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CHAPTER 10 ■ BATTERIES INCLUDED 223
There are various in-place operations as well, with corresponding methods, as well as the
basic methods add and remove. For more information, see the Python Library Reference, in the
section about set types (http://python.org/doc/lib/types-set.html).
■Tip If you need a function for finding, say, the union of two sets, you can simply use the unbound version
of the union method, from the set type. This could be useful, for example, in concert with reduce:
>>> mySets = []
>>> for i in range(10):
... mySets.append(set(range(i,i+5)))
...
>>> reduce(set.union, mySets)
set([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13])
Sets are mutable, and may therefore not be used, for example, as keys in dictionaries.
Another problem is that sets themselves may only contain immutable (hashable) values, and
thus may not contain other sets. Because sets of sets often occur in practice, this is something
of a problem . . . Luckily, there is the frozenset type, which represents immutable (and, therefore,
hashable) sets:
>>> a = set()
>>> b = set()
>>> a.add(b)
Traceback (most recent call last):
File "", line 1, in ?
TypeError: set objects are unhashable
>>> a.add(frozenset(b))
The frozenset constructor creates a copy of the given set, and is useful whenever you want
to use a set either as a member of another set or as the key to a dictionary.
Heaps
Another well-known data structure is the heap, a kind of priority queue. A priority queue lets
you add objects in an arbitrary order and at any time (possibly in-between the adding) find
(and possibly remove) the smallest element. It does so much more efficiently than, say, using
min on a list.
In fact, there is no separate heap type in Python—only a module with some heapmanipulating
functions. The module is called heapq (with the q standing for queue), and it
contains six functions, the first four of which are directly related to heap manipulation. You
must use a list as the heap object itself.
The heappush function is used to add an item to a heap. Note that you shouldn’t use it on
any old list—only one that has been built through the use of the various heap functions. The
reason for this is that the order of the elements is important (even though it may look a bit
haphazard; the elements aren’t exactly sorted).