def _lfc(content, equality=False):
"""
EXAMPLES::
sage: from sage.combinat.necklace import _lfc
sage: list(_lfc([3,3])) #necklaces
[[0, 1, 0, 1, 0, 1],
[0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 1, 1],
[0, 0, 0, 1, 1, 1]]
sage: list(_lfc([3,3], equality=True)) #Lyndon words
[[0, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1]]
"""
content = list(content)
a = [0] * sum(content)
content[0] -= 1
k = len(content)
rng_k = range(k)
rng_k.reverse()
dll = DoublyLinkedList(rng_k)
if not content[0]: # == 0
dll.hide(0)
for z in _list_fixed_content(a, content, 2, 1, k, dll, equality=equality):
yield z
def _ffc(content, equality=False):
"""
EXAMPLES::
sage: from sage.combinat.necklace import _ffc
sage: list(_ffc([3,3])) #necklaces
[[0, 1, 0, 1, 0, 1],
[0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 1, 1],
[0, 0, 0, 1, 1, 1]]
sage: list(_ffc([3,3], equality=True)) #Lyndon words
[[0, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1]]
"""
e = list(content)
a = [len(e) - 1] * sum(e)
r = [0] * sum(e)
a[0] = 0
e[0] -= 1
k = len(e)
rng_k = range(k)
rng_k.reverse()
dll = DoublyLinkedList(rng_k)
if not e[0]: # == 0
dll.hide(0)
for x in _fast_fixed_content(a, e, 2, 1, k, r, 2, dll, equality=equality):
yield x
def _lfc(content, equality=False):
"""
EXAMPLES::
sage: from sage.combinat.necklace import _lfc
sage: list(_lfc([3,3])) #necklaces
[[0, 1, 0, 1, 0, 1],
[0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 1, 1],
[0, 0, 0, 1, 1, 1]]
sage: list(_lfc([3,3], equality=True)) #Lyndon words
[[0, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1]]
"""
content = list(content)
a = [0]*sum(content)
content[0] -= 1
k = len(content)
rng_k = range(k)
rng_k.reverse()
dll = DoublyLinkedList(rng_k)
if content[0] == 0:
dll.hide(0)
for z in _list_fixed_content(a, content, 2, 1, k, dll, equality=equality):
yield z
def _ffc(content, equality=False):
"""
EXAMPLES::
sage: from sage.combinat.necklace import _ffc
sage: list(_ffc([3,3])) #necklaces
[[0, 1, 0, 1, 0, 1],
[0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 1, 1],
[0, 0, 0, 1, 1, 1]]
sage: list(_ffc([3,3], equality=True)) #Lyndon words
[[0, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 1, 1]]
"""
e = list(content)
a = [len(e)-1]*sum(e)
r = [0] * sum(e)
a[0] = 0
e[0] -= 1
k = len(e)
rng_k = range(k)
rng_k.reverse()
dll = DoublyLinkedList(rng_k)
if e[0] == 0:
dll.hide(0)
for x in _fast_fixed_content(a, e, 2, 1, k, r, 2, dll, equality=equality):
yield x
def __iter__(self):
"""
An iterator for all permutations of k things from range(n).
EXAMPLES::
sage: from sage.combinat.permutation_nk import PermutationsNK
sage: [ p for p in PermutationsNK(3,2)]
[[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1]]
sage: len(PermutationsNK(5,4).list())
120
sage: [1, 2, 2, 0] in PermutationsNK(5,4).list()
False
"""
n, k = self._n, self._k
if k == 0:
yield []
return
if k > n:
return
range_n = range(n)
available = range(n)
available = DoublyLinkedList(range_n)
L = range(k)
L[-1] = 'begin'
for i in range(k - 1):
available.hide(i)
finished = False
while not finished:
L[-1] = available.next_value[L[-1]]
if L[-1] != 'end':
yield L[:]
continue
finished = True
for i in reversed(range(k - 1)):
value = L[i]
available.unhide(value)
value = available.next_value[value]
if value != 'end':
L[i] = value
available.hide(value)
value = 'begin'
for i in range(i + 1, k - 1):
L[i] = value = available.next_value[value]
available.hide(value)
L[-1] = available.next_value[value]
yield L[:]
finished = False
break
return
def __iter__(self):
"""
An iterator for all permutations of k things from range(n).
EXAMPLES::
sage: from sage.combinat.permutation_nk import PermutationsNK
sage: [ p for p in PermutationsNK(3,2)]
[[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1]]
sage: len(PermutationsNK(5,4).list())
120
sage: [1, 2, 2, 0] in PermutationsNK(5,4).list()
False
"""
n, k = self._n, self._k
if k == 0:
yield []
return
if k>n:
return
range_n = range(n)
available = range(n)
available = DoublyLinkedList(range_n)
L = range(k)
L[-1] = 'begin'
for i in range(k-1):
available.hide(i)
finished = False
while not finished:
L[-1] = available.next_value[L[-1]]
if L[-1] != 'end':
yield L[:]
continue
finished = True
for i in reversed(range(k-1)):
value = L[i]
available.unhide(value)
value = available.next_value[value]
if value != 'end':
L[i] = value
available.hide(value)
value = 'begin'
for i in range(i+1, k-1):
L[i] = value = available.next_value[value]
available.hide(value)
L[-1] = available.next_value[value]
yield L[:]
finished = False
break
return
