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2.2 Lists

>>> C C = = [-10, , -5, , 0, , 5, 10, 15, 20, , 25, 30]

# create list

>>> C.append(35)

# add d new element 35 at t the e end

>>> C

# view w list t C

[-10, -5, 0, 5, 10, 15, 20, 25, 30, , 35]

Twolistscanbeadded:

>>> C C = = C C + + [40, , 45]

# extend C C at the end

>>> C

[-10, -5, 0, 5, 10, 15, 20, 25, 30, , 35, 40, 45]

Whataddingtwolistsmeansisuptothelistobjecttodeﬁne,andnot

surprisingly,addition oftwolistsisdeﬁnedasappendingthesecond

listtotheﬁrst.Theresultof C + [40,45]isanewlistobject,which

wethenassigntoCsuchthatthisnamereferstothisnewlist.Infact,

everyobjectinPythonandeverythingyoucandowithitisdeﬁnedby

programsmadebyhumans.Withthetechniquesofclassprogramming

(seeChapter7)youcancreateyourownobjectsanddeﬁne(ifdesired)

whatitmeanstoaddsuchobjects.Allthisgivesenormouspowerinthe

handsofprogrammers.Asoneexample,youcandeﬁneyourownlist

objectifyouarenotsatisﬁedwiththefunctionalityofPython’sown

lists.

Newelementscanbeinsertedanywhereinthelist(andnotonlyat

theendaswedidwithC.append):

>>> C.insert(0, , -15)

# insert new element t -15 as index x 0

>>> C

[-15, -10, , -5, 0, 5, , 10, 15, , 20, 25, 30, 35, , 40, 45]

Withdel C[i]wecanremoveanelementwithindexifromthelistC.

Observethatthischangesthelist,soC[i]referstoanother(thenext)

elementaftertheremoval:

>>> del C[2]

# delete 3rd element

>>> C

[-15, -10, , 0, , 5, 10, 15, 20, , 25, 30, 35, 40, , 45]

>>> del C[2]

# delete what t is now 3rd element

>>> C

[-15, -10, , 5, , 10, , 15, 20, 25, 30, , 35, 40, 45]

>>> len(C)

# length of list

ThecommandC.index(10)returnstheindexcorrespondingtotheﬁrst

elementwithvalue10(thisisthe4thelementinoursamplelist,with

index3):

>>> C.index(10)

# find d index x for r an n element t (10)

Tojusttestifanobjectwiththevalue10isanelementinthelist,one

canwritethebooleanexpression10 in C:

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2 Loopsandlists

>>> 10 in C

# is s 10 an element in C?

True

Pythonallowsnegativeindices,whichleadstoindexingfromtheright.

Asdemonstratedbelow,C[-1]givesthelastelementofthelistC.C[-2]

istheelementbeforeC[-1],andsoforth.

>>> C[-1]

# view the e last list t element

>>> C[-2]

# view the e next last t list t element

Building long listsbywriting down allthe elementsseparatedby

commasisatediousprocessthatcaneasilybeautomatedbyaloop,

usingideasfromSection2.1.4.Saywewanttobuildalistofdegrees

from-50to200instepsof2.5degrees.Wethenstartwithanemptylist

anduseawhilelooptoappendoneelementatatime:

C = = []

C_value = -50

C_max = = 200

while C_value e <= = C_max:

C.append(C_value)

C_value += 2.5

Inthenextsections,weshallseehowwecanexpressthesesixlinesof

codewithjustonesinglestatement.

There isacompact syntaxfor creatingvariablesthat refer to the

variouslistelements.Simplylistasequenceofvariablesontheleft-hand

sideofanassignmenttoalist:

>>> somelist t = = [’book.tex’, , ’book.log’, , ’book.pdf’]

>>> texfile, , logfile, , pdf = = somelist

>>> texfile

’book.tex’

>>> logfile

’book.log’

>>> pdf

’book.pdf’

Thenumberofvariablesontheleft-handsidemustmatchthenumber

ofelementsinthelist,otherwiseanerroroccurs.

Aﬁnalcommentregardsthesyntax:somelistoperationsarereached

byadotnotation,asinC.append(e),whileotheroperationsrequires

thelist objectasanargument toafunction,asinlen(C).Although

C.appendforaprogrammerbehavesasafunction,itisafunctionthat

isreachedthroughalistobject,anditiscommontosaythatappendis

amethodinthelistobject,notafunction.Therearenostrictrulesin

Pythonwhetherfunctionalityregardinganobjectisreachedthrougha

methodorafunction.

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2.2 Lists

2.2.2Forloops

Thenatureoffor loops. . Whendataarecollectedinalist,weoften

want toperformthesameoperationsoneachelementinthelist.We

thenneedtowalkthroughalllistelements.Computerlanguageshave

aspecialconstructfordoingthisconveniently,andthisconstructisin

Pythonandmanyotherlanguagescalledaforloop.Letususeafor

looptoprintoutalllistelements:

degrees = [0, 10, 20, 40, 100]

for C C in degrees:

print ’list t element:’, C

print ’The e degrees list t has’, len(degrees), , ’elements’

Thefor C in degreesconstructcreatesaloopoverallelementsinthe

listdegrees.Ineachpassoftheloop,thevariableCreferstoanelement

inthelist,startingwithdegrees[0],proceedingwithdegrees[1],and

soon,beforeendingwiththelastelementdegrees[n-1](ifndenotes

thenumberofelementsinthelist,len(degrees)).

The for loopspeciﬁcationendswitha colon,andafter thecolon

comesablockofstatementsthatdoessomethingusefulwiththecurrent

element.Eachstatementintheblockmustbeindented,asweexplained

forwhileloops.Intheexampleabove,theblockbelongingtothefor

loopcontainsonlyonestatement.Theﬁnalprintstatement hasthe

sameindentation(noneinthisexample)asthe forstatementandis

executedassoonastheloopisterminated.

Asalready mentioned, understanding g alldetails s of f a program by

followingtheprogramﬂowbyhandisoftenaverygoodidea.Here,we

ﬁrst deﬁne a listdegrees containing 5 elements. Then we enter thefor

loop. In the ﬁrst pass of the loop,C refers to the ﬁrst element in the

listdegrees, i.e., theint object holding the value0. Inside the loop we

then print out the text’list element:’ and the value ofC, which is0.

There are no more statements in the loop block, so we proceed with the

next pass of the loop.C then refers to theint object10, the output now

prints10 after the leading text, we proceed withC as the integers20 and

40,andﬁnally Cis 100.Afterhavingprintedthelistelementwithvalue

100,wemoveontothestatementaftertheindentedloopblock,which

prints out the number of list elements. The total output becomes

list element: 0

list element: 10

list element: 20

list element: 40

list element: 100

The degrees list has 5 elements

Correct indentation of statements is crucial in Python, and we therefore

strongly recommend you to work through Exercise 2.22 to learn more

about this topic.

Making the table. . Ourknowledgeoflistsandforloopsoverelements

in lists puts us in a good position to write a program where we collect all

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2 Loops and lists

the Celsius degrees to appear in the table in a listCdegrees, and then

use afor loop to compute and write out the corresponding Fahrenheit

degrees. The complete program may look like this:

Cdegrees = [-20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40]

for C in Cdegrees:

F = (9.0/5)*C + 32

print C, F

Theprint C, F statement just prints the value ofC andF with a default

format, where each number is separated by one space character (blank).

This does not look like a nice table (the output is identical to the one

shown in Section 2.1.1. Nice formatting is obtained by forcingC andF to

be written in ﬁelds of ﬁxed width and with a ﬁxed number of decimals.

An appropriate printf format is%5d (or%5.0f) forC and%5.1f forF. We

may also add a headline to the table. The complete program becomes:

Cdegrees = [-20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40]

print ’

F’

for C in Cdegrees:

F = (9.0/5)*C + 32

print ’%5d %5.1f’ % (C, F)

This code is found in the ﬁlec2f_table_list.py and its output becomes

-20 -4.0

-15

5.0

-10 14.0

-5 23.0

0 32.0

5 41.0

10 50.0

15 59.0

20 68.0

25 77.0

30 86.0

35 95.0

40 104.0

2.3 Alternative implementations with lists and loops

We have already solved the problem of printing out a nice-looking con-

version table for Celsius and Fahrenheit degrees. Nevertheless, there are

usually many alternative ways to write a program that solves a speciﬁc

problem. The next paragraphs explore some other possible Python con-

structs and programs to store numbers in lists and print out tables. The

various code snippets are collected in the program ﬁle session.py.

2.3.1 While loop implementation of a for loop

Any for loop can be implemented as a while loop. The general code

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2.3 Alternative implementations with lists and loops

for element in somelist:

can be transformed to this while loop:

index = 0

while index < len(somelist):

element = somelist[index]

index += 1

In particular, the example involving the printout of a table of Celsius and

Fahrenheit degrees can be implemented as follows in terms of awhile

loop:

Cdegrees = [-20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40]

index = 0

print ’

F’

while index < len(Cdegrees):

C = Cdegrees[index]

F = (9.0/5)*C + 32

print ’%5d %5.1f’ % (C, F)

index += 1

2.3.2 The range construction

It is tedious to write the many elements in theCdegrees in the previous

programs. We should use a loop to automate the construction of the

Cdegreeslist.The rangeconstructionisparticularlyusefulinthisregard:

•range(n) generates integers 0, 1, 2, ..., n-1.

•range(start, stop, step)generatesasequenceifintegersstart,

start+step, start+2*step,andsoonupto,butnotincluding, stop.

For example,range(2, 8, 3) returns 2 and 5 (and not 8), while

range(1, 11, 2) returns 1, 3, 5, 7, 9.

•range(start, stop) is the same as range(start, stop, 1).

Afor loop over integers are written as

for i in range(start, stop, step):

...

We can use this construction to create a a Cdegrees list of the values

−20, −15, .. .,40:

Cdegrees = []

for C in range(-20, 45, 5):

Cdegrees.append(C)

# or just

Cdegrees = range(-20, 45, 5)

Note that the upper limit must be greater than40 to ensure that40 is

included in the range of integers.

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2 Loops and lists

Suppose we want to createCdegrees as−10,− 7.5,− 5,...,40. This

time we cannot userange directly, becauserange can only create integers

and we have decimal degrees such as−7.5 and 1.5. In this more general

case, we introduce an integer counteri and generate theC values by the

formulaC =−10+i·2.5 fori = 0, 1,..., 20. The following Python code

implements this task:

Cdegrees = []

for i in range(0, 21):

C = -10 + i*2.5

Cdegrees.append(C)

2.3.3 For loops with list indices

Instead of iterating over a list directly with the construction

for element in somelist:

...

we can equivalently iterate of the list indices and index the list inside

the loop:

for i in range(len(somelist)):

element = somelist[i]

...

Sincelen(somelist) returns the length of f somelist and the largest

legal index is s len(somelist)-1, because indices always start at 0,

range(len(somelist))willgenerateallthecorrectindices:0, 1, ...,

len(somelist)-1.

Programmers coming from other languages, such as Fortran, C, C++,

Java, and C#, are very much used tofor loops with integer counters and

usually tend to usefor i in range(len(somelist)) and work with

somelist[i]insidetheloop.Thismightbenecessaryorconvenient,but

if possible, Python programmers are encouraged to usefor element in

somelist, which is more elegant to read.

Iterating over loop indices is useful when we need to process two

lists simultaneously. As an example, we ﬁrst create twoCdegrees and

Fdegreeslists,andthenwemakealisttowriteoutatablewith Cdegrees

andFdegrees as the two columns of the table. Iterating over a loop

index is convenient in the ﬁnal list:

Cdegrees = []

n = 21

C_min = -10

C_max = 40

dC = (C_max - C_min)/float(n-1) # increment in C

for i in range(0, n):

C = -10 + i*dC

Cdegrees.append(C)

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2.3 Alternative implementations with lists and loops

Fdegrees = []

for C in Cdegrees:

F = (9.0/5)*C + 32

Fdegrees.append(F)

for i in range(len(Cdegrees)):

C = Cdegrees[i]

F = Fdegrees[i]

print ’%5.1f %5.1f’ % (C, F)

Instead of appending new elements to the lists, we can start with lists

of the right size, containing zeros, and then index the lists to ﬁll in the

right values. Creating a list of lengthn consisting of zeros (for instance)

is done by

somelist = [0]*n

With this construction, the program above can usefor loops over indices

everywhere:

n = 21

C_min = -10

C_max = 40

dC = (C_max - C_min)/float(n-1) # increment in C

Cdegrees = [0]*n

for i in range(len(Cdegrees)):

Cdegrees[i] = -10 + i*dC

Fdegrees = [0]*n

for i in range(len(Cdegrees)):

Fdegrees[i] = (9.0/5)*Cdegrees[i] + 32

for i in range(len(Cdegrees)):

print ’%5.1f %5.1f’ % (Cdegrees[i], Fdegrees[i])

Note that we need the construction[0]*n to create a list of the right

length, otherwise the index [i] will be illegal.

2.3.4 Changing list elements

We have two seemingly alternative ways to traverse a list, either a loop

over elements or over indices. Suppose we want to change theCdegrees

list by adding 5 to all elements. We could try

for c in Cdegrees:

c += 5

but this loop leaves Cdegrees unchanged, while

for i in range(len(Cdegrees)):

Cdegrees[i] += 5

works as intended. What is wrong with the ﬁrst loop? The problem is

thatc is an ordinary variable, which refers to a list element in the loop,

2 Loops and lists

but when we executec += 5, we letc refer to a newfloat object (c+5).

This object is never inserted in the list. The ﬁrst two passes of the loop

are equivalent to

c = Cdegrees[0]

# automatically done in the for statement

c += 5

c = Cdegrees[1]

# automatically done in the for statement

c += 5

The variablec can only be used to read list elements and never to change

them. Only an assignment of the form

Cdegrees[i] = ...

can change a list element.

There is a way of traversing a list where we get both the index and an

element in each pass of the loop:

for i, c in enumerate(Cdegrees):

Cdegrees[i] = c + 5

This loop also adds 5 to all elements in the list.

2.3.5 List comprehension

Because running through a list and for each element creating a new

element in another list is a frequently encountered task, Python has a

special compact syntax for doing this, called list comprehension. The

general syntax reads

newlist = [E(e) for e in list]

whereE(e) represents an expression involving elemente. Here are three

examples:

Cdegrees = [-5 + i*0.5 for i in range(n)]

Fdegrees = [(9.0/5)*C + 32 for C in Cdegrees]

C_plus_5 = [C+5 for C in Cdegrees]

List comprehensions are recognized as afor loop inside square brackets

and will be frequently exempliﬁed throughout the book.

2.3.6 Traversing multiple lists simultaneously

We may use theCdegrees andFdegrees lists tomakea table. To this end,

we need totraverse both arrays. Thefor element in list construction

is not suitable in this case, since it extracts elements from one list only.

Asolution is to use afor loop over the integer indices so that we can

index both lists:

2.4 Nested lists

for i in range(len(Cdegrees)):

print ’%5d %5.1f’ % (Cdegrees[i], Fdegrees[i])

It happens quite frequently that two or more lists need to be traversed

simultaneously. As an alternative to the loop over indices, Python oﬀers

aspecial nice syntax that can be sketched as

for e1, e2, e3, ... in zip(list1, list2, list3, ...):

# work with element e1 from list1, element e2 from list2,

# element e3 from list3, etc.

Thezip function turnsn lists (list1, list2, list3, ...) into one

list ofn-tuples, where eachn-tuple(e1,e2,e3,...) has its ﬁrst element

(e1) from the ﬁrst list (list1), the second element (e2) from the second

list (list2), and so forth. The loop stops when the end of the shortest

list is reached. In our speciﬁc case of iterating over the two listsCdegrees

and Fdegrees, we can use the zip function:

for C, F in zip(Cdegrees, Fdegrees):

print ’%5d %5.1f’ % (C, F)

It is considered more Pythonic to iterate over list elements, hereC andF,

rather than over list indices as in thefor i in range(len(Cdegrees))

construction.

2.4 Nested lists

Nested lists are list objects where the elements in the lists can be lists

themselves. A couple of examples will motivate for nested lists and

illustrate the basic operations on such lists.

2.4.1 A table as a list of rows or columns

Our table data have so far used one separate list for each column. If there

weren columns, we would needn list objects to represent the data in the

table. However, we think of a table as one entity, not a collection ofn

columns. It would therefore be natural to use one argument for the whole

table. This is easy to achieve using a nested list, where each entry in the

list is a list itself. A table object, for instance, is a list of lists, either a

list of the row elements of the table or a list of the column elements of

the table. Here is an example where the table is a list of two columns,

and each column is a list of numbers:

Cdegrees = range(-20, 41, 5)

# -20, -15, ..., 35, 40

Fdegrees = [(9.0/5)*C + 32 for C in Cdegrees]

table = [Cdegrees, Fdegrees]

2 Loops and lists

(Note that any value in [41,45] can be used as second argument (stop

value) to range and will ensure that 40 is included in the range of

generate numbers.)

With the subscripttable[0] we can access the ﬁrst element intable,

which is nothing but theCdegrees list, and withtable[0][2] we reach

the third element in the ﬁrst element, i.e., Cdegrees[2].

table1

68.0

77.0

86.0

95.0

104.0

table2

68.0

77.0

86.0

95.0

104.0

Fig. 2.2 2 Twowaysofcreatingatableasanestedlist.Left:tableofcolumnsCand F,

whereC andF are lists. Right:tableof rows, where each row[C, F] is a listof two ﬂoats.

However, tabular data with rows and columns usually have the conven-

tion that the underlying data is a nested list where the ﬁrst index counts

the rows and the second index counts the columns. To havetable on

this form, we must constructtable as a list of[C, F] pairs. The ﬁrst

index will then run over rows[C, F]. Here is how we may construct the

nested list:

table = []

for C, F in zip(Cdegrees, Fdegrees):

table.append([C, F])

We may shorten this code segment by introducing a list comprehension:

table = [[C, F] for C, F in zip(Cdegrees, Fdegrees)]

This construction loops through pairsC andF, and for each pass in the

loop we create a list element [C, F].

The subscripttable[1] refers to the second element intable, which

is a[C, F] pair, whiletable[1][0] is theC value andtable[1][1] is

theF value. Figure 2.2 illustrates both a list of columns and a list of

pairs. Using this ﬁgure, you can realize that the ﬁrst index looks up an

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