 1)
a = lst[0]
c = a.copy()
self.assertEqual(a.endian, endian)
self.assertEqual(len(a), n)
if v:
self.assertTrue(a.all())
else:
self.assertFalse(a.any())
self.assertEqual(next_perm(a), a)
self.assertEqual(a, c)
def test_next_perm_explicit(self):
a = bitarray('00010011', 'big')
for s in ['00010101', '00010110', '00011001',
'00011010', '00011100', '00100011']:
a = next_perm(a)
self.assertEqual(a.count(), 3)
self.assertEqual(a, bitarray(s, 'big'))
def test_next_perm_turnover(self):
for a in [bitarray('11111110000', 'big'),
bitarray('0000001111111', 'little')]:
self.assertEqual(next_perm(a), a[::-1])
def test_next_perm_random(self):
for _ in range(100):
n = randrange(2, 1_000_000)
k = randrange(1, n)
a = random_k(n, k, endian=choice(["little", "big"]))
b = next_perm(a)
self.assertEqual(len(b), n)
self.assertEqual(b.count(), k)
self.assertEqual(b.endian, a.endian)
self.assertNotEqual(a, b)
if ba2int(a) > ba2int(b):
print(n)
c = a.copy()
c.sort(c.endian == 'big')
self.assertEqual(a, c)
self.assertEqual(b, a[::-1])
def check_perm_cycle(self, start):
n, k = len(start), start.count()
a = bitarray(start)
coll = set()
c = 0
while True:
a = next_perm(a)
coll.add(frozenbitarray(a))
self.assertEqual(len(a), n)
self.assertEqual(a.count(), k)
self.assertEqual(a.endian, start.endian)
c += 1
if a == start:
break
self.assertEqual(c, comb(n, k))
self.assertEqual(len(coll), c)
def test_all_perm_explicit(self):
for n, k, res in [
(0, 0, ['']),
(1, 0, ['0']),
(1, 1, ['1']),
(2, 0, ['00']),
(2, 1, ['01', '10']),
(2, 2, ['11']),
(3, 0, ['000']),
(3, 1, ['001', '010', '100']),
(3, 2, ['011', '101', '110']),
(3, 3, ['111']),
(4, 2, ['0011', '0101', '0110', '1001', '1010', '1100']),
]:
lst = list(all_perm(n, k, 'big'))
self.assertEqual(len(lst), comb(n, k))
self.assertEqual(lst, [bitarray(s) for s in res])
if n == 0:
continue
a = lst[0]
for i in range(20):
self.assertEqual(a, bitarray(res[i % len(lst)]))
a = next_perm(a)
def test_all_perm(self):
n, k = 17, 5
endian=choice(["little", "big"])
prev = None
cnt = 0
coll = set()
for a in all_perm(n, k, endian):
self.assertEqual(type(a), bitarray)
self.assertEqual(len(a), n)
self.assertEqual(a.count(), k)
self.assertEqual(a.endian, endian)
coll.add(frozenbitarray(a))
if prev is None:
first = a.copy()
c = a.copy()
c.sort(c.endian == "little")
self.assertEqual(a, c)
else:
self.assertNotEqual(a, first)
self.assertEqual(next_perm(prev), a)
self.assertTrue(ba2int(prev) < ba2int(a))
prev = a
cnt += 1
self.assertEqual(cnt, comb(n, k))
self.assertEqual(len(coll), cnt)
# a is now the last permutation
last = a.copy()
self.assertTrue(ba2int(first) < ba2int(last))
self.assertEqual(last, first[::-1])
def test_all_perm_order(self):
n, k = 10, 5
for a, b in pairwise(all_perm(n, k, 'little')):
self.assertTrue(ba2int(b) > ba2int(a))
self.assertEqual(next_perm(a), b)
if __name__ == '__main__':
unittest.main()
|
