^^&&^^

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 <div class="section" id="data-structures">
<h1>5. Data Structures<a class="headerlink" href="#data-structures" title="Permalink to this headline">¶</a></h1>
This chapter describes some things you&#8217;ve learned about already in more detail,
and adds some new things as well.
<div class="section" id="more-on-lists">
<h2>5.1. More on Lists<a class="headerlink" href="#more-on-lists" title="Permalink to this headline">¶</a></h2>
The list data type has some more methods. Here are all of the methods of list
objects:
<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">append</tt><big>(</big>x<big>)</big></dt>
<dd>Add an item to the end of the list; equivalent to <tt class="docutils literal">a[len(a):] = [x]</tt>.
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">extend</tt><big>(</big>L<big>)</big></dt>
<dd>Extend the list by appending all the items in the given list; equivalent to
<tt class="docutils literal">a[len(a):] = L</tt>.
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">insert</tt><big>(</big>i, x<big>)</big></dt>
<dd>Insert an item at a given position. The first argument is the index of the
element before which to insert, so <tt class="docutils literal">a.insert(0, x)</tt> inserts at the front of
the list, and <tt class="docutils literal">a.insert(len(a), x)</tt> is equivalent to <tt class="docutils literal">a.append(x)</tt>.
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">remove</tt><big>(</big>x<big>)</big></dt>
<dd>Remove the first item from the list whose value is x. It is an error if there
is no such item.
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">pop</tt><big>(</big>[i]<big>)</big></dt>
<dd>Remove the item at the given position in the list, and return it. If no index
is specified, <tt class="docutils literal">a.pop()</tt> removes and returns the last item in 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.)
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">index</tt><big>(</big>x<big>)</big></dt>
<dd>Return the index in the list of the first item whose value is x. It is an
error if there is no such item.
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">count</tt><big>(</big>x<big>)</big></dt>
<dd>Return the number of times x appears in the list.
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">sort</tt><big>(</big><big>)</big></dt>
<dd>Sort the items of the list, in place.
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">reverse</tt><big>(</big><big>)</big></dt>
<dd>Reverse the elements of the list, in place.
</dd></dl>

An example that uses most of the list methods:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; a = [66.25, 333, 333, 1, 1234.5]
&gt;&gt;&gt; print a.count(333), a.count(66.25), a.count(&#39;x&#39;)
2 1 0
&gt;&gt;&gt; a.insert(2, -1)
&gt;&gt;&gt; a.append(333)
&gt;&gt;&gt; a
[66.25, 333, -1, 333, 1, 1234.5, 333]
&gt;&gt;&gt; a.index(333)
1
&gt;&gt;&gt; a.remove(333)
&gt;&gt;&gt; a
[66.25, -1, 333, 1, 1234.5, 333]
&gt;&gt;&gt; a.reverse()
&gt;&gt;&gt; a
[333, 1234.5, 1, 333, -1, 66.25]
&gt;&gt;&gt; a.sort()
&gt;&gt;&gt; a
[-1, 1, 66.25, 333, 333, 1234.5]
</pre></div>
</div>
<div class="section" id="using-lists-as-stacks">
<h3>5.1.1. Using Lists as Stacks<a class="headerlink" href="#using-lists-as-stacks" title="Permalink to this headline">¶</a></h3>
The list methods make it very easy to use a list as a stack, where the last
element added is the first element retrieved (&#8220;last-in, first-out&#8221;). To add an
item to the top of the stack, use <tt class="xref py py-meth docutils literal">append()</tt>. To retrieve an item from the
top of the stack, use <tt class="xref py py-meth docutils literal">pop()</tt> without an explicit index. For example:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; stack = [3, 4, 5]
&gt;&gt;&gt; stack.append(6)
&gt;&gt;&gt; stack.append(7)
&gt;&gt;&gt; stack
[3, 4, 5, 6, 7]
&gt;&gt;&gt; stack.pop()
7
&gt;&gt;&gt; stack
[3, 4, 5, 6]
&gt;&gt;&gt; stack.pop()
6
&gt;&gt;&gt; stack.pop()
5
&gt;&gt;&gt; stack
[3, 4]
</pre></div>
</div>
</div>
<div class="section" id="using-lists-as-queues">
<h3>5.1.2. Using Lists as Queues<a class="headerlink" href="#using-lists-as-queues" title="Permalink to this headline">¶</a></h3>
It is also possible to use a list as a queue, where the first element added is
the first element retrieved (&#8220;first-in, first-out&#8221;); however, lists are not
efficient for this purpose. While appends and pops from the end of list are
fast, doing inserts or pops from the beginning of a list is slow (because all
of the other elements have to be shifted by one).
To implement a queue, use <a class="reference internal" href="../library/collections.html#collections.deque" title="collections.deque"><tt class="xref py py-class docutils literal">collections.deque</tt></a> which was designed to
have fast appends and pops from both ends. For example:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; from collections import deque
&gt;&gt;&gt; queue = deque([&quot;Eric&quot;, &quot;John&quot;, &quot;Michael&quot;])
&gt;&gt;&gt; queue.append(&quot;Terry&quot;) # Terry arrives
&gt;&gt;&gt; queue.append(&quot;Graham&quot;) # Graham arrives
&gt;&gt;&gt; queue.popleft() # The first to arrive now leaves
&#39;Eric&#39;
&gt;&gt;&gt; queue.popleft() # The second to arrive now leaves
&#39;John&#39;
&gt;&gt;&gt; queue # Remaining queue in order of arrival
deque([&#39;Michael&#39;, &#39;Terry&#39;, &#39;Graham&#39;])
</pre></div>
</div>
</div>
<div class="section" id="functional-programming-tools">
<h3>5.1.3. Functional Programming Tools<a class="headerlink" href="#functional-programming-tools" title="Permalink to this headline">¶</a></h3>
There are three built-in functions that are very useful when used with lists:
<a class="reference internal" href="../library/functions.html#filter" title="filter"><tt class="xref py py-func docutils literal">filter()</tt></a>, <a class="reference internal" href="../library/functions.html#map" title="map"><tt class="xref py py-func docutils literal">map()</tt></a>, and <a class="reference internal" href="../library/functions.html#reduce" title="reduce"><tt class="xref py py-func docutils literal">reduce()</tt></a>.
<tt class="docutils literal">filter(function, sequence)</tt> returns a sequence consisting of those items from
the sequence for which <tt class="docutils literal">function(item)</tt> is true. If sequence is a
<a class="reference internal" href="../library/string.html#module-string" title="string: Common string operations."><tt class="xref py py-class docutils literal">string</tt></a> or <a class="reference internal" href="../library/functions.html#tuple" title="tuple"><tt class="xref py py-class docutils literal">tuple</tt></a>, the result will be of the same type;
otherwise, it is always a <a class="reference internal" href="../library/functions.html#list" title="list"><tt class="xref py py-class docutils literal">list</tt></a>. For example, to compute a sequence of
numbers not divisible by 2 and 3:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def f(x): return x % 2 != 0 and x % 3 != 0
...
&gt;&gt;&gt; filter(f, range(2, 25))
[5, 7, 11, 13, 17, 19, 23]
</pre></div>
</div>
<tt class="docutils literal">map(function, sequence)</tt> calls <tt class="docutils literal">function(item)</tt> for each of the sequence&#8217;s
items and returns a list of the return values. For example, to compute some
cubes:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def cube(x): return x*x*x
...
&gt;&gt;&gt; map(cube, range(1, 11))
[1, 8, 27, 64, 125, 216, 343, 512, 729, 1000]
</pre></div>
</div>
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 <tt class="docutils literal">None</tt> if some sequence is shorter than another). For
example:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; seq = range(8)
&gt;&gt;&gt; def add(x, y): return x+y
...
&gt;&gt;&gt; map(add, seq, seq)
[0, 2, 4, 6, 8, 10, 12, 14]
</pre></div>
</div>
<tt class="docutils literal">reduce(function, sequence)</tt> returns a single value constructed by calling the
binary function function 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:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def add(x,y): return x+y
...
&gt;&gt;&gt; reduce(add, range(1, 11))
55
</pre></div>
</div>
If there&#8217;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,
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def sum(seq):
... def add(x,y): return x+y
... return reduce(add, seq, 0)
...
&gt;&gt;&gt; sum(range(1, 11))
55
&gt;&gt;&gt; sum([])
0
</pre></div>
</div>
Don&#8217;t use this example&#8217;s definition of <a class="reference internal" href="../library/functions.html#sum" title="sum"><tt class="xref py py-func docutils literal">sum()</tt></a>: since summing numbers is
such a common need, a built-in function <tt class="docutils literal">sum(sequence)</tt> is already provided,
and works exactly like this.
</div>
<div class="section" id="list-comprehensions">
<h3>5.1.4. List Comprehensions<a class="headerlink" href="#list-comprehensions" title="Permalink to this headline">¶</a></h3>
List comprehensions provide a concise way to create lists.
Common applications are to make new lists where each element is the result of
some operations applied to each member of another sequence or iterable, or to
create a subsequence of those elements that satisfy a certain condition.
For example, assume we want to create a list of squares, like:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; squares = []
&gt;&gt;&gt; for x in range(10):
... squares.append(x**2)
...
&gt;&gt;&gt; squares
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
</pre></div>
</div>
We can obtain the same result with:
<div class="highlight-python"><div class="highlight"><pre>squares = [x**2 for x in range(10)]
</pre></div>
</div>
This is also equivalent to <tt class="docutils literal">squares = map(lambda x: x**2, range(10))</tt>,
but it&#8217;s more concise and readable.
A list comprehension consists of brackets containing an expression followed
by a <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal">for</tt></a> clause, then zero or more <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal">for</tt></a> or <a class="reference internal" href="../reference/compound_stmts.html#if"><tt class="xref std std-keyword docutils literal">if</tt></a>
clauses. The result will be a new list resulting from evaluating the expression
in the context of the <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal">for</tt></a> and <a class="reference internal" href="../reference/compound_stmts.html#if"><tt class="xref std std-keyword docutils literal">if</tt></a> clauses which follow it.
For example, this listcomp combines the elements of two lists if they are not
equal:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; [(x, y) for x in [1,2,3] for y in [3,1,4] if x != y]
[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]
</pre></div>
</div>
and it&#8217;s equivalent to:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; combs = []
&gt;&gt;&gt; for x in [1,2,3]:
... for y in [3,1,4]:
... if x != y:
... combs.append((x, y))
...
&gt;&gt;&gt; combs
[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]
</pre></div>
</div>
Note how the order of the <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal">for</tt></a> and <a class="reference internal" href="../reference/compound_stmts.html#if"><tt class="xref std std-keyword docutils literal">if</tt></a> statements is the
same in both these snippets.
If the expression is a tuple (e.g. the <tt class="docutils literal">(x, y)</tt> in the previous example),
it must be parenthesized.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; vec = [-4, -2, 0, 2, 4]
&gt;&gt;&gt; # create a new list with the values doubled
&gt;&gt;&gt; [x*2 for x in vec]
[-8, -4, 0, 4, 8]
&gt;&gt;&gt; # filter the list to exclude negative numbers
&gt;&gt;&gt; [x for x in vec if x &gt;= 0]
[0, 2, 4]
&gt;&gt;&gt; # apply a function to all the elements
&gt;&gt;&gt; [abs(x) for x in vec]
[4, 2, 0, 2, 4]
&gt;&gt;&gt; # call a method on each element
&gt;&gt;&gt; freshfruit = [&#39; banana&#39;, &#39; loganberry &#39;, &#39;passion fruit &#39;]
&gt;&gt;&gt; [weapon.strip() for weapon in freshfruit]
[&#39;banana&#39;, &#39;loganberry&#39;, &#39;passion fruit&#39;]
&gt;&gt;&gt; # create a list of 2-tuples like (number, square)
&gt;&gt;&gt; [(x, x**2) for x in range(6)]
[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)]
&gt;&gt;&gt; # the tuple must be parenthesized, otherwise an error is raised
&gt;&gt;&gt; [x, x**2 for x in range(6)]
 File &quot;&lt;stdin&gt;&quot;, line 1
 [x, x**2 for x in range(6)]
 ^
SyntaxError: invalid syntax
&gt;&gt;&gt; # flatten a list using a listcomp with two &#39;for&#39;
&gt;&gt;&gt; vec = [[1,2,3], [4,5,6], [7,8,9]]
&gt;&gt;&gt; [num for elem in vec for num in elem]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
</pre></div>
</div>
List comprehensions can contain complex expressions and nested functions:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; from math import pi
&gt;&gt;&gt; [str(round(pi, i)) for i in range(1, 6)]
[&#39;3.1&#39;, &#39;3.14&#39;, &#39;3.142&#39;, &#39;3.1416&#39;, &#39;3.14159&#39;]
</pre></div>
</div>
<div class="section" id="nested-list-comprehensions">
<h4>5.1.4.1. Nested List Comprehensions<a class="headerlink" href="#nested-list-comprehensions" title="Permalink to this headline">¶</a></h4>
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 of
3 lists of length 4:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; matrix = [
... [1, 2, 3, 4],
... [5, 6, 7, 8],
... [9, 10, 11, 12],
... ]
</pre></div>
</div>
The following list comprehension will transpose rows and columns:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; [[row[i] for row in matrix] for i in range(4)]
[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]
</pre></div>
</div>
As we saw in the previous section, the nested listcomp is evaluated in
the context of the <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal">for</tt></a> that follows it, so this example is
equivalent to:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; transposed = []
&gt;&gt;&gt; for i in range(4):
... transposed.append([row[i] for row in matrix])
...
&gt;&gt;&gt; transposed
[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]
</pre></div>
</div>
which, in turn, is the same as:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; transposed = []
&gt;&gt;&gt; for i in range(4):
... # the following 3 lines implement the nested listcomp
... transposed_row = []
... for row in matrix:
... transposed_row.append(row[i])
... transposed.append(transposed_row)
...
&gt;&gt;&gt; transposed
[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]
</pre></div>
</div>
In the real world, you should prefer built-in functions to complex flow statements.
The <a class="reference internal" href="../library/functions.html#zip" title="zip"><tt class="xref py py-func docutils literal">zip()</tt></a> function would do a great job for this use case:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; zip(*matrix)
[(1, 5, 9), (2, 6, 10), (3, 7, 11), (4, 8, 12)]
</pre></div>
</div>
See <a class="reference internal" href="controlflow.html#tut-unpacking-arguments">Unpacking Argument Lists</a> for details on the asterisk in this line.
</div>
</div>
</div>
<div class="section" id="the-del-statement">
<h2>5.2. The <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal">del</tt></a> statement<a class="headerlink" href="#the-del-statement" title="Permalink to this headline">¶</a></h2>
There is a way to remove an item from a list given its index instead of its
value: the <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal">del</tt></a> statement. This differs from the <tt class="xref py py-meth docutils literal">pop()</tt> method
which returns a value. The <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal">del</tt></a> statement can also be used to remove
slices from a list or clear the entire list (which we did earlier by assignment
of an empty list to the slice). For example:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; a = [-1, 1, 66.25, 333, 333, 1234.5]
&gt;&gt;&gt; del a[0]
&gt;&gt;&gt; a
[1, 66.25, 333, 333, 1234.5]
&gt;&gt;&gt; del a[2:4]
&gt;&gt;&gt; a
[1, 66.25, 1234.5]
&gt;&gt;&gt; del a[:]
&gt;&gt;&gt; a
[]
</pre></div>
</div>
<a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal">del</tt></a> can also be used to delete entire variables:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; del a
</pre></div>
</div>
Referencing the name <tt class="docutils literal">a</tt> hereafter is an error (at least until another value
is assigned to it). We&#8217;ll find other uses for <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal">del</tt></a> later.
</div>
<div class="section" id="tuples-and-sequences">
<h2>5.3. Tuples and Sequences<a class="headerlink" href="#tuples-and-sequences" title="Permalink to this headline">¶</a></h2>
We saw that lists and strings have many common properties, such as indexing and
slicing operations. They are two examples of sequence data types (see
<a class="reference internal" href="../library/stdtypes.html#typesseq">Sequence Types &#8212; str, unicode, list, tuple, bytearray, buffer, xrange</a>). 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:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; t = 12345, 54321, &#39;hello!&#39;
&gt;&gt;&gt; t[0]
12345
&gt;&gt;&gt; t
(12345, 54321, &#39;hello!&#39;)
&gt;&gt;&gt; # Tuples may be nested:
... u = t, (1, 2, 3, 4, 5)
&gt;&gt;&gt; u
((12345, 54321, &#39;hello!&#39;), (1, 2, 3, 4, 5))
&gt;&gt;&gt; # Tuples are immutable:
... t[0] = 88888
Traceback (most recent call last):
 File &quot;&lt;stdin&gt;&quot;, line 1, in &lt;module&gt;
TypeError: &#39;tuple&#39; object does not support item assignment
&gt;&gt;&gt; # but they can contain mutable objects:
... v = ([1, 2, 3], [3, 2, 1])
&gt;&gt;&gt; v
([1, 2, 3], [3, 2, 1])
</pre></div>
</div>
As you see, on output tuples are always 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). It is not possible to assign to the individual
items of a tuple, however it is possible to create tuples which contain mutable
objects, such as lists.
Though tuples may seem similar to lists, they are often used in different
situations and for different purposes.
Tuples are <a class="reference internal" href="../glossary.html#term-immutable">immutable</a>, and usually contain an heterogeneous sequence of
elements that are accessed via unpacking (see later in this section) or indexing
(or even by attribute in the case of <a class="reference internal" href="../library/collections.html#collections.namedtuple" title="collections.namedtuple"><tt class="xref py py-func docutils literal">namedtuples</tt></a>).
Lists are <a class="reference internal" href="../glossary.html#term-mutable">mutable</a>, and their elements are usually homogeneous and are
accessed by iterating over the list.
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:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; empty = ()
&gt;&gt;&gt; singleton = &#39;hello&#39;, # &lt;-- note trailing comma
&gt;&gt;&gt; len(empty)
0
&gt;&gt;&gt; len(singleton)
1
&gt;&gt;&gt; singleton
(&#39;hello&#39;,)
</pre></div>
</div>
The statement <tt class="docutils literal">t = 12345, 54321, 'hello!'</tt> is an example of tuple packing:
the values <tt class="docutils literal">12345</tt>, <tt class="docutils literal">54321</tt> and <tt class="docutils literal">'hello!'</tt> are packed together in a tuple.
The reverse operation is also possible:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; x, y, z = t
</pre></div>
</div>
This is called, appropriately enough, sequence unpacking and works for any
sequence on the right-hand side. Sequence unpacking requires the list of
variables on the left to 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.
</div>
<div class="section" id="sets">
<h2>5.4. Sets<a class="headerlink" href="#sets" title="Permalink to this headline">¶</a></h2>
Python also includes a data type for sets. A set is an unordered collection
with no duplicate elements. Basic uses include membership testing and
eliminating duplicate entries. Set objects also support mathematical operations
like union, intersection, difference, and symmetric difference.
Curly braces or the <a class="reference internal" href="../library/stdtypes.html#set" title="set"><tt class="xref py py-func docutils literal">set()</tt></a> function can be used to create sets. Note: to
create an empty set you have to use <tt class="docutils literal">set()</tt>, not <tt class="docutils literal">{}</tt>; the latter creates an
empty dictionary, a data structure that we discuss in the next section.
Here is a brief demonstration:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; basket = [&#39;apple&#39;, &#39;orange&#39;, &#39;apple&#39;, &#39;pear&#39;, &#39;orange&#39;, &#39;banana&#39;]
&gt;&gt;&gt; fruit = set(basket) # create a set without duplicates
&gt;&gt;&gt; fruit
set([&#39;orange&#39;, &#39;pear&#39;, &#39;apple&#39;, &#39;banana&#39;])
&gt;&gt;&gt; &#39;orange&#39; in fruit # fast membership testing
True
&gt;&gt;&gt; &#39;crabgrass&#39; in fruit
False

&gt;&gt;&gt; # Demonstrate set operations on unique letters from two words
...
&gt;&gt;&gt; a = set(&#39;abracadabra&#39;)
&gt;&gt;&gt; b = set(&#39;alacazam&#39;)
&gt;&gt;&gt; a # unique letters in a
set([&#39;a&#39;, &#39;r&#39;, &#39;b&#39;, &#39;c&#39;, &#39;d&#39;])
&gt;&gt;&gt; a - b # letters in a but not in b
set([&#39;r&#39;, &#39;d&#39;, &#39;b&#39;])
&gt;&gt;&gt; a | b # letters in either a or b
set([&#39;a&#39;, &#39;c&#39;, &#39;r&#39;, &#39;d&#39;, &#39;b&#39;, &#39;m&#39;, &#39;z&#39;, &#39;l&#39;])
&gt;&gt;&gt; a &amp; b # letters in both a and b
set([&#39;a&#39;, &#39;c&#39;])
&gt;&gt;&gt; a ^ b # letters in a or b but not both
set([&#39;r&#39;, &#39;d&#39;, &#39;b&#39;, &#39;m&#39;, &#39;z&#39;, &#39;l&#39;])
</pre></div>
</div>
Similarly to <a class="reference internal" href="#tut-listcomps">list comprehensions</a>, set comprehensions
are also supported:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; a = {x for x in &#39;abracadabra&#39; if x not in &#39;abc&#39;}
&gt;&gt;&gt; a
set([&#39;r&#39;, &#39;d&#39;])
</pre></div>
</div>
</div>
<div class="section" id="dictionaries">
<h2>5.5. Dictionaries<a class="headerlink" href="#dictionaries" title="Permalink to this headline">¶</a></h2>
Another useful data type built into Python is the dictionary (see
<a class="reference internal" href="../library/stdtypes.html#typesmapping">Mapping Types &#8212; dict</a>). Dictionaries are sometimes found in other languages as
&#8220;associative memories&#8221; or &#8220;associative arrays&#8221;. 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&#8217;t use lists as keys, since lists can be modified in place using index
assignments, slice assignments, or methods like <tt class="xref py py-meth docutils literal">append()</tt> and
<tt class="xref py py-meth docutils literal">extend()</tt>.
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: <tt class="docutils literal">{}</tt>. 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 <tt class="docutils literal">del</tt>. 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 <tt class="xref py py-meth docutils literal">keys()</tt> method of a dictionary object returns a list of all the keys
used in the dictionary, in arbitrary order (if you want it sorted, just apply
the <a class="reference internal" href="../library/functions.html#sorted" title="sorted"><tt class="xref py py-func docutils literal">sorted()</tt></a> function to it). To check whether a single key is in the
dictionary, use the <a class="reference internal" href="../reference/expressions.html#in"><tt class="xref std std-keyword docutils literal">in</tt></a> keyword.
Here is a small example using a dictionary:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; tel = {&#39;jack&#39;: 4098, &#39;sape&#39;: 4139}
&gt;&gt;&gt; tel[&#39;guido&#39;] = 4127
&gt;&gt;&gt; tel
{&#39;sape&#39;: 4139, &#39;guido&#39;: 4127, &#39;jack&#39;: 4098}
&gt;&gt;&gt; tel[&#39;jack&#39;]
4098
&gt;&gt;&gt; del tel[&#39;sape&#39;]
&gt;&gt;&gt; tel[&#39;irv&#39;] = 4127
&gt;&gt;&gt; tel
{&#39;guido&#39;: 4127, &#39;irv&#39;: 4127, &#39;jack&#39;: 4098}
&gt;&gt;&gt; tel.keys()
[&#39;guido&#39;, &#39;irv&#39;, &#39;jack&#39;]
&gt;&gt;&gt; &#39;guido&#39; in tel
True
</pre></div>
</div>
The <a class="reference internal" href="../library/stdtypes.html#dict" title="dict"><tt class="xref py py-func docutils literal">dict()</tt></a> constructor builds dictionaries directly from sequences of
key-value pairs:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; dict([(&#39;sape&#39;, 4139), (&#39;guido&#39;, 4127), (&#39;jack&#39;, 4098)])
{&#39;sape&#39;: 4139, &#39;jack&#39;: 4098, &#39;guido&#39;: 4127}
</pre></div>
</div>
In addition, dict comprehensions can be used to create dictionaries from
arbitrary key and value expressions:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; {x: x**2 for x in (2, 4, 6)}
{2: 4, 4: 16, 6: 36}
</pre></div>
</div>
When the keys are simple strings, it is sometimes easier to specify pairs using
keyword arguments:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; dict(sape=4139, guido=4127, jack=4098)
{&#39;sape&#39;: 4139, &#39;jack&#39;: 4098, &#39;guido&#39;: 4127}
</pre></div>
</div>
</div>
<div class="section" id="looping-techniques">
<h2>5.6. Looping Techniques<a class="headerlink" href="#looping-techniques" title="Permalink to this headline">¶</a></h2>
When looping through a sequence, the position index and corresponding value can
be retrieved at the same time using the <a class="reference internal" href="../library/functions.html#enumerate" title="enumerate"><tt class="xref py py-func docutils literal">enumerate()</tt></a> function.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; for i, v in enumerate([&#39;tic&#39;, &#39;tac&#39;, &#39;toe&#39;]):
... print i, v
...
0 tic
1 tac
2 toe
</pre></div>
</div>
To loop over two or more sequences at the same time, the entries can be paired
with the <a class="reference internal" href="../library/functions.html#zip" title="zip"><tt class="xref py py-func docutils literal">zip()</tt></a> function.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; questions = [&#39;name&#39;, &#39;quest&#39;, &#39;favorite color&#39;]
&gt;&gt;&gt; answers = [&#39;lancelot&#39;, &#39;the holy grail&#39;, &#39;blue&#39;]
&gt;&gt;&gt; for q, a in zip(questions, answers):
... print &#39;What is your {0}? It is {1}.&#39;.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.
</pre></div>
</div>
To loop over a sequence in reverse, first specify the sequence in a forward
direction and then call the <a class="reference internal" href="../library/functions.html#reversed" title="reversed"><tt class="xref py py-func docutils literal">reversed()</tt></a> function.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; for i in reversed(xrange(1,10,2)):
... print i
...
9
7
5
3
1
</pre></div>
</div>
To loop over a sequence in sorted order, use the <a class="reference internal" href="../library/functions.html#sorted" title="sorted"><tt class="xref py py-func docutils literal">sorted()</tt></a> function which
returns a new sorted list while leaving the source unaltered.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; basket = [&#39;apple&#39;, &#39;orange&#39;, &#39;apple&#39;, &#39;pear&#39;, &#39;orange&#39;, &#39;banana&#39;]
&gt;&gt;&gt; for f in sorted(set(basket)):
... print f
...
apple
banana
orange
pear
</pre></div>
</div>
When looping through dictionaries, the key and corresponding value can be
retrieved at the same time using the <tt class="xref py py-meth docutils literal">iteritems()</tt> method.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; knights = {&#39;gallahad&#39;: &#39;the pure&#39;, &#39;robin&#39;: &#39;the brave&#39;}
&gt;&gt;&gt; for k, v in knights.iteritems():
... print k, v
...
gallahad the pure
robin the brave
</pre></div>
</div>
To change a sequence you are iterating over while inside the loop (for
example to duplicate certain items), it is recommended that you first make
a copy. Looping over a sequence does not implicitly make a copy. The slice
notation makes this especially convenient:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; words = [&#39;cat&#39;, &#39;window&#39;, &#39;defenestrate&#39;]
&gt;&gt;&gt; for w in words[:]: # Loop over a slice copy of the entire list.
... if len(w) &gt; 6:
... words.insert(0, w)
...
&gt;&gt;&gt; words
[&#39;defenestrate&#39;, &#39;cat&#39;, &#39;window&#39;, &#39;defenestrate&#39;]
</pre></div>
</div>
</div>
<div class="section" id="more-on-conditions">
<h2>5.7. More on Conditions<a class="headerlink" href="#more-on-conditions" title="Permalink to this headline">¶</a></h2>
The conditions used in <tt class="docutils literal">while</tt> and <tt class="docutils literal">if</tt> statements can contain any
operators, not just comparisons.
The comparison operators <tt class="docutils literal">in</tt> and <tt class="docutils literal">not in</tt> check whether a value occurs
(does not occur) in a sequence. The operators <tt class="docutils literal">is</tt> and <tt class="docutils literal">is not</tt> 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, <tt class="docutils literal">a &lt; b == c</tt> tests whether <tt class="docutils literal">a</tt> is
less than <tt class="docutils literal">b</tt> and moreover <tt class="docutils literal">b</tt> equals <tt class="docutils literal">c</tt>.
Comparisons may be combined using the Boolean operators <tt class="docutils literal">and</tt> and <tt class="docutils literal">or</tt>, and
the outcome of a comparison (or of any other Boolean expression) may be negated
with <tt class="docutils literal">not</tt>. These have lower priorities than comparison operators; between
them, <tt class="docutils literal">not</tt> has the highest priority and <tt class="docutils literal">or</tt> the lowest, so that <tt class="docutils literal">A and
not B or C</tt> is equivalent to <tt class="docutils literal">(A and (not B)) or C</tt>. As always, parentheses
can be used to express the desired composition.
The Boolean operators <tt class="docutils literal">and</tt> and <tt class="docutils literal">or</tt> 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 <tt class="docutils literal">A</tt> and <tt class="docutils literal">C</tt> are
true but <tt class="docutils literal">B</tt> is false, <tt class="docutils literal">A and B and C</tt> does not evaluate the expression
<tt class="docutils literal">C</tt>. When used as a general value and not as a Boolean, the return value of a
short-circuit operator is the last evaluated argument.
It is possible to assign the result of a comparison or other Boolean expression
to a variable. For example,
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; string1, string2, string3 = &#39;&#39;, &#39;Trondheim&#39;, &#39;Hammer Dance&#39;
&gt;&gt;&gt; non_null = string1 or string2 or string3
&gt;&gt;&gt; non_null
&#39;Trondheim&#39;
</pre></div>
</div>
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 <tt class="docutils literal">=</tt> in an expression when <tt class="docutils literal">==</tt> was
intended.
</div>
<div class="section" id="comparing-sequences-and-other-types">
<h2>5.8. Comparing Sequences and Other Types<a class="headerlink" href="#comparing-sequences-and-other-types" title="Permalink to this headline">¶</a></h2>
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 of the same type:
<div class="highlight-python"><div class="highlight"><pre>(1, 2, 3) &lt; (1, 2, 4)
[1, 2, 3] &lt; [1, 2, 4]
&#39;ABC&#39; &lt; &#39;C&#39; &lt; &#39;Pascal&#39; &lt; &#39;Python&#39;
(1, 2, 3, 4) &lt; (1, 2, 4)
(1, 2) &lt; (1, 2, -1)
(1, 2, 3) == (1.0, 2.0, 3.0)
(1, 2, (&#39;aa&#39;, &#39;ab&#39;)) &lt; (1, 2, (&#39;abc&#39;, &#39;a&#39;), 4)
</pre></div>
</div>
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.
<a class="footnote-reference" href="#id2" id="id1">[1]</a> Mixed numeric types are compared according to their numeric value, so 0
equals 0.0, etc.
Footnotes
<table class="docutils footnote" frame="void" id="id2" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[1]</a></td><td>The rules for comparing objects of different types should not be relied upon;
they may change in a future version of the language.</td></tr>
</tbody>
</table>
</div>
</div>

</div>
 </div>
 </div>
 <div class="sphinxsidebar">
 <div class="sphinxsidebarwrapper">
 <h3><a href="../contents.html">Table Of Contents</a></h3>
 <ul>
<li><a class="reference internal" href="#">5. Data Structures</a><ul>
<li><a class="reference internal" href="#more-on-lists">5.1. More on Lists</a><ul>
<li><a class="reference internal" href="#using-lists-as-stacks">5.1.1. Using Lists as Stacks</a></li>
<li><a class="reference internal" href="#using-lists-as-queues">5.1.2. Using Lists as Queues</a></li>
<li><a class="reference internal" href="#functional-programming-tools">5.1.3. Functional Programming Tools</a></li>
<li><a class="reference internal" href="#list-comprehensions">5.1.4. List Comprehensions</a><ul>
<li><a class="reference internal" href="#nested-list-comprehensions">5.1.4.1. Nested List Comprehensions</a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#the-del-statement">5.2. The <tt class="docutils literal">del</tt> statement</a></li>
<li><a class="reference internal" href="#tuples-and-sequences">5.3. Tuples and Sequences</a></li>
<li><a class="reference internal" href="#sets">5.4. Sets</a></li>
<li><a class="reference internal" href="#dictionaries">5.5. Dictionaries</a></li>
<li><a class="reference internal" href="#looping-techniques">5.6. Looping Techniques</a></li>
<li><a class="reference internal" href="#more-on-conditions">5.7. More on Conditions</a></li>
<li><a class="reference internal" href="#comparing-sequences-and-other-types">5.8. Comparing Sequences and Other Types</a></li>
</ul>
</li>
</ul>

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