Source code for pqdict

"""Copyright (c) 2012 Nezar Abdennur

Permission is hereby granted, free of charge, to any person obtaining a copy of
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the Software without restriction, including without limitation the rights to
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The above copyright notice and this permission notice shall be included in all
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"""

"""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