def unrank(self, r):
"""
Return the subset of ``s`` that has rank ``k``.
EXAMPLES::
sage: Subsets(3).unrank(0)
{}
sage: Subsets([2,4,5]).unrank(1)
{2}
sage: Subsets([1,2,3]).unrank(257)
Traceback (most recent call last):
...
IndexError: index out of range
"""
r = Integer(r)
if r >= self.cardinality() or r < 0:
raise IndexError("index out of range")
else:
k = ZZ_0
n = self._s.cardinality()
bin = Integer(1)
while r >= bin:
r -= bin
k += 1
bin = binomial(n, k)
return self.element_class(
[self._s.unrank(i) for i in combination.from_rank(r, n, k)])
def unrank(self, r):
"""
Return the subset of ``s`` that has rank ``k``.
EXAMPLES::
sage: Subsets(3).unrank(0)
{}
sage: Subsets([2,4,5]).unrank(1)
{2}
sage: Subsets([1,2,3]).unrank(257)
Traceback (most recent call last):
...
IndexError: index out of range
"""
r = Integer(r)
if r >= self.cardinality() or r < 0:
raise IndexError("index out of range")
else:
k = ZZ_0
n = self._s.cardinality()
bin = Integer(1)
while r >= bin:
r -= bin
k += 1
bin = binomial(n,k)
return self.element_class([self._s.unrank(i) for i in combination.from_rank(r, n, k)])
def unrank(self, r):
"""
Return the subset of ``s`` of size ``k`` that has rank ``r``.
EXAMPLES::
sage: Subsets(3,2).unrank(0)
{1, 2}
sage: Subsets([2,4,5],2).unrank(0)
{2, 4}
sage: Subsets([1,2,8],3).unrank(42)
Traceback (most recent call last):
...
IndexError: index out of range
"""
lset = self._ls
n = len(lset)
if self._k > n or r >= self.cardinality() or r < 0:
raise IndexError("index out of range")
else:
return self.element_class([lset[i] for i in combination.from_rank(r, n, self._k)])
def unrank(self, r):
"""
Return the subset of ``s`` of size ``k`` that has rank ``r``.
EXAMPLES::
sage: Subsets(3,2).unrank(0)
{1, 2}
sage: Subsets([2,4,5],2).unrank(0)
{2, 4}
sage: Subsets([1,2,8],3).unrank(42)
Traceback (most recent call last):
...
IndexError: index out of range
"""
lset = self._ls
n = len(lset)
if self._k > n or r >= self.cardinality() or r < 0:
raise IndexError("index out of range")
else:
return self.element_class(
[lset[i] for i in combination.from_rank(r, n, self._k)])
def unrank(self, r):
"""
Return the subset which has rank ``r``.
EXAMPLES::
sage: from sage.combinat.subset import SubsetsSorted
sage: S = SubsetsSorted(range(3))
sage: S.unrank(4)
(0, 1)
"""
r = Integer(r)
if r >= self.cardinality() or r < 0:
raise IndexError("index out of range")
k = ZZ_0
n = self._s.cardinality()
binom = ZZ.one()
while r >= binom:
r -= binom
k += 1
binom = binomial(n, k)
C = combination.from_rank(r, n, k)
return self.element_class(sorted([self._s.unrank(i) for i in C]))
def unrank(self, r):
"""
Return the subset which has rank ``r``.
EXAMPLES::
sage: from sage.combinat.subset import SubsetsSorted
sage: S = SubsetsSorted(range(3))
sage: S.unrank(4)
(0, 1)
"""
r = Integer(r)
if r >= self.cardinality() or r < 0:
raise IndexError("index out of range")
k = ZZ_0
n = self._s.cardinality()
binom = ZZ.one()
while r >= binom:
r -= binom
k += 1
binom = binomial(n,k)
C = combination.from_rank(r, n, k)
return self.element_class(sorted([self._s.unrank(i) for i in C]))
