"""Copyright (c) 2012 Nezar Abdennur
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
"""
"""Priority Queue Dictionary -- An indexed priority queue data structure.
Inspired by the Python implementation of the heapq module, which was written by
Kevin O'Connor and augmented by Tim Peters and Raymond Hettinger.
A dict-like heap queue to prioritize hashable objects while providing random
access and mutable priorities.
The priority queue is implemented as a binary heap, which supports:
- O(1) access to the top priority element
- O(log n) removal of the top priority element
- O(log n) insertion of a new element
In addition, an internal dictionary or "index" maps elements to their position
in the heap array. This index is kept up-to-date when the heap is manipulated.
As a result, PQD also supports:
- O(1) lookup of an arbitrary element's priority key
- O(log n) removal of an arbitrary element
- O(log n) updating of an arbitrary element's priority key
The standard heap operations used internally are based on those in the python
heapq module (here, called "sink" and "swim").* These operations are extended to
maintain the internal dictionary.
* The names of the methods in heapq (sift up/down) refer to the motion of the
items being compared to, rather than the item being operated on as is usually
done in textbooks (i.e. bubble down/up, instead). I stuck to the textbook
convention, but using the sink/swim nomenclature from Sedgewick et al: the way
I like to think of it, an item that is too "heavy" (low-priority) should sink
down the tree, while one that is too "light" should float or swim up.
Implementation details:
heap (list): stores (dkey, pkey) pairs as "entry" objects that implement
__lt__ which defines how their priority keys are compared
position (dict): maps each dkey to the index of its entry in the heap
"""
__version__ = (0, 4, 0)
__author__ = ('Nezar Abdennur', 'nabdennur@gmail.com')
__all__ = ['PQDict', 'sort_by_value', 'nlargest', 'nsmallest', 'consume']
import sys
from collections import Mapping, MutableMapping
if sys.version_info[0] < 3:
range = xrange
class _AbstractEntry(object):
"""
The internal heap items of a PQDict.
The heap algorithms use the "<" comparator to compare entries, so
subclasses must implement __lt__.
"""
__slots__ = ('dkey', 'pkey')
def __init__(self, dkey, pkey):
self.dkey = dkey
self.pkey = pkey
def __lt__(self, other):
raise NotImplementedError
def __repr__(self):
return self.__class__.__name__ + \
"(%s: %s)" % (repr(self.dkey), self.pkey)
class _MinEntry(_AbstractEntry):
"""
Entries for a PQDict backed by a min-heap.
"""
__slots__ = ()
__init__ = _AbstractEntry.__init__
def __eq__(self, other):
return self.pkey == other.pkey
def __lt__(self, other):
return self.pkey < other.pkey
class _MaxEntry(_AbstractEntry):
"""
Entries for a PQDict backed by a max-heap.
"""
__slots__ = ()
__init__ = _AbstractEntry.__init__
def __eq__(self, other):
return self.pkey == other.pkey
def __lt__(self, other):
return self.pkey > other.pkey
def new_entry_class(comparator):
"""
Define entries for a PQDict that uses a custom comparator to sort entries.
The comparator should have the form:
cmp( self, other ) --> bool
where self and other are entry instances (have dkey and pkey attributes).
The function should return True if self has higher priority than other and
False otherwise.
"""
class _CustomEntry(_AbstractEntry):
__lt__ = comparator
return _CustomEntry
[docs]class PQDict(MutableMapping):
"""
A mapping object that maps dictionary keys (dkeys) to priority keys (pkeys).
PQDicts maintain an internal heap so that the highest priority item can
always be obtained in constant time. The mapping is mutable so items may be
added, removed and have their priorities updated without breaking the heap.
"""
_entry_class = _MinEntry
__eq__ = MutableMapping.__eq__
__ne__ = MutableMapping.__ne__
keys = MutableMapping.keys
values = prioritykeys = MutableMapping.values
items = MutableMapping.items
get = MutableMapping.get
clear = MutableMapping.clear
update = MutableMapping.update
setdefault = MutableMapping.setdefault
def __init__(self, *args, **kwargs):
"""
Same input signature as dict:
Accepts at most one positional argument:
- a sequence/iterator of (dkey, pkey) pairs
- a mapping object
Accepts keyword arguments
The default priority ordering for entries is in decreasing pkey value
(i.e., a min-pq: SMALLER pkey values have a HIGHER rank).
"""
if len(args) > 1:
raise TypeError('Too many arguments')
self._heap = []
self._position = {}
pos = 0
if args:
if isinstance(args[0], Mapping):
seq = args[0].items()
else:
seq = args[0]
for dkey, pkey in seq:
entry = self._entry_class(dkey, pkey)
self._heap.append(entry)
self._position[dkey] = pos
pos += 1
if kwargs:
for dkey, pkey in kwargs.items():
entry = self._entry_class(dkey, pkey)
self._heap.append(entry)
self._position[dkey] = pos
pos += 1
self._heapify()
@classmethod
[docs] def minpq(cls, *args, **kwargs):
"""
Create a new Min-PQDict. Smaller priority keys give higher rank.
"""
pq = cls()
pq._entry_class = _MinEntry
pq.__init__(*args, **kwargs)
return pq
@classmethod
[docs] def maxpq(cls, *args, **kwargs):
"""
Create a new Max-PQDict. Larger priority keys give higher rank.
"""
pq = cls()
pq._entry_class = _MaxEntry
pq.__init__(*args, **kwargs)
return pq
@classmethod
[docs] def fromkeys(cls, iterable, value=None, sort_by=None, maxpq=False):
"""
Create a new PQDict with dictionary keys from an iterable and priority
keys set to value (default value is infinite to start items off at the
bottom of the queue). If a function sort_by is provided, that function
is used to compute priority keys for each item in the iterable.
"""
if value is None:
value = float('-inf') if maxpq else float('inf')
if maxpq:
cls = cls.maxpq
if sort_by is None:
return cls( (dkey, value) for dkey in iterable )
else:
return cls( (dkey, sort_by(dkey)) for dkey in iterable )
@classmethod
[docs] def create(cls, cmp):
"""
Create an empty PQDict that uses a custom comparator. The comparator
should have the form:
cmp( self, other ) --> bool
where self and other are entry instances (have dkey and pkey members).
The function should return True if self has higher priority than other
and False otherwise.
If cmp is a PQDict instance instead of a function, then a PQDict using
the same comparator is returned.
"""
pq = cls()
if isinstance(cmp, PQDict):
pq._entry_class = cmp._entry_class
else:
pq._entry_class = new_entry_class(cmp)
pq.__init__(*args, **kwargs)
return pq
def pq_type(self):
if self._entry_class == _MinEntry:
return 'min'
elif self._entry_class == _MaxEntry:
return 'max'
else:
return 'custom'
def __len__(self):
"""
Return number of items in the PQD.
"""
return len(self._heap)
def __contains__(self, dkey):
"""
Return True if dkey is in the PQD else return False.
"""
return dkey in self._position
def __iter__(self):
"""
Return an iterator over the dictionary keys of the PQD. The order
of iteration is arbitrary! Use iterkeys() to iterate over dictionary
keys in order of priority.
"""
for entry in self._heap:
yield entry.dkey
def __getitem__(self, dkey):
"""
Return the priority of dkey. Raises a KeyError if not in the PQD.
"""
return self._heap[self._position[dkey]].pkey #raises KeyError
def __setitem__(self, dkey, pkey):
"""
Assign priority to dictionary key.
"""
heap = self._heap
position = self._position
try:
pos = position[dkey]
except KeyError:
# add new entry:
# put the new entry at the end and let it bubble up
n = len(self._heap)
self._heap.append(self._entry_class(dkey, pkey))
self._position[dkey] = n
self._swim(n)
else:
# update existing entry:
# bubble up or down depending on pkeys of parent and children
heap[pos].pkey = pkey
parent_pos = (pos - 1) >> 1
child_pos = 2*pos + 1
if parent_pos > -1 and heap[pos] < heap[parent_pos]:
self._swim(pos)
elif child_pos < len(heap):
other_pos = child_pos + 1
if (other_pos < len(heap)
and not heap[child_pos] < heap[other_pos]):
child_pos = other_pos
if heap[child_pos] < heap[pos]:
self._sink(pos)
def __delitem__(self, dkey):
"""
Remove item. Raises a KeyError if dkey is not in the PQD.
"""
heap = self._heap
position = self._position
pos = position.pop(dkey) #raises appropriate KeyError
# Take the very last entry and place it in the vacated spot. Let it
# sink or swim until it reaches its new resting place.
entry_to_delete = heap[pos]
end = heap.pop(-1)
if end is not entry_to_delete:
heap[pos] = end
position[end.dkey] = pos
parent_pos = (pos - 1) >> 1
child_pos = 2*pos + 1
if parent_pos > -1 and heap[pos] < heap[parent_pos]:
self._swim(pos)
elif child_pos < len(heap):
other_pos = child_pos + 1
if (other_pos < len(heap) and
not heap[child_pos] < heap[other_pos]):
child_pos = other_pos
if heap[child_pos] < heap[pos]:
self._sink(pos)
del entry_to_delete
def __copy__(self):
"""
Return a new PQD with the same dkeys associated with the same priority
key values.
"""
from copy import copy
other = self.__class__()
# Entry objects are mutable and should not be shared by different PQDs.
other._heap = [copy(entry) for entry in self._heap]
# It's safe to just copy the _position dict (dkeys->int)
other._position = copy(self._position)
return other
copy = __copy__
def __repr__(self):
things = ', '.join(['%s: %s' % (repr(entry.dkey), entry.pkey)
for entry in self._heap])
return self.__class__.__name__ + '({' + things + '})'
__marker = object()
[docs] def pop(self, dkey=__marker, default=__marker):
"""
If dkey is in the PQD, remove it and return its priority key, else
return default. If default is not provided and dkey is not in the PQD,
raise a KeyError.
If dkey is not provided, remove and return the top-priority dictionary
key or raise KeyError if the PQD is empty.
"""
heap = self._heap
position = self._position
if dkey is self.__marker:
if not heap:
raise KeyError('PQDict is empty')
dkey = heap[0].dkey
del self[dkey]
return dkey
try:
pos = position.pop(dkey) #raises appropriate KeyError
except KeyError:
if default is self.__marker:
raise
return default
else:
entry_to_delete = heap[pos]
pkey = entry_to_delete.pkey
end = heap.pop(-1)
if end is not entry_to_delete:
heap[pos] = end
position[end.dkey] = pos
parent_pos = (pos - 1) >> 1
child_pos = 2*pos + 1
if parent_pos > -1 and heap[pos] < heap[parent_pos]:
self._swim(pos)
elif child_pos < len(heap):
other_pos = child_pos + 1
if (other_pos < len(heap)
and not heap[child_pos] < heap[other_pos]):
child_pos = other_pos
if heap[child_pos] < heap[pos]:
self._sink(pos)
del entry_to_delete
return pkey
[docs] def top(self):
"""
Get the top priority item. Raises KeyError if PQD is empty.
"""
try:
entry = self._heap[0]
except IndexError:
raise KeyError('PQDict is empty')
return entry.dkey
[docs] def popitem(self):
"""
Extract top priority item and priority. Raises KeyError if PQD is empty.
"""
heap = self._heap
position = self._position
try:
end = heap.pop(-1)
except IndexError:
raise KeyError('PQDict is empty')
if heap:
entry = heap[0]
heap[0] = end
position[end.dkey] = 0
self._sink(0)
else:
entry = end
del position[entry.dkey]
return entry.dkey, entry.pkey
[docs] def topitem(self):
"""
Get top priority item and priority. Raises KeyError if PQD is empty.
"""
try:
entry = self._heap[0]
except IndexError:
raise KeyError('PQDict is empty')
return entry.dkey, entry.pkey
[docs] def additem(self, dkey, pkey):
"""
Add a new item. Raises KeyError if item is already in the PQD.
"""
if dkey in self._position:
raise KeyError('%s is already in the queue' % repr(dkey))
self[dkey] = pkey
[docs] def pushpopitem(self, dkey, pkey):
"""
Equivalent to inserting a new item followed by removing the top priority
item, but faster. Raises KeyError if the new item is already in the PQD.
"""
heap = self._heap
position = self._position
entry = self._entry_class(dkey, pkey)
if dkey in self:
raise KeyError('%s is already in the queue' % repr(dkey))
if heap and heap[0] < entry:
entry, heap[0] = heap[0], entry
position[dkey] = 0
del position[entry.dkey]
self._sink(0)
return entry.dkey, entry.pkey
[docs] def updateitem(self, dkey, new_pkey):
"""
Update the priority key of an existing item. Raises KeyError if item is
not in the PQD.
"""
if dkey not in self._position:
raise KeyError(dkey)
self[dkey] = new_pkey
[docs] def replace_key(self, dkey, new_dkey):
"""
Replace the dictionary key of an existing heap entry in place. Raises
KeyError if the item to replace does not exist or if the new item is
already in the PQD.
"""
heap = self._heap
position = self._position
if new_dkey in self:
raise KeyError('%s is already in the queue' % repr(new_dkey))
pos = position.pop(dkey) #raises appropriate KeyError
position[new_dkey] = pos
heap[pos].dkey = new_dkey
[docs] def swap_priority(self, dkey1, dkey2):
"""
Fast way to swap the priorities of two items in the PQD. Raises KeyError
if either item does not exist.
"""
heap = self._heap
position = self._position
if dkey1 not in self or dkey2 not in self:
raise KeyError
pos1, pos2 = position[dkey1], position[dkey2]
heap[pos1].dkey, heap[pos2].dkey = dkey2, dkey1
position[dkey1], position[dkey2] = pos2, pos1
[docs] def iterkeys(self):
"""
Destructive heapsort iterator over dictionary keys, ordered by priority
key.
"""
try:
while True:
yield self.popitem()[0]
except KeyError:
return
[docs] def itervalues(self):
"""
Destructive heapsort iterator over priority keys.
"""
try:
while True:
yield self.popitem()[1]
except KeyError:
return
iterprioritykeys = itervalues
[docs] def iteritems(self):
"""
Destructive heapsort iterator over items, ordered by priority key.
"""
try:
while True:
yield self.popitem()
except KeyError:
return
def _heapify(self):
n = len(self._heap)
for pos in reversed(range(n//2)):
self._sink(pos)
def _sink(self, top=0):
# "Sink-to-the-bottom-then-swim" algorithm (Floyd, 1964)
# Tends to reduce the number of comparisons when inserting "heavy" items
# at the top, e.g. during a heap pop. See heapq for more details.
heap = self._heap
position = self._position
endpos = len(heap)
# Grab the top entry
pos = top
entry = heap[pos]
# Sift up a chain of child nodes
child_pos = 2*pos + 1
while child_pos < endpos:
# Choose the smaller child.
other_pos = child_pos + 1
if other_pos < endpos and not heap[child_pos] < heap[other_pos]:
child_pos = other_pos
child_entry = heap[child_pos]
# Move it up one level.
heap[pos] = child_entry
position[child_entry.dkey] = pos
# Next level
pos = child_pos
child_pos = 2*pos + 1
# We are left with a "vacant" leaf. Put our entry there and let it swim
# until it reaches its new resting place.
heap[pos] = entry
position[entry.dkey] = pos
self._swim(pos, top)
def _swim(self, pos, top=0):
heap = self._heap
position = self._position
# Grab the entry from its place
entry = heap[pos]
# Sift parents down until we find a place where the entry fits.
while pos > top:
parent_pos = (pos - 1) >> 1
parent_entry = heap[parent_pos]
if entry < parent_entry:
heap[pos] = parent_entry
position[parent_entry.dkey] = pos
pos = parent_pos
continue
break
# Put entry in its new place
heap[pos] = entry
position[entry.dkey] = pos
[docs]def sort_by_value(mapping, reverse=False):
"""
Takes a mapping and, treating the values as priority keys, sorts its items
by value via heapsort using a PQDict.
Equivalent to: sorted(mapping.items(), key=itemgetter(1), reverse=reverse)
Returns:
a list of the dictionary items sorted by value
"""
if reverse:
pq = PQDict.maxpq(mapping)
else:
pq = PQDict(mapping)
return list(pq.iteritems)
[docs]def nlargest(n, mapping):
"""
Takes a mapping and returns the n keys with the largest values.
Returns:
a list of n dictionary keys
"""
try:
it = mapping.iteritems()
except AttributeError:
it = mapping.items()
pq = PQDict.minpq()
try:
for i in range(n):
pq.additem(*next(it))
except StopIteration:
pass
try:
while it:
pq.pushpopitem(*next(it))
except StopIteration:
pass
out = list(pq.iterkeys())
out.reverse()
return out
[docs]def nsmallest(n, mapping):
"""
Takes a mapping and returns the n keys with the smallest values.
Returns:
a list of n dictionary keys
"""
try:
it = mapping.iteritems()
except AttributeError:
it = mapping.items()
pq = PQDict.maxpq()
try:
for i in range(n):
pq.additem(*next(it))
except StopIteration:
pass
try:
while it:
pq.pushpopitem(*next(it))
except StopIteration:
pass
out = list(pq.iterkeys())
out.reverse()
return out
[docs]def consume(*pq_dicts):
"""
Combine multiple priority queue dictionaries into a single prioritized
output stream. Assumes all the priority queues use the same comparator and
all priority keys are comparable.
Returns:
a generator that yields (dkey, pkey) pairs from all the PQDs
"""
iterators = []
for pq in pq_dicts:
iterators.append(pq.iteritems())
collector = PQDict.create(pq)
for i, it in enumerate(iterators):
try:
collector[i] = next(it)
except StopIteration:
pass
while collector:
i, item = collector.popitem()
yield item
try:
collector[i] = next(iterators[i])
except StopIteration:
pass
return