[<< wikibooks] Think Python/Lists
== A list is a sequence ==
Like a string, a list is a sequence of values. In a string, the
values are characters; in a list, they can be any type. The values in
list are called elements or sometimes items.
There are several ways to create a new list; the simplest is to
enclose the elements in square brackets ([ and ]):

[10, 20, 30, 40]
['crunchy frog', 'ram bladder', 'lark vomit']

The first example is a list of four integers. The second is a list of
three strings. The elements of a list don’t have to be the same type.
The following list contains a string, a float, an integer, and
(lo!) another list:

['spam', 2.0, 5, [10, 20]]

A list within another list is nested.
A list that contains no elements is
called an empty list; you can create one with empty
brackets, [].
As you might expect, you can assign list values to variables:

>>> cheeses = ['Cheddar', 'Edam', 'Gouda']
>>> numbers = [17, 123]
>>> empty = []
>>> print cheeses, numbers, empty
['Cheddar', 'Edam', 'Gouda'] [17, 123] []

== Lists are mutable ==
The syntax for accessing the elements of a list is the same as for
accessing the characters of a string—the bracket operator. The
expression inside the brackets specifies the index. Remember that the
indices start at 0:

>>> print cheeses[0]

Unlike strings, lists are mutable. When the bracket operator appears
on the left side of an assignment, it identifies the element of the
list that will be assigned.

>>> numbers = [17, 123]
>>> numbers[1] = 5
>>> print numbers
[17, 5]

The one-eth element of numbers, which
used to be 123, is now 5.
You can think of a list as a relationship between indices and
elements. This relationship is called a mapping; each index
“maps to” one of the elements. Here is a state diagram showing cheeses, numbers and empty:

Lists are represented by boxes with the word “list” outside
and the elements of the list inside. cheeses refers to
a list with three elements indexed 0, 1 and 2.
numbers contains two elements; the diagram shows that the
value of the second element has been reassigned from 123 to 5.
empty refers to a list with no elements.
List indices work the same way as string indices:

Any integer expression can be used as an index.
If you try to read or write an element that does not exist, you get an IndexError.
If an index has a negative value, it counts backward from the end of the list.The in operator also works on lists.

>>> cheeses = ['Cheddar', 'Edam', 'Gouda']
>>> 'Edam' in cheeses
>>> 'Brie' in cheeses

== Traversing a list ==
The most common way to traverse the elements of a list is
with a for loop. The syntax is the same as for strings:

for cheese in cheeses:
    print cheese

This works well if you only need to read the elements of the
list. But if you want to write or update the elements, you
need the indices. A common way to do that is to combine
the functions range and len:

for i in range(len(numbers)):
    numbers[i] = numbers[i] * 2

This loop traverses the list and updates each element. len
returns the number of elements in the list. range returns
a list of indices from 0 to n−1, where n is the length of
the list. Each time through the loop i gets the index
of the next element. The assignment statement in the body uses
i to read the old value of the element and to assign the
new value.
A for loop over an empty list never executes the body:

for x in empty:
    print 'This never happens.'

Although a list can contain another list, the nested
list still counts as a single element. The length of this list is

['spam', 1, ['Brie', 'Roquefort', 'Pol le Veq'], [1, 2, 3]]

== List operations ==
The + operator concatenates lists:

>>> a = [1, 2, 3]
>>> b = [4, 5, 6]
>>> c = a + b
>>> print c
[1, 2, 3, 4, 5, 6]

Similarly, the * operator repeats a list a given number of times:

>>> [0] * 4
[0, 0, 0, 0]
>>> [1, 2, 3] * 3
[1, 2, 3, 1, 2, 3, 1, 2, 3]

The first example repeats [0] four times. The second example
repeats the list [1, 2, 3] three times.

== List slices ==
The slice operator also works on lists:

>>> t = ['a', 'b', 'c', 'd', 'e', 'f']
>>> t[1:3]
['b', 'c']
>>> t[:4]
['a', 'b', 'c', 'd']
>>> t[3:]
['d', 'e', 'f']

If you omit the first index, the slice starts at the beginning.
If you omit the second, the slice goes to the end. So if you
omit both, the slice is a copy of the whole list.

>>> t[:]
['a', 'b', 'c', 'd', 'e', 'f']

Since lists are mutable, it is often useful to make a copy
before performing operations that fold, spindle or mutilate
A slice operator on the left side of an assignment
can update multiple elements:

>>> t = ['a', 'b', 'c', 'd', 'e', 'f']
>>> t[1:3] = ['x', 'y']
>>> print t
['a', 'x', 'y', 'd', 'e', 'f']

== List methods ==
Python provides methods that operate on lists. For example,
append adds a new element to the end of a list:

>>> t = ['a', 'b', 'c']
>>> t.append('d')
>>> print t
['a', 'b', 'c', 'd']

extend takes a list as an argument and appends all of
the elements:

>>> t1 = ['a', 'b', 'c']
>>> t2 = ['d', 'e']
>>> t1.extend(t2)
>>> print t1
['a', 'b', 'c', 'd', 'e']

This example leaves t2 unmodified.
sort arranges the elements of the list from low to high:

>>> t = ['d', 'c', 'e', 'b', 'a']
>>> t.sort()
>>> print t
['a', 'b', 'c', 'd', 'e']

List methods are all void; they modify the list and return None.
If you accidentally write t = t.sort(), you will be disappointed
with the result.

== Map, filter and reduce ==
To add up all the numbers in a list, you can use a loop like this:

def add_all(t):
    total = 0
    for x in t:
        total += x
    return total

total is initialized to 0. Each time through the loop,
x gets one element from the list. The += operator
provides a short way to update a variable:

    total += x

is equivalent to:

    total = total + x

As the loop executes, total accumulates the sum of the
elements; a variable used this way is sometimes called an
Adding up the elements of a list is such a common operation
that Python provides it as a built-in function, sum:

>>> t = [1, 2, 3]
>>> sum(t)

An operation like this that combines a sequence of elements into
a single value is sometimes called reduce.
Sometimes you want to traverse one list while building
another. For example, the following function takes a list of strings
and returns a new list that contains capitalized strings:

def capitalize_all(t):
    res = []
    for s in t:
    return res

res is initialized with an empty list; each time through
the loop, we append the next element. So res is another
kind of accumulator.
An operation like capitalize_all is sometimes called a map because it “maps” a function (in this case the method capitalize) onto each of the elements in a sequence.
Another common operation is to select some of the elements from
a list and return a sublist. For example, the following
function takes a list of strings and returns a list that contains
only the uppercase strings:

def only_upper(t):
    res = []
    for s in t:
        if s.isupper():
    return res

isupper is a string method that returns True if
the string contains only upper case letters.
An operation like only_upper is called a filter because
it selects some of the elements and filters out the others.
Most common list operations can be expressed as a combination
of map, filter and reduce. Because these operations are
so common, Python provides language features to support them,
including the built-in function map and an operator
called a “list comprehension.”

=== Exercise 1 ===
Write a function that takes a list of numbers and returns the
cumulative sum; that is, a new list where the 'i'th element
is the sum of the first 'i+1' elements from the original list.
For example, the cumulative sum of '[1, 2, 3]' is
'[1, 3, 6]'.

== Deleting elements ==
There are several ways to delete elements from a list. If you
know the index of the element you want, you can use

>>> t = ['a', 'b', 'c']
>>> x = t.pop(1)
>>> print t
['a', 'c']
>>> print x

pop modifies the list and returns the element that was removed.
If you don’t provide an index, it deletes and returns the
last element.
If you don’t need the removed value, you can use the del

>>> t = ['a', 'b', 'c']
>>> del t[1]
>>> print t
['a', 'c']

If you know the element you want to remove (but not the index), you
can use remove:

>>> t = ['a', 'b', 'c']
>>> t.remove('b')
>>> print t
['a', 'c']

The return value from remove is None.
To remove more than one element, you can use del with
a slice index:

>>> t = ['a', 'b', 'c', 'd', 'e', 'f']
>>> del t[1:5]
>>> print t
['a', 'f']

As usual, the slice selects all the elements up to, but not
including, the second index.

== Lists and strings ==
A string is a sequence of characters and a list is a sequence
of values, but a list of characters is not the same as a
string. To convert from a string to a list of characters,
you can use list:

>>> s = 'spam'
>>> t = list(s)
>>> print t
['s', 'p', 'a', 'm']

Because list is the name of a built-in function, you should
avoid using it as a variable name. I also avoid l because
it looks too much like 1. So that’s why I use t.
The list function breaks a string into individual letters. If
you want to break a string into words, you can use the split

>>> s = 'pining for the fjords'
>>> t = s.split()
>>> print t
['pining', 'for', 'the', 'fjords']

An optional argument called a delimiter specifies which
characters to use as word boundaries. The following example uses a hyphen as a delimiter:

>>> s = 'spam-spam-spam'
>>> delimiter = '-'
>>> s.split(delimiter)
['spam', 'spam', 'spam']

join is the inverse of split. It
takes a list of strings and
concatenates the elements. join is a string method,
so you have to invoke it on the delimiter and pass the
list as a parameter:

>>> t = ['pining', 'for', 'the', 'fjords']
>>> delimiter = ' '
>>> delimiter.join(t)
'pining for the fjords'

In this case the delimiter is a space character, so
join puts a space between words. To concatenate
strings without spaces, you can use the empty string,
, as a delimiter. 

== Objects and values ==
If we execute these assignment statements:

a = 'banana'
b = 'banana'

We know that a and b both refer to a
string, but we don’t
know whether they refer to the same string.
There are two possible states:

In one case, a and b refer to two different objects that
have the same value. In the second case, they refer to the same
To check whether two variables refer to the same object, you can
use the is operator.

>>> a = 'banana'
>>> b = 'banana'
>>> a is b

In this example, Python only created one string object,
and both a and b refer to it.
But when you create two lists, you get two objects:

>>> a = [1, 2, 3]
>>> b = [1, 2, 3]
>>> a is b

So the state diagram looks like this:

In this case we would say that the two lists are equivalent,
because they have the same elements, but not identical, because
they are not the same object. If two objects are identical, they are
also equivalent, but if they are equivalent, they are not necessarily
Until now, we have been using “object” and “value”
interchangeably, but it is more precise to say that an object has a
value. If you execute a = [1,2,3], a refers to a list
object whose value is a particular sequence of elements. If another
list has the same elements, we would say it has the same value.

== Aliasing ==
If a refers to an object and you assign b = a,
then both variables refer to the same object:

>>> a = [1, 2, 3]
>>> b = a
>>> b is a

The state diagram looks like this:

The association of a variable with an object is called a reference. In this example, there are two references to the same
An object with more than one reference has more
than one name, so we say that the object is aliased.
If the aliased object is mutable, 
changes made with one alias affect
the other:

>>> b[0] = 17
>>> print a
[17, 2, 3]

Although this behavior can be useful, it is error-prone. In general,
it is safer to avoid aliasing when you are working with mutable
For immutable objects like strings, aliasing is not as much of a
problem. In this example:

a = 'banana'
b = 'banana'

It almost never makes a difference whether a and b refer
to the same string or not.

== List arguments ==
When you pass a list to a function, the function gets a reference
to the list.
If the function modifies a list parameter, the caller sees the change.
For example, delete_head removes the first element from a list:

def delete_head(t):
    del t[0]

Here’s how it is used:

>>> letters = ['a', 'b', 'c']
>>> delete_head(letters)
>>> print letters
['b', 'c']

The parameter t and the variable letters are
aliases for the same object. The stack diagram looks like

Since the list is shared by two frames, I drew
it between them.
It is important to distinguish between operations that
modify lists and operations that create new lists. For
example, the append method modifies a list, but the
+ operator creates a new list:

>>> t1 = [1, 2]
>>> t2 = t1.append(3)
>>> print t1
[1, 2, 3]
>>> print t2

>>> t3 = t1 + [3]
>>> print t3
[1, 2, 3]
>>> t2 is t3

This difference is important when you write functions that
are supposed to modify lists. For example, this function
does not delete the head of a list:

def bad_delete_head(t):
    t = t[1:]              # WRONG!

The slice operator creates a new list and the assignment
makes t refer to it, but none of that has any effect
on the list that was passed as an argument.
An alternative is to write a function that creates and
returns a new list. For
example, tail returns all but the first
element of a list:

def tail(t):
    return t[1:]

This function leaves the original list unmodified.
Here’s how it is used:

>>> letters = ['a', 'b', 'c']
>>> rest = tail(letters)
>>> print rest
['b', 'c']

=== Exercise 2 ===
Write a function called 'chop' that takes a list and modifies
it, removing the first and last elements, and returns 'None'.
Then write a function called 'middle' that takes a list and
returns a new list that contains all but the first and last

== Debugging ==
Careless use of lists (and other mutable objects) can lead to long hours of debugging. Here are some common pitfalls and ways to avoid them:

Don’t forget that most list methods modify the argument andreturn None. This is the opposite of the string methods,
which return a new string and leave the original alone.
If you are used to writing string code like this:

word = word.strip()

It is tempting to write list code like this:

t = t.sort()           # WRONG!

Because sort returns None, the
next operation you perform with t is likely to fail.
Before using list methods and operators, you should read the
documentation carefully and then test them in interactive mode. The
methods and operators that lists share with other sequences (like
strings) are documented at
docs.python.org/lib/typesseq.html. The
methods and operators that only apply to mutable sequences
are documented at docs.python.org/lib/typesseq-mutable.html.

Pick an idiom and stick with it.Part of the problem with lists is that there are too many
ways to do things. For example, to remove an element from
a list, you can use pop, remove, del,
or even a slice assignment.
To add an element, you can use the append method or
the + operator. But don’t forget that these are right: 

t = t + [x]

And these are wrong:

t.append([x])          # WRONG!
t = t.append(x)        # WRONG!
t + [x]                # WRONG!
t = t + x              # WRONG!

Try out each of these examples in interactive mode to make sure
you understand what they do. Notice that only the last
one causes a runtime error; the other three are legal, but they
do the wrong thing.

Make copies to avoid aliasing.If you want to use a method like sort that modifies
the argument, but you need to keep the original list as
well, you can make a copy.

orig = t[:]

In this example you could also use the built-in function sorted,
which returns a new, sorted list and leaves the original alone.
But in that case you should avoid using sorted as a variable

== Glossary ==
list: A sequence of values.
element: One of the values in a list (or other sequence),
also called items.
index: An integer value that indicates an element in a list.
nested list: A list that is an element of another list.
list traversal: The sequential accessing of each element in a list.
mapping: A relationship in which each element of one set
corresponds to an element of another set. For example, a list is
a mapping from indices to elements.
accumulator: A variable used in a loop to add up or
accumulate a result.

reduce: A processing pattern that traverses a sequence 
and accumulates the elements into a single result.

map: A processing pattern that traverses a sequence and
performs an operation on each element.

filter: A processing pattern that traverses a list and
selects the elements that satisfy some criterion.

object: Something a variable can refer to. An object
has a type and a value.
equivalent: Having the same value.
identical: Being the same object (which implies equivalence).
reference: The association between a variable and its value.
aliasing: A circumstance where two variables refer to the same
delimiter: A character or string used to indicate where a
string should be split.

== Exercises ==

=== Exercise 3 ===
Write a function called is_sorted that takes a list as a
parameter and returns 'True' if the list is sorted in ascending
order and 'False' otherwise. You can assume (as a precondition)
that the elements of the list can be compared with the comparison
operators '<', '>', etc.
For example, is_sorted([1,2,2]) should return 'True'
and is_sorted(['b','a']) should return 'False'.

=== Exercise 4 ===
Two words are anagrams if you can rearrange the letters from one
to spell the other. Write a function called is_anagram
that takes two strings and returns 'True' if they are anagrams.

1This exercise is inspired by an example at