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The collections package provides the collectionsdefaultdict dictionary and the collectionsnamedtuple collection data types that we have previously discussed In addition, this package provides the collectionsUserList and collectionsUserDict types, although subclassing the built-in list and dict types is probably more common than using these types Another type is collectionsdeque, which is similar to a list, but whereas a list is very fast for adding and removing items at the end, a collectionsdeque is very fast for adding and removing items both at the beginning and at the end Python 31 introduced the collectionsOrderedDict and the collectionsCounter classes OrderedDicts have the same API as normal dicts, although when iterated the items are always returned in insertion order (ie, from rst to last inserted), and the popitem() method always returns the most recently added (ie, last) item The Counter class is a dict subclass used to provide a fast and easy way of keeping various counts Given an iterable or a mapping (such as a dictionary), a Counter instance can, for example, return a list of the unique elements or a list of the most common elements as (element, count) 2-tuples Python s non-numeric abstract base classes (classes that can be inherited from but that cannot be used directly) are also in the collections package They are discussed in 8 The array module provides the arrayarray sequence type that can store numbers or characters in a very space-ef cient way It has similar behavior to lists except that the type of object it can store is xed when it is created, so unlike lists it cannot store objects of different types The third-party NumPy package mentioned earlier also provides ef cient arrays The weakref module provides functionality for creating weak references these behave like normal object references, except that if the only reference to an object is a weak reference, the object can still be scheduled for garbage collection This prevents objects from being kept in memory simply because we have a reference to them Naturally, we can check whether the object a weak reference refers to still exists, and can access the object if it does.

If F has the form G<, Yk-1, extends U, Yk+1, >, where U is a type expression that involves Tj, then:

The heapq module provides functions for converting a list into a heap and for adding and removing items from the heap while preserving the heap property A heap is a binary tree that respects the heap property, which is that the rst item (at index position 0) is always the smallest item Each of a heap s subtrees is also a heap, so they too respect the heap property Here is how a heap could be created from scratch:

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Once again restricting the analysis to the unary case, we have the constraint A >> F = G< extends U> A must be a supertype of the generic type G However, since A is not a parameterized type, it cannot depend upon U in any way It is a supertype of the type G< extends X> for every X such that extends X is a valid type argument to G No meaningful constraint on U can be derived from A

Persistent Search: A Simple LDAP Change Noti cation Mechanism (draft-ietf-ldapextpsearch-01txt)

Strictly speaking, the heapq module provides a min heap; heaps where the rst item is always the largest are max heaps

If A is an invocation of a generic type declaration H, where H is either G or superclass or superinterface of G, then: If H G , then let S1, , Sn be the formal type parameters of G, and let H<U1, , Ul> be the unique invocation of H that is a supertype of G<S1 , , Sn>, and let V = H< extends U1, , extends Ul>[Sk = U] Then this algorithm is applied recursively to the constraint A >> V

This document de nes two controls that extend the LDAPv3 search operation to provide a simple mechanism by which an LDAP client can receive noti cation of changes

import heapq heap = [] heapqheappush(heap, (5, "rest")) heapqheappush(heap, (2, "work")) heapqheappush(heap, (4, "study"))

We have A = G< extends W> >> F = G< extends U> for some type expression W By the subtyping rules for wildcards it must be the case that W >> U

If we already have a list, we can turn it into a heap with heapqheapify(alist); this will do any necessary reordering in-place The smallest item can be removed from the heap using heapqheappop(heap)

that occur in an LDAP server The mechanism is designed to be very exible, yet easy for clients and servers to implement

Otherwise, if A is of the form G<, Xk-1, extends W, Xk+1, >, this algorithm is applied recursively to the constraint W >>U

for x in heapqmerge([1, 3, 5, 8], [2, 4, 7], [0, 1, 6, 8, 9]): print(x, end=" ") # prints: 0 1 1 2 3 4 5 6 7 8 8 9

If F has the form G< , Yk-1, super U, Yk+1, >, where U is a type expression that involves Tj, then A is either: If A is an instance of a non-generic type, then no constraint is implied on Tj

Other Extensions Families of Entries (draft-ietf-ldapext-families-00txt)

The heapqmerge() function takes any number of sorted iterables as arguments and returns an iterator that iterates over all the items from all the iterables in order

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