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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 lexico_all(n, k, endian=None):
"""lexico_all(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 lexico_next(__a):
"""lexico_next(a, /) -> bitarray
Return the next lexicographical permutation of bitarray `a`.
The length and population count of the result remains unchanged.
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.
"""
if not __a:
return __a
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]
# ---------------------- lexicographical permutations -----------------------
import math
import unittest
from random import choice, getrandbits, randrange
from itertools import pairwise
from bitarray import frozenbitarray
from bitarray.util import random_k
class LexicoTests(unittest.TestCase):
def test_errors(self):
N = lexico_next
self.assertRaises(TypeError, N)
self.assertRaises(TypeError, N, bitarray('1'), 1)
self.assertRaises(TypeError, N, '1')
A = lexico_all
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(30):
endian = choice(["little", "big"])
a = bitarray(n, endian)
a.setall(getrandbits(1))
b = lexico_next(a)
self.assertEqual(b.endian, endian)
# nothing to permute
self.assertEqual(b, a)
def test_next_explicit(self):
for perm, endian in [
(['100', '010', '001', '100'], 'little'),
(['00001', '00010', '00100', '01000', '10000'], 'big'),
(['0011', '0101', '0110', '1001', '1010',
'1100', '0011'], 'big'),
(['0000111', '1110000'], 'little'),
]:
a = bitarray(perm[0], endian)
for s in perm[1:]:
a = lexico_next(a)
self.assertEqual(a, bitarray(s))
def check_cycle(self, n, k):
endian = choice(["little", "big"])
a0 = bitarray(n, endian)
a0[:k] = 1
if endian == "big":
a0.reverse()
ncycle = math.comb(n, k) # cycle length
self.assertTrue(ncycle >= 2)
coll = set()
a = a0.copy()
for i in range(ncycle):
coll.add(frozenbitarray(a))
b = lexico_next(a)
self.assertEqual(len(b), n)
self.assertEqual(b.count(), k)
self.assertEqual(b.endian, endian)
self.assertNotEqual(a, b)
if b == a0:
self.assertEqual(i, ncycle - 1)
self.assertTrue(ba2int(b) < ba2int(a))
break
self.assertTrue(ba2int(b) > ba2int(a))
a = b
else:
self.fail()
self.assertEqual(len(coll), ncycle)
def test_cycle(self):
for _ in range(20):
n = randrange(2, 10)
k = randrange(1, n)
self.check_cycle(n, k)
def test_next_random(self):
for _ in range(100):
endian = choice(["little", "big"])
n = randrange(2, 1_000)
k = randrange(1, n)
a = random_k(n, k, endian)
b = lexico_next(a)
self.assertEqual(len(b), n)
self.assertEqual(b.count(), k)
self.assertEqual(b.endian, endian)
self.assertNotEqual(a, b)
if ba2int(a) > ba2int(b):
c = a.copy()
c.sort(endian == 'big')
self.assertEqual(a, c)
self.assertEqual(b, a[::-1])
# ------------------- lexico_all -------------------
def test_all_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(lexico_all(n, k, 'big'))
self.assertEqual(len(lst), math.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 = lexico_next(a)
def test_all_perm(self):
n, k = 17, 5
endian=choice(["little", "big"])
prev = None
cnt = 0
coll = set()
for a in lexico_all(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(lexico_next(prev), a)
self.assertTrue(ba2int(prev) < ba2int(a))
prev = a
cnt += 1
self.assertEqual(cnt, math.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_order(self):
n, k = 10, 5
for a, b in pairwise(lexico_all(n, k, 'little')):
self.assertTrue(ba2int(b) > ba2int(a))
self.assertEqual(lexico_next(a), b)
if __name__ == '__main__':
unittest.main()
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