def greedyCliquesSemiExhaustive(this, weight=None, progressStack=False):
untouched = set(xrange(this.size))
weights = None
maxormin = max
if isinstance(weight, (int, float)):
if weight < 0:
maxormin = min
elif weight is not None:
weights = [weight(v) for v in this.sections]
wMax = -common.Infinity
QMax = set()
if progressStack is not None:
progressStack.push(title="Iterating remaining initial conditions for clique searching", maximum=this.size)
while len(untouched) != 0:
v0 = this.pickMaxWeightNode(untouched, weights=weights, maxormin=maxormin)
curGC = this.greedyCliques(v0, weight=weight, progressStack=None)
if curGC[1] > wMax:
(QMax, wMax) = curGC
untouched.difference_update(curGC[0])
if progressStack is not None:
if not progressStack.update(this.size - len(untouched), message="Evaluating initial conditions: %d candidates left (current score: %g)..." % (len(untouched), wMax)):
break
if progressStack is not None:
progressStack.pop()
return (QMax, wMax)
def reduceNet(this, progressStack=None):
if len(this.sectionBuffer) != 0:
if not progressStack is None:
progressStack.push(title='Simplying course structure', maximum=len(this.sectionBuffer))
for newsects in this.sectionBuffer:
noEquiv = True
for oldsects in this.sections:
if oldsects == newsects:
h = str(oldsects)
if h in this.otherEquivalentSections:
this.otherEquivalentSections[h].append(newsects)
else:
this.otherEquivalentSections[h] = [newsects]
noEquiv = False
break
if noEquiv:
this.sections.append(newsects)
if not progressStack is None:
progressStack.increase(1, message='Evaluating section %s for network construction...'%str(newsects))
oldsize = this.size
this.size = len(this.sections)
this.adjlist.extend([set() for i in xrange(this.size - oldsize)]) # cannot use * operator because we need N *copies* of set().
if not progressStack is None:
progressStack.pop()
def greedyCliques(this, initNode=None, weight=None, progressStack=None):
maxormin = max
weights = None
if isinstance(weight, (int, float)) and weight < 0:
maxormin = min
elif weight is not None:
weights = [weight(s) for s in this.sections]
rg = common.randomGenerator()
xr = xrange(this.size)
V0 = this.pickMaxWeightNode(xrange(this.size), weights=weights, maxormin=maxormin, rg=rg) if initNode is None else initNode
Q = set((V0,))
rho = set(this.adjlist[V0])
totalweight = 1 if weights is None else weights[V0]
initRhoSize = len(rho)
hasProgress = isinstance(progressStack, IProgressStack)
if hasProgress:
progressStack.push(title="Searching for cliques", maximum=initRhoSize)
while len(rho) != 0: # O(k)*
if hasProgress:
if not progressStack.update(initRhoSize - len(rho), message="Enlarging cliques: %d candidates left (current score: %g)..." % (len(rho), totalweight)):
break
# find all new common neighbors, and
# pick the one with most common neighbors
maxv = None
if weights is None:
vmax = maxormin([(len(rho & this.adjlist[v]), rg, v) for v in rho])[2] # O(k^2)
Q.add(vmax)
rho.intersection_update(this.adjlist[vmax])
totalweight += 1
else:
adjweights = dict((v, sum(weights[u] for u in this.adjlist[v] & rho)) for v in rho)
maxp = max((weights[v], adjweights[v], rg, v) for v in rho)
Q.add(maxp[-1])
rho.intersection_update(this.adjlist[maxp[-1]])
totalweight += weights[maxp[-1]]
if hasProgress:
progressStack.pop()
return (Q, totalweight if maxormin == max else -totalweight) # O(k^3)
def evaluateAllVertices(this, progressStack=None):
if progressStack is not None:
progressStack.push(title='Constructing course network', maximum=this.size)
for v in xrange(this.size):
this.evaluateVertex(v)
if progressStack is not None:
progressStack.increase(1, message='Evaluating vertex #%d for network construction...'%v)
if progressStack is not None:
progressStack.pop()
def __shuffle(self, x, random=None):
"""x, random=random.random -> shuffle list x in place; return None.
Optional arg random is a 0-argument function returning a random
float in [0.0, 1.0); by default, the standard random.random.
taken from python2.7 because 3.5 does something different with
different results
"""
if random is None:
random = self.random
_int = int
for i in reversed(xrange(1, len(x))):
# pick an element in x[:i+1] with which to exchange x[i]
j = _int(random() * (i+1))
x[i], x[j] = x[j], x[i]
def greedyCliquesExhaustive(this, weight=None, progressStack=False):
hasProgress = isinstance(progressStack, IProgressStack)
if hasProgress:
progressStack.push(title="Iterating initial conditions for clique searching", maximum=this.size)
#if not allResults:
QMax = set()
wMax = -common.Infinity
for v in xrange(this.size):
if hasProgress:
if not progressStack.increase(1, message="Evaluating vertex #%d for cliques (current score: %g)"%(v,wMax)):
break
curGC = this.greedyCliques(v, weight=weight, progressStack=None)
if curGC[1] > wMax:
(QMax, wMax) = curGC
if hasProgress:
progressStack.pop()
return (QMax, wMax)
def __sample(self, population, k):
"""Chooses k unique random elements from a population sequence.
Returns a new list containing elements from the population while
leaving the original population unchanged. The resulting list is
in selection order so that all sub-slices will also be valid random
samples. This allows raffle winners (the sample) to be partitioned
into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the
population contains repeats, then each occurrence is a possible
selection in the sample.
To choose a sample in a range of integers, use xrange as an argument.
This is especially fast and space efficient for sampling from a
large population: sample(xrange(10000000), 60)
taken from python2.7 because 3.5 does something different with
different results
"""
# Sampling without replacement entails tracking either potential
# selections (the pool) in a list or previous selections in a set.
# When the number of selections is small compared to the
# population, then tracking selections is efficient, requiring
# only a small set and an occasional reselection. For
# a larger number of selections, the pool tracking method is
# preferred since the list takes less space than the
# set and it doesn't suffer from frequent reselections.
n = len(population)
if not 0 <= k <= n:
raise ValueError("sample larger than population")
random = self.random
_int = int
result = [None] * k
setsize = 21 # size of a small set minus size of an empty list
if k > 5:
setsize += 4 ** _ceil(_log(k * 3, 4)) # table size for big sets
if n <= setsize or hasattr(population, "keys"):
# An n-length list is smaller than a k-length set, or this is a
# mapping type so the other algorithm wouldn't work.
pool = list(population)
for i in xrange(k): # invariant: non-selected at [0,n-i)
j = _int(random() * (n-i))
result[i] = pool[j]
pool[j] = pool[n-i-1] # move non-selected item into vacancy
else:
try:
selected = set()
selected_add = selected.add
for i in xrange(k):
j = _int(random() * n)
while j in selected:
j = _int(random() * n)
selected_add(j)
result[i] = population[j]
except (TypeError, KeyError): # handle (at least) sets
if isinstance(population, list):
raise
return self.sample(tuple(population), k)
return result
def evaluateVertex(this, v):
for i in xrange(v+1, this.size):
if this.sections[i].course != this.sections[v].course and not this.sections[i].intersect(this.sections[v]):
this.adjlist[i].add(v)
this.adjlist[v].add(i)
def exactCliques(this, weight=None, progressStack=False):
hasProgress = isinstance(progressStack, IProgressStack)
if hasProgress:
progressStack.push(title="Search for cliques exactly", maximum=this.size, unitstep=1)
QMax = []
wMax = -common.Infinity
QsPrev = dict( ((v,), 1) for v in xrange(this.size) )
weights = None
searchformax = True
if isinstance(weight, (int, float)):
if weight < 0:
searchformax = False
elif weight is not None:
weights = [weight(v) for v in this.sections]
QsPrev = dict( ((v,), w) for (v, w) in enumerate(weights) )
for QSize in xrange(this.size):
if hasProgress:
progressStack.push(message="Current clique size: %d (current score: %g)"%(QSize, wMax), maximum=len(QsPrev))
QsNext = dict()
# find all total neighbors and append to list.
for (Q, W) in QsPrev.items():
if hasProgress:
if not progressStack.increase(1, message="Current clique size %d (current score: %g)"%(QSize, wMax)):
progressStack.pop()
progressStack.pop()
return (QMax, wMax)
neis = [this.adjlist[v] for v in Q]
totalNeis = set(neis[0])
for nei in neis[1:]:
totalNeis.intersection_update(nei)
if len(totalNeis) == 0:
if not searchformax:
if hasProgress:
progressStack.pop()
progressStack.pop()
return (set(Q), -W)
else:
if W > wMax:
(QMax, wMax) = (set(Q), W)
for n in totalNeis:
Q2 = common.appendSorted(Q, n)
W2 = W
if weights is not None:
W2 += weights[n]
else:
W2 += 1
QsNext[Q2] = W2
QsPrev = QsNext
if hasProgress:
progressStack.pop()
if len(QsPrev) == 0:
break
if hasProgress:
progressStack.pop()
return (QMax, wMax)
def vertexWithMaxDegree(this):
this.evaluateAllVertices()
return max(xrange(this.size), key=lambda v:len(this.adjlist[v]))
def verticesWithDegree(this, k):
this.evaluateAllVertices()
return [v for v in xrange(this.size) if len(this.adjlist[v]) == k]
