/
partitions.py
174 lines (154 loc) · 6.11 KB
/
partitions.py
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"""
Partition utilities -
taken from `Stack Overflow <https://stackoverflow.com/questions/19368375/set-partitions-in-python>`_
"""
from itertools import permutations
from typing import List, Iterator, Tuple, Set
from pyshex.shapemap_structure_and_language.p1_notation_and_terminology import RDFGraph
def algorithm_u(ns, m):
"""
taken from `Stack Overflow <https://codereview.stackexchange.com/questions/1526/finding-all-k-subset-partitions>`_
"""
def visit(nv, av):
ps = [[] for _ in range(m)]
for jv in range(nv):
ps[av[jv + 1]].append(ns[jv])
return ps
def f(mu, nu, sigma, n, a):
if mu == 2:
yield visit(n, a)
else:
for v in f(mu - 1, nu - 1, (mu + sigma) % 2, n, a):
yield v
if nu == mu + 1:
a[mu] = mu - 1
yield visit(n, a)
while a[nu] > 0:
a[nu] = a[nu] - 1
yield visit(n, a)
elif nu > mu + 1:
if (mu + sigma) % 2 == 1:
a[nu - 1] = mu - 1
else:
a[mu] = mu - 1
if (a[nu] + sigma) % 2 == 1:
for v in b(mu, nu - 1, 0, n, a):
yield v
else:
for v in f(mu, nu - 1, 0, n, a):
yield v
while a[nu] > 0:
a[nu] = a[nu] - 1
if (a[nu] + sigma) % 2 == 1:
for v in b(mu, nu - 1, 0, n, a):
yield v
else:
for v in f(mu, nu - 1, 0, n, a):
yield v
def b(mu, nu, sigma, n, a):
if nu == mu + 1:
while a[nu] < mu - 1:
yield visit(n, a)
a[nu] = a[nu] + 1
yield visit(n, a)
a[mu] = 0
elif nu > mu + 1:
if (a[nu] + sigma) % 2 == 1:
for v in f(mu, nu - 1, 0, n, a):
yield v
else:
for v in b(mu, nu - 1, 0, n, a):
yield v
while a[nu] < mu - 1:
a[nu] = a[nu] + 1
if (a[nu] + sigma) % 2 == 1:
for v in f(mu, nu - 1, 0, n, a):
yield v
else:
for v in b(mu, nu - 1, 0, n, a):
yield v
if (mu + sigma) % 2 == 1:
a[nu - 1] = 0
else:
a[mu] = 0
if mu == 2:
yield visit(n, a)
else:
for v in b(mu - 1, nu - 1, (mu + sigma) % 2, n, a):
yield v
ng = len(ns)
ag = [0] * (ng + 1)
for j in range(1, m + 1):
ag[ng - m + j] = j - 1
return f(m, ng, 0, ng, ag) if m > 1 else [[ns]]
def integer_partition(size: int, nparts: int) -> Iterator[List[List[int]]]:
""" Partition a list of integers into a list of partitions """
for part in algorithm_u(range(size), nparts):
yield part
def filtered_integer_partition(nelements: int, nparts: int) -> Iterator[Tuple[Tuple[int]]]:
seen: Set[Tuple[Tuple[int, ...], ...]] = set()
# Start with the entire set
if nelements == 0:
yield tuple(tuple() for _ in range(nparts))
else:
for npart in range(min(nelements, nparts), 0, -1):
if npart == 1:
t1 = tuple(range(nelements))
t2 = [() for _ in range(nparts - 1)]
total = tuple([t1] + t2)
for permutation in permutations(total):
pt = tuple(permutation)
if pt not in seen:
seen.add(pt)
yield pt
else:
for int_partition in integer_partition(nelements, npart):
t1 = [tuple(e) for e in int_partition]
t2 = [() for _ in range(nparts - npart)]
total = tuple(t1 + t2)
for permutation in permutations(total):
for permutation in permutations(total):
pt = tuple(permutation)
if pt not in seen:
seen.add(pt)
yield pt
# def strip_empty_members(partition: List[List[int]]) -> Tuple[Tuple[int, ...], ...]:
# return tuple(tuple([p for p in part if p < nelements]) for part in partition)
#
# if nelements == 0:
# yield tuple(tuple() for _ in range(nparts))
# else:
# for int_partition in integer_partition(nelements + nparts - 1, nparts):
# for permutation in permutations(int_partition):
# stripped_perm = strip_empty_members(permutation)
# if stripped_perm not in seen:
# seen.add(stripped_perm)
# yield stripped_perm
def partition_t(T: RDFGraph, nparts: int) -> Iterator[Tuple[RDFGraph, ...]]:
"""
Partition T into all possible partitions of T of size nparts
:param T: Set of RDF triples to be partitioned
:param nparts: number of partitions (e.g. 2 means return all possible 2 set partitions
:return: Iterator that returns partitions
We don't actually partition the triples directly -- instead, we partition a set of integers that
reference elements in the (ordered) set and return those
"""
def partition_map(partition: List[List[int]]) -> Tuple[RDFGraph, ...]:
rval: List[RDFGraph, ...] = []
for part in partition:
if len(part) == 1 and part[0] >= t_list_len:
rval.append(RDFGraph())
else:
rval.append(RDFGraph([t_list[e] for e in part if e < t_list_len]))
return tuple(rval)
t_list = sorted(list(T)) # Sorted not strictly necessary, but aids testing
t_list_len = len(t_list)
return map(lambda partition: partition_map(partition), filtered_integer_partition(t_list_len, nparts))
def partition_2(T: RDFGraph) -> List[Tuple[RDFGraph, RDFGraph]]:
"""
Partition T into all possible combinations of two subsets
:param T: RDF Graph to partition
:return:
"""
for p in partition_t(T, 2):
yield p