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 listobjects:

list.append(x)

Add an item to the end of the list. Similar toa[len(a):]=[x].

list.extend(iterable)

Extend the list by appending all the items from the iterable. Similar toa[len(a):]=iterable.

list.insert(i,x)

Insert an item at a given position. The first argument is the index of theelement before which to insert, soa.insert(0,x) inserts at the front ofthe list, anda.insert(len(a),x) is equivalent toa.append(x).

list.remove(x)

Remove the first item from the list whose value is equal tox. It raises aValueError if there is no such item.

list.pop([i])

Remove the item at the given position in the list, and return it. If no indexis specified,a.pop() removes and returns the last item in the list.It raises anIndexError if the list is empty or the index isoutside the list range.

list.clear()

Remove all items from the list. Similar todela[:].

list.index(x[,start[,end]])

Return zero-based index in the list of the first item whose value is equal tox.Raises aValueError if there is no such item.

The optional argumentsstart andend are interpreted as in the slicenotation and are used to limit the search to a particular subsequence ofthe list. The returned index is computed relative to the beginning of the fullsequence rather than thestart argument.

list.count(x)

Return the number of timesx appears in the list.

list.sort(*,key=None,reverse=False)

Sort the items of the list in place (the arguments can be used for sortcustomization, seesorted() for their explanation).

list.reverse()

Reverse the elements of the list in place.

list.copy()

Return a shallow copy of the list. Similar toa[:].

An example that uses most of the list methods:

>>>fruits=['orange','apple','pear','banana','kiwi','apple','banana']>>>fruits.count('apple')2>>>fruits.count('tangerine')0>>>fruits.index('banana')3>>>fruits.index('banana',4)# Find next banana starting at position 46>>>fruits.reverse()>>>fruits['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange']>>>fruits.append('grape')>>>fruits['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange', 'grape']>>>fruits.sort()>>>fruits['apple', 'apple', 'banana', 'banana', 'grape', 'kiwi', 'orange', 'pear']>>>fruits.pop()'pear'

You might have noticed that methods likeinsert,remove orsort thatonly modify the list have no return value printed – they return the defaultNone.[1] This is a design principle for all mutable data structures inPython.

Another thing you might notice is that not all data can be sorted orcompared. For instance,[None,'hello',10] doesn’t sort becauseintegers can’t be compared to strings andNone can’t be compared toother types. Also, there are some types that don’t have a definedordering relation. For example,3+4j<5+7j isn’t a validcomparison.

5.1.1.Using Lists as Stacks

The list methods make it very easy to use a list as a stack, where the lastelement added is the first element retrieved (“last-in, first-out”). To add anitem to the top of the stack, useappend(). To retrieve an item from thetop of the stack, usepop() 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

It is also possible to use a list as a queue, where the first element added isthe first element retrieved (“first-in, first-out”); however, lists are notefficient for this purpose. While appends and pops from the end of list arefast, doing inserts or pops from the beginning of a list is slow (because allof the other elements have to be shifted by one).

To implement a queue, usecollections.deque which was designed tohave fast appends and pops from both ends. For example:

>>>fromcollectionsimportdeque>>>queue=deque(["Eric","John","Michael"])>>>queue.append("Terry")# Terry arrives>>>queue.append("Graham")# Graham arrives>>>queue.popleft()# The first to arrive now leaves'Eric'>>>queue.popleft()# The second to arrive now leaves'John'>>>queue# Remaining queue in order of arrivaldeque(['Michael', 'Terry', 'Graham'])

5.1.3.List Comprehensions

List comprehensions provide a concise way to create lists.Common applications are to make new lists where each element is the result ofsome operations applied to each member of another sequence or iterable, or tocreate a subsequence of those elements that satisfy a certain condition.

For example, assume we want to create a list of squares, like:

>>>squares=[]>>>forxinrange(10):...squares.append(x**2)...>>>squares[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Note that this creates (or overwrites) a variable namedx that still existsafter the loop completes. We can calculate the list of squares without anyside effects using:

squares=list(map(lambdax:x**2,range(10)))

or, equivalently:

squares=[x**2forxinrange(10)]

which is more concise and readable.

A list comprehension consists of brackets containing an expression followedby afor clause, then zero or morefor orifclauses. The result will be a new list resulting from evaluating the expressionin the context of thefor andif clauses which follow it.For example, this listcomp combines the elements of two lists if they are notequal:

>>>[(x,y)forxin[1,2,3]foryin[3,1,4]ifx!=y][(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]

and it’s equivalent to:

>>>combs=[]>>>forxin[1,2,3]:...foryin[3,1,4]:...ifx!=y:...combs.append((x,y))...>>>combs[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]

Note how the order of thefor andif statements is thesame in both these snippets.

If the expression is a tuple (e.g. the(x,y) in the previous example),it must be parenthesized.

>>>vec=[-4,-2,0,2,4]>>># create a new list with the values doubled>>>[x*2forxinvec][-8, -4, 0, 4, 8]>>># filter the list to exclude negative numbers>>>[xforxinvecifx>=0][0, 2, 4]>>># apply a function to all the elements>>>[abs(x)forxinvec][4, 2, 0, 2, 4]>>># call a method on each element>>>freshfruit=['  banana','  loganberry ','passion fruit  ']>>>[weapon.strip()forweaponinfreshfruit]['banana', 'loganberry', 'passion fruit']>>># create a list of 2-tuples like (number, square)>>>[(x,x**2)forxinrange(6)][(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)]>>># the tuple must be parenthesized, otherwise an error is raised>>>[x,x**2forxinrange(6)]  File"<stdin>", line1[x,x**2forxinrange(6)]^^^^^^^SyntaxError:did you forget parentheses around the comprehension target?>>># flatten a list using a listcomp with two 'for'>>>vec=[[1,2,3],[4,5,6],[7,8,9]]>>>[numforeleminvecfornuminelem][1, 2, 3, 4, 5, 6, 7, 8, 9]

List comprehensions can contain complex expressions and nested functions:

>>>frommathimportpi>>>[str(round(pi,i))foriinrange(1,6)]['3.1', '3.14', '3.142', '3.1416', '3.14159']

5.1.4.Nested List Comprehensions

The initial expression in a list comprehension can be any arbitrary expression,including another list comprehension.

Consider the following example of a 3x4 matrix implemented as a list of3 lists of length 4:

>>>matrix=[...[1,2,3,4],...[5,6,7,8],...[9,10,11,12],...]

The following list comprehension will transpose rows and columns:

>>>[[row[i]forrowinmatrix]foriinrange(4)][[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]

As we saw in the previous section, the inner list comprehension is evaluated inthe context of thefor that follows it, so this example isequivalent to:

>>>transposed=[]>>>foriinrange(4):...transposed.append([row[i]forrowinmatrix])...>>>transposed[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]

which, in turn, is the same as:

>>>transposed=[]>>>foriinrange(4):...# the following 3 lines implement the nested listcomp...transposed_row=[]...forrowinmatrix:...transposed_row.append(row[i])...transposed.append(transposed_row)...>>>transposed[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]

In the real world, you should prefer built-in functions to complex flow statements.Thezip() function would do a great job for this use case:

>>>list(zip(*matrix))[(1, 5, 9), (2, 6, 10), (3, 7, 11), (4, 8, 12)]

SeeUnpacking Argument Lists for details on the asterisk in this line.

5.2.Thedel statement

There is a way to remove an item from a list given its index instead of itsvalue: thedel statement. This differs from thepop() methodwhich returns a value. Thedel statement can also be used to removeslices from a list or clear the entire list (which we did earlier by assignmentof an empty list to the slice). For example:

>>>a=[-1,1,66.25,333,333,1234.5]>>>dela[0]>>>a[1, 66.25, 333, 333, 1234.5]>>>dela[2:4]>>>a[1, 66.25, 1234.5]>>>dela[:]>>>a[]

del can also be used to delete entire variables:

>>>dela

Referencing the namea hereafter is an error (at least until another valueis assigned to it). We’ll find other uses fordel later.

5.3.Tuples and Sequences

We saw that lists and strings have many common properties, such as indexing andslicing operations. They are two examples ofsequence data types (seeSequence Types — list, tuple, range). Since Python is an evolving language, other sequence datatypes may be added. There is also another standard sequence data type: thetuple.

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))>>># Tuples are immutable:>>>t[0]=88888Traceback (most recent call last):  File"<stdin>", line1, in<module>TypeError:'tuple' object does not support item assignment>>># but they can contain mutable objects:>>>v=([1,2,3],[3,2,1])>>>v([1, 2, 3], [3, 2, 1])

As you see, on output tuples are always enclosed in parentheses, so that nestedtuples are interpreted correctly; they may be input with or without surroundingparentheses, although often parentheses are necessary anyway (if the tuple ispart of a larger expression). It is not possible to assign to the individualitems of a tuple, however it is possible to create tuples which contain mutableobjects, such as lists.

Though tuples may seem similar to lists, they are often used in differentsituations and for different purposes.Tuples areimmutable, and usually contain a heterogeneous sequence ofelements that are accessed via unpacking (see later in this section) or indexing(or even by attribute in the case ofnamedtuples).Lists aremutable, and their elements are usually homogeneous and areaccessed by iterating over the list.

A special problem is the construction of tuples containing 0 or 1 items: thesyntax has some extra quirks to accommodate these. Empty tuples are constructedby an empty pair of parentheses; a tuple with one item is constructed byfollowing a value with a comma (it is not sufficient to enclose a single valuein parentheses). Ugly, but effective. For example:

>>>empty=()>>>singleton='hello',# <-- note trailing comma>>>len(empty)0>>>len(singleton)1>>>singleton('hello',)

The statementt=12345,54321,'hello!' is an example oftuple packing:the values12345,54321 and'hello!' are packed together in a tuple.The reverse operation is also possible:

>>>x,y,z=t

This is called, appropriately enough,sequence unpacking and works for anysequence on the right-hand side. Sequence unpacking requires that there are asmany variables on the left side of the equals sign as there are elements in thesequence. Note that multiple assignment is really just a combination of tuplepacking and sequence unpacking.

5.4.Sets

Python also includes a data type forsets. A set is an unordered collectionwith no duplicate elements. Basic uses include membership testing andeliminating duplicate entries. Set objects also support mathematical operationslike union, intersection, difference, and symmetric difference.

Curly braces or theset() function can be used to create sets. Note: tocreate an empty set you have to useset(), not{}; the latter creates anempty dictionary, a data structure that we discuss in the next section.

Here is a brief demonstration:

>>>basket={'apple','orange','apple','pear','orange','banana'}>>>print(basket)# show that duplicates have been removed{'orange', 'banana', 'pear', 'apple'}>>>'orange'inbasket# fast membership testingTrue>>>'crabgrass'inbasketFalse>>># Demonstrate set operations on unique letters from two words>>>>>>a=set('abracadabra')>>>b=set('alacazam')>>>a# unique letters in a{'a', 'r', 'b', 'c', 'd'}>>>a-b# letters in a but not in b{'r', 'd', 'b'}>>>a|b# letters in a or b or both{'a', 'c', 'r', 'd', 'b', 'm', 'z', 'l'}>>>a&b# letters in both a and b{'a', 'c'}>>>a^b# letters in a or b but not both{'r', 'd', 'b', 'm', 'z', 'l'}

Similarly tolist comprehensions, set comprehensionsare also supported:

>>>a={xforxin'abracadabra'ifxnotin'abc'}>>>a{'r', 'd'}

5.5.Dictionaries

Another useful data type built into Python is thedictionary (seeMapping Types — dict). Dictionaries are sometimes found in other languages as“associative memories” or “associative arrays”. Unlike sequences, which areindexed by a range of numbers, dictionaries are indexed bykeys, which can beany immutable type; strings and numbers can always be keys. Tuples can be usedas keys if they contain only strings, numbers, or tuples; if a tuple containsany 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 indexassignments, slice assignments, or methods likeappend() andextend().

It is best to think of a dictionary as a set ofkey: value pairs,with the requirement that the keys are unique (within one dictionary). A pair ofbraces creates an empty dictionary:{}. Placing a comma-separated list ofkey:value pairs within the braces adds initial key:value pairs to thedictionary; this is also the way dictionaries are written on output.

The main operations on a dictionary are storing a value with some key andextracting the value given the key. It is also possible to delete a key:valuepair withdel. If you store using a key that is already in use, the oldvalue associated with that key is forgotten. It is an error to extract a valueusing a non-existent key.

Performinglist(d) on a dictionary returns a list of all the keysused in the dictionary, in insertion order (if you want it sorted, just usesorted(d) instead). To check whether a single key is in thedictionary, use thein keyword.

Here is a small example using a dictionary:

>>>tel={'jack':4098,'sape':4139}>>>tel['guido']=4127>>>tel{'jack': 4098, 'sape': 4139, 'guido': 4127}>>>tel['jack']4098>>>deltel['sape']>>>tel['irv']=4127>>>tel{'jack': 4098, 'guido': 4127, 'irv': 4127}>>>list(tel)['jack', 'guido', 'irv']>>>sorted(tel)['guido', 'irv', 'jack']>>>'guido'intelTrue>>>'jack'notintelFalse

Thedict() constructor builds dictionaries directly from sequences ofkey-value pairs:

>>>dict([('sape',4139),('guido',4127),('jack',4098)]){'sape': 4139, 'guido': 4127, 'jack': 4098}

In addition, dict comprehensions can be used to create dictionaries fromarbitrary key and value expressions:

>>>{x:x**2forxin(2,4,6)}{2: 4, 4: 16, 6: 36}

When the keys are simple strings, it is sometimes easier to specify pairs usingkeyword arguments:

>>>dict(sape=4139,guido=4127,jack=4098){'sape': 4139, 'guido': 4127, 'jack': 4098}

5.6.Looping Techniques

When looping through dictionaries, the key and corresponding value can beretrieved at the same time using theitems() method.

>>>knights={'gallahad':'the pure','robin':'the brave'}>>>fork,vinknights.items():...print(k,v)...gallahad the purerobin the brave

When looping through a sequence, the position index and corresponding value canbe retrieved at the same time using theenumerate() function.

>>>fori,vinenumerate(['tic','tac','toe']):...print(i,v)...0 tic1 tac2 toe

To loop over two or more sequences at the same time, the entries can be pairedwith thezip() function.

>>>questions=['name','quest','favorite color']>>>answers=['lancelot','the holy grail','blue']>>>forq,ainzip(questions,answers):...print('What is your{0}?  It is{1}.'.format(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 forwarddirection and then call thereversed() function.

>>>foriinreversed(range(1,10,2)):...print(i)...97531

To loop over a sequence in sorted order, use thesorted() function whichreturns a new sorted list while leaving the source unaltered.

>>>basket=['apple','orange','apple','pear','orange','banana']>>>foriinsorted(basket):...print(i)...appleapplebananaorangeorangepear

Usingset() on a sequence eliminates duplicate elements. The use ofsorted() in combination withset() over a sequence is an idiomaticway to loop over unique elements of the sequence in sorted order.

>>>basket=['apple','orange','apple','pear','orange','banana']>>>forfinsorted(set(basket)):...print(f)...applebananaorangepear

It is sometimes tempting to change a list while you are looping over it;however, it is often simpler and safer to create a new list instead.

>>>importmath>>>raw_data=[56.2,float('NaN'),51.7,55.3,52.5,float('NaN'),47.8]>>>filtered_data=[]>>>forvalueinraw_data:...ifnotmath.isnan(value):...filtered_data.append(value)...>>>filtered_data[56.2, 51.7, 55.3, 52.5, 47.8]

5.7.More on Conditions

The conditions used inwhile andif statements can contain anyoperators, not just comparisons.

The comparison operatorsin andnotin are membership tests thatdetermine whether a value is in (or not in) a container. The operatorsisandisnot compare whether two objects are really the same object. Allcomparison operators have the same priority, which is lower than that of allnumerical operators.

Comparisons can be chained. For example,a<b==c tests whethera isless thanb and moreoverb equalsc.

Comparisons may be combined using the Boolean operatorsand andor, andthe outcome of a comparison (or of any other Boolean expression) may be negatedwithnot. These have lower priorities than comparison operators; betweenthem,not has the highest priority andor the lowest, so thatAandnotBorC is equivalent to(Aand(notB))orC. As always, parenthesescan be used to express the desired composition.

The Boolean operatorsand andor are so-calledshort-circuitoperators: their arguments are evaluated from left to right, and evaluationstops as soon as the outcome is determined. For example, ifA andC aretrue butB is false,AandBandC does not evaluate the expressionC. When used as a general value and not as a Boolean, the return value of ashort-circuit operator is the last evaluated argument.

It is possible to assign the result of a comparison or other Boolean expressionto a variable. For example,

>>>string1,string2,string3='','Trondheim','Hammer Dance'>>>non_null=string1orstring2orstring3>>>non_null'Trondheim'

Note that in Python, unlike C, assignment inside expressions must be doneexplicitly with thewalrus operator:=.This avoids a common class of problems encountered in C programs: typing=in an expression when== was intended.

5.8.Comparing Sequences and Other Types

Sequence objects typically may be compared to other objects with the same sequencetype. The comparison useslexicographical ordering: first the first twoitems are compared, and if they differ this determines the outcome of thecomparison; if they are equal, the next two items are compared, and so on, untileither sequence is exhausted. If two items to be compared are themselvessequences of the same type, the lexicographical comparison is carried outrecursively. If all items of two sequences compare equal, the sequences areconsidered equal. If one sequence is an initial sub-sequence of the other, theshorter sequence is the smaller (lesser) one. Lexicographical ordering forstrings uses the Unicode code point number to order individual characters.Some examples of comparisons between sequences of the same type:

(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 with< or> is legalprovided that the objects have appropriate comparison methods. For example,mixed numeric types are compared according to their numeric value, so 0 equals0.0, etc. Otherwise, rather than providing an arbitrary ordering, theinterpreter will raise aTypeError exception.

Footnotes

[1]

Other languages may return the mutated object, which allows methodchaining, such asd->insert("a")->remove("b")->sort();.