5. Data Structures
This chapter describes some things you've learned about already in more detail, and
adds some new things as well.
5.1 More on Lists
The list data type has some more methods. Here are all of the methods of list objects:
-
- Add an item to the end of the list; equivalent to
a[len(a):] = [x].
-
- Extend the list by appending all the items in the given list; equivalent to
a[len(a):]
= L.
-
- Insert an item at a given position. The first argument is the index of the element
before which to insert, so
a.insert(0, x) inserts at the front
of the list, and a.insert(len(a), x) is equivalent to a.append(x).
-
- Remove the first item from the list whose value is x. It is an error if
there is no such item.
-
- Remove the item at the given position in the list, and return it. If no index is
specified,
a.pop() returns the last item in the list. The item is also
removed from the list. (The square brackets around the i in the method
signature denote that the parameter is optional, not that you should type square
brackets at that position. You will see this notation frequently in the Python
Library Reference.)
-
- Return the index in the list of the first item whose value is x. It is an
error if there is no such item.
- Return the number of times x appears in the list.
-
- Sort the items of the list, in place.
-
- Reverse the elements of the list, in place.
An example that uses most of the list methods:
>>> a = [66.6, 333, 333, 1, 1234.5]
>>> print a.count(333), a.count(66.6), a.count('x')
2 1 0
>>> a.insert(2, -1)
>>> a.append(333)
>>> a
[66.6, 333, -1, 333, 1, 1234.5, 333]
>>> a.index(333)
1
>>> a.remove(333)
>>> a
[66.6, -1, 333, 1, 1234.5, 333]
>>> a.reverse()
>>> a
[333, 1234.5, 1, 333, -1, 66.6]
>>> a.sort()
>>> a
[-1, 1, 66.6, 333, 333, 1234.5]
5.1.1 Using Lists as Stacks
The list methods make it very easy to use a list as a stack, where the last element
added is the first element retrieved (``last-in, first-out''). To add an item to the top
of the stack, use append(). To retrieve an item from the top of
the stack, use pop() without an explicit index. For example:
>>> stack = [3, 4, 5]
>>> stack.append(6)
>>> stack.append(7)
>>> stack
[3, 4, 5, 6, 7]
>>> stack.pop()
7
>>> stack
[3, 4, 5, 6]
>>> stack.pop()
6
>>> stack.pop()
5
>>> stack
[3, 4]
5.1.2 Using Lists as Queues
You can also use a list conveniently as a queue, where the first element added is the
first element retrieved (``first-in, first-out''). To add an item to the back of the
queue, use append(). To retrieve an item from the front of the
queue, use pop() with 0 as the index. For example:
>>> queue = ["Eric", "John", "Michael"]
>>> queue.append("Terry") # Terry arrives
>>> queue.append("Graham") # Graham arrives
>>> queue.pop(0)
'Eric'
>>> queue.pop(0)
'John'
>>> queue
['Michael', 'Terry', 'Graham']
5.1.3 Functional Programming Tools
There are three built-in functions that are very useful when used with lists: filter(), map(), and reduce().
"filter(function, sequence)"
returns a sequence (of the same type, if possible) consisting of those items from the
sequence for which function(item) is true. For example,
to compute some primes:
>>> def f(x): return x % 2 != 0 and x % 3 != 0
...
>>> filter(f, range(2, 25))
[5, 7, 11, 13, 17, 19, 23]
"map(function, sequence)" calls function(item)
for each of the sequence's items and returns a list of the return values. For example, to
compute some cubes:
>>> def cube(x): return x*x*x
...
>>> map(cube, range(1, 11))
[1, 8, 27, 64, 125, 216, 343, 512, 729, 1000]
More than one sequence may be passed; the function must then have as many arguments as
there are sequences and is called with the corresponding item from each sequence (or None
if some sequence is shorter than another). For example:
>>> seq = range(8)
>>> def add(x, y): return x+y
...
>>> map(add, seq, seq)
[0, 2, 4, 6, 8, 10, 12, 14]
"reduce(func, sequence)" returns
a single value constructed by calling the binary function func on the first two
items of the sequence, then on the result and the next item, and so on. For example, to
compute the sum of the numbers 1 through 10:
>>> def add(x,y): return x+y
...
>>> reduce(add, range(1, 11))
55
If there's only one item in the sequence, its value is returned; if the sequence is
empty, an exception is raised.
A third argument can be passed to indicate the starting value. In this case the
starting value is returned for an empty sequence, and the function is first applied to the
starting value and the first sequence item, then to the result and the next item, and so
on. For example,
>>> def sum(seq):
... def add(x,y): return x+y
... return reduce(add, seq, 0)
...
>>> sum(range(1, 11))
55
>>> sum([])
0
Don't use this example's definition of sum(): since summing
numbers is such a common need, a built-in function sum(sequence)
is already provided, and works exactly like this. New in version
2.3.
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List comprehensions provide a concise way to create lists without resorting to use of map(), filter() and/or lambda.
The resulting list definition tends often to be clearer than lists built using those
constructs. Each list comprehension consists of an expression followed by a for clause, then zero or more for or if clauses. The result will be a list resulting from evaluating the
expression in the context of the for and if
clauses which follow it. If the expression would evaluate to a tuple, it must be
parenthesized.
>>> freshfruit = [' banana', ' loganberry ', 'passion fruit ']
>>> [weapon.strip() for weapon in freshfruit]
['banana', 'loganberry', 'passion fruit']
>>> vec = [2, 4, 6]
>>> [3*x for x in vec]
[6, 12, 18]
>>> [3*x for x in vec if x > 3]
[12, 18]
>>> [3*x for x in vec if x < 2]
[]
>>> [[x,x**2] for x in vec]
[[2, 4], [4, 16], [6, 36]]
>>> [x, x**2 for x in vec] # error - parens required for tuples
File "<stdin>", line 1, in ?
[x, x**2 for x in vec]
^
SyntaxError: invalid syntax
>>> [(x, x**2) for x in vec]
[(2, 4), (4, 16), (6, 36)]
>>> vec1 = [2, 4, 6]
>>> vec2 = [4, 3, -9]
>>> [x*y for x in vec1 for y in vec2]
[8, 6, -18, 16, 12, -36, 24, 18, -54]
>>> [x+y for x in vec1 for y in vec2]
[6, 5, -7, 8, 7, -5, 10, 9, -3]
>>> [vec1[i]*vec2[i] for i in range(len(vec1))]
[8, 12, -54]
List comprehensions are much more flexible than map() and can
be applied to functions with more than one argument and to nested functions:
>>> [str(round(355/113.0, i)) for i in range(1,6)]
['3.1', '3.14', '3.142', '3.1416', '3.14159']
5.2 The del statement
There is a way to remove an item from a list given its index instead of its value: the del statement. This can also be used to remove slices from a list
(which we did earlier by assignment of an empty list to the slice). For example:
>>> a = [-1, 1, 66.6, 333, 333, 1234.5]
>>> del a[0]
>>> a
[1, 66.6, 333, 333, 1234.5]
>>> del a[2:4]
>>> a
[1, 66.6, 1234.5]
del can also be used to delete entire variables:
Referencing the name a hereafter is an error (at least until another value
is assigned to it). We'll find other uses for del later.
5.3 Tuples and Sequences
We saw that lists and strings have many common properties, such as indexing and slicing
operations. They are two examples of sequence
data types. Since Python is an evolving language, other sequence data types may be
added. There is also another standard sequence data type: the tuple.
A tuple consists of a number of values separated by commas, for instance:
>>> t = 12345, 54321, 'hello!'
>>> t[0]
12345
>>> t
(12345, 54321, 'hello!')
>>> # Tuples may be nested:
... u = t, (1, 2, 3, 4, 5)
>>> u
((12345, 54321, 'hello!'), (1, 2, 3, 4, 5))
As you see, on output tuples are alway enclosed in parentheses, so that nested tuples
are interpreted correctly; they may be input with or without surrounding parentheses,
although often parentheses are necessary anyway (if the tuple is part of a larger
expression).
Tuples have many uses. For example: (x, y) coordinate pairs, employee records from a
database, etc. Tuples, like strings, are immutable: it is not possible to assign to the
individual items of a tuple (you can simulate much of the same effect with slicing and
concatenation, though). It is also possible to create tuples which contain mutable
objects, such as lists.
A special problem is the construction of tuples containing 0 or 1 items: the syntax has
some extra quirks to accommodate these. Empty tuples are constructed by an empty pair of
parentheses; a tuple with one item is constructed by following a value with a comma (it is
not sufficient to enclose a single value in parentheses). Ugly, but effective. For
example:
>>> empty = ()
>>> singleton = 'hello', # <-- note trailing comma
>>> len(empty)
0
>>> len(singleton)
1
>>> singleton
('hello',)
The statement t = 12345, 54321, 'hello!' is an example of tuple packing:
the values 12345, 54321 and 'hello!' are packed
together in a tuple. The reverse operation is also possible:
This is called, appropriately enough, sequence unpacking. Sequence unpacking
requires that the list of variables on the left have the same number of elements as the
length of the sequence. Note that multiple assignment is really just a combination of
tuple packing and sequence unpacking!
There is a small bit of asymmetry here: packing multiple values always creates a tuple,
and unpacking works for any sequence.
5.4 Dictionaries
Another useful data type built into Python is the dictionary. Dictionaries are sometimes found in
other languages as ``associative memories'' or ``associative arrays''. Unlike sequences,
which are indexed by a range of numbers, dictionaries are indexed by keys, which
can be any immutable type; strings and numbers can always be keys. Tuples can be used as
keys if they contain only strings, numbers, or tuples; if a tuple contains any mutable
object either directly or indirectly, it cannot be used as a key. You can't use lists as
keys, since lists can be modified in place using their append()
and extend() methods, as well as slice and indexed assignments.
It is best to think of a dictionary as an unordered set of key: value pairs,
with the requirement that the keys are unique (within one dictionary). A pair of braces
creates an empty dictionary: {}. Placing a comma-separated list of key:value
pairs within the braces adds initial key:value pairs to the dictionary; this is also the
way dictionaries are written on output.
The main operations on a dictionary are storing a value with some key and extracting
the value given the key. It is also possible to delete a key:value pair with del.
If you store using a key that is already in use, the old value associated with that key is
forgotten. It is an error to extract a value using a non-existent key.
The keys() method of a dictionary object returns a list of all
the keys used in the dictionary, in random order (if you want it sorted, just apply the sort() method to the list of keys). To check whether a single key is
in the dictionary, use the has_key() method of the dictionary.
Here is a small example using a dictionary:
>>> tel = {'jack': 4098, 'sape': 4139}
>>> tel['guido'] = 4127
>>> tel
{'sape': 4139, 'guido': 4127, 'jack': 4098}
>>> tel['jack']
4098
>>> del tel['sape']
>>> tel['irv'] = 4127
>>> tel
{'guido': 4127, 'irv': 4127, 'jack': 4098}
>>> tel.keys()
['guido', 'irv', 'jack']
>>> tel.has_key('guido')
True
The dict() constructor builds dictionaries directly from
lists of key-value pairs stored as tuples. When the pairs form a pattern, list
comprehensions can compactly specify the key-value list.
>>> dict([('sape', 4139), ('guido', 4127), ('jack', 4098)])
{'sape': 4139, 'jack': 4098, 'guido': 4127}
>>> dict([(x, x**2) for x in vec]) # use a list comprehension
{2: 4, 4: 16, 6: 36}
5.5 Looping Techniques
When looping through dictionaries, the key and corresponding value can be retrieved at
the same time using the iteritems() method.
>>> knights = {'gallahad': 'the pure', 'robin': 'the brave'}
>>> for k, v in knights.iteritems():
... print k, v
...
gallahad the pure
robin the brave
When looping through a sequence, the position index and corresponding value can be
retrieved at the same time using the enumerate() function.
>>> for i, v in enumerate(['tic', 'tac', 'toe']):
... print i, v
...
0 tic
1 tac
2 toe
To loop over two or more sequences at the same time, the entries can be paired with the
zip() function.
>>> questions = ['name', 'quest', 'favorite color']
>>> answers = ['lancelot', 'the holy grail', 'blue']
>>> for q, a in zip(questions, answers):
... print 'What is your %s? It is %s.' % (q, a)
...
What is your name? It is lancelot.
What is your quest? It is the holy grail.
What is your favorite color? It is blue.
To loop over a sequence in reverse, first specify the sequence in a forward direction
and then call the reversed() function.
>>> for i in reversed(xrange(1,10,2)):
... print i
...
9
7
5
3
1
5.6 More on Conditions
The conditions used in while and if statements above can
contain other operators besides comparisons.
The comparison operators in and not in check whether a value
occurs (does not occur) in a sequence. The operators is and is not
compare whether two objects are really the same object; this only matters for mutable
objects like lists. All comparison operators have the same priority, which is lower than
that of all numerical operators.
Comparisons can be chained. For example, a < b == c tests whether a
is less than b and moreover b equals c.
Comparisons may be combined by the Boolean operators and and or,
and the outcome of a comparison (or of any other Boolean expression) may be negated with not.
These all have lower priorities than comparison operators again; between them, not
has the highest priority, and or the lowest, so that A and not B or C
is equivalent to (A and (not B)) or C. Of course, parentheses can be used to
express the desired composition.
The Boolean operators and and or are so-called short-circuit
operators: their arguments are evaluated from left to right, and evaluation stops as soon
as the outcome is determined. For example, if A and C are true
but B is false, A and B and C does not evaluate the expression C.
In general, the return value of a short-circuit operator, when used as a general value and
not as a Boolean, is the last evaluated argument.
It is possible to assign the result of a comparison or other Boolean expression to a
variable. For example,
>>> string1, string2, string3 = '', 'Trondheim', 'Hammer Dance'
>>> non_null = string1 or string2 or string3
>>> non_null
'Trondheim'
Note that in Python, unlike C, assignment cannot occur inside expressions. C
programmers may grumble about this, but it avoids a common class of problems encountered
in C programs: typing = in an expression when == was intended.
5.7 Comparing Sequences and Other Types
Sequence objects may be compared to other objects with the same sequence type. The
comparison uses lexicographical ordering: first the first two items are compared,
and if they differ this determines the outcome of the comparison; if they are equal, the
next two items are compared, and so on, until either sequence is exhausted. If two items
to be compared are themselves sequences of the same type, the lexicographical comparison
is carried out recursively. If all items of two sequences compare equal, the sequences are
considered equal. If one sequence is an initial sub-sequence of the other, the shorter
sequence is the smaller (lesser) one. Lexicographical ordering for strings uses the ASCII
ordering for individual characters. Some examples of comparisons between sequences with
the same types:
(1, 2, 3) < (1, 2, 4)
[1, 2, 3] < [1, 2, 4]
'ABC' < 'C' < 'Pascal' < 'Python'
(1, 2, 3, 4) < (1, 2, 4)
(1, 2) < (1, 2, -1)
(1, 2, 3) == (1.0, 2.0, 3.0)
(1, 2, ('aa', 'ab')) < (1, 2, ('abc', 'a'), 4)
Note that comparing objects of different types is legal. The outcome is deterministic
but arbitrary: the types are ordered by their name. Thus, a list is always smaller than a
string, a string is always smaller than a tuple, etc. Mixed numeric types are compared
according to their numeric value, so 0 equals 0.0, etc.5.1
Footnotes
- ... etc.5.1
- The rules for comparing objects of different types should not be relied upon; they
may change in a future version of the language.
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