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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’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>
<code class="descclassname">list.</code><code class="descname">append</code>(x)</dt>
<dd>Add an item to the end of the list. Equivalent to <code class="docutils literal notranslate">a[len(a):] = [x]</code>.
</dd></dl>

<dl class="method">
<dt>
<code class="descclassname">list.</code><code class="descname">extend</code>(iterable)</dt>
<dd>Extend the list by appending all the items from the iterable. Equivalent to
<code class="docutils literal notranslate">a[len(a):] = iterable</code>.
</dd></dl>

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

<dl class="method">
<dt>
<code class="descclassname">list.</code><code class="descname">remove</code>(x)</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>
<code class="descclassname">list.</code><code class="descname">pop</code>([i])</dt>
<dd>Remove the item at the given position in the list, and return it. If no index
is specified, <code class="docutils literal notranslate">a.pop()</code> 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>
<code class="descclassname">list.</code><code class="descname">clear</code>()</dt>
<dd>Remove all items from the list. Equivalent to <code class="docutils literal notranslate">del a[:]</code>.
</dd></dl>

<dl class="method">
<dt>
<code class="descclassname">list.</code><code class="descname">index</code>(x[, start[, end]])</dt>
<dd>Return zero-based index in the list of the first item whose value is x.
Raises a <a class="reference internal" href="../library/exceptions.html#ValueError" title="ValueError"><code class="xref py py-exc docutils literal notranslate">ValueError</code></a> if there is no such item.
The optional arguments start and end are interpreted as in the slice
notation and are used to limit the search to a particular subsequence of
the list. The returned index is computed relative to the beginning of the full
sequence rather than the start argument.
</dd></dl>

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

<dl class="method">
<dt>
<code class="descclassname">list.</code><code class="descname">sort</code>(key=None, reverse=False)</dt>
<dd>Sort the items of the list in place (the arguments can be used for sort
customization, see <a class="reference internal" href="../library/functions.html#sorted" title="sorted"><code class="xref py py-func docutils literal notranslate">sorted()</code></a> for their explanation).
</dd></dl>

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

<dl class="method">
<dt>
<code class="descclassname">list.</code><code class="descname">copy</code>()</dt>
<dd>Return a shallow copy of the list. Equivalent to <code class="docutils literal notranslate">a[:]</code>.
</dd></dl>

An example that uses most of the list methods:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; fruits = [&#39;orange&#39;, &#39;apple&#39;, &#39;pear&#39;, &#39;banana&#39;, &#39;kiwi&#39;, &#39;apple&#39;, &#39;banana&#39;]
&gt;&gt;&gt; fruits.count(&#39;apple&#39;)
2
&gt;&gt;&gt; fruits.count(&#39;tangerine&#39;)
0
&gt;&gt;&gt; fruits.index(&#39;banana&#39;)
3
&gt;&gt;&gt; fruits.index(&#39;banana&#39;, 4) # Find next banana starting a position 4
6
&gt;&gt;&gt; fruits.reverse()
&gt;&gt;&gt; fruits
[&#39;banana&#39;, &#39;apple&#39;, &#39;kiwi&#39;, &#39;banana&#39;, &#39;pear&#39;, &#39;apple&#39;, &#39;orange&#39;]
&gt;&gt;&gt; fruits.append(&#39;grape&#39;)
&gt;&gt;&gt; fruits
[&#39;banana&#39;, &#39;apple&#39;, &#39;kiwi&#39;, &#39;banana&#39;, &#39;pear&#39;, &#39;apple&#39;, &#39;orange&#39;, &#39;grape&#39;]
&gt;&gt;&gt; fruits.sort()
&gt;&gt;&gt; fruits
[&#39;apple&#39;, &#39;apple&#39;, &#39;banana&#39;, &#39;banana&#39;, &#39;grape&#39;, &#39;kiwi&#39;, &#39;orange&#39;, &#39;pear&#39;]
&gt;&gt;&gt; fruits.pop()
&#39;pear&#39;
</pre></div>
</div>
You might have noticed that methods like <code class="docutils literal notranslate">insert</code>, <code class="docutils literal notranslate">remove</code> or <code class="docutils literal notranslate">sort</code> that
only modify the list have no return value printed – they return the default
<code class="docutils literal notranslate">None</code>. <a class="footnote-reference" href="#id3" id="id1">[1]</a> This is a design principle for all mutable data structures in
Python.
<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 (“last-in, first-out”). To add an
item to the top of the stack, use <code class="xref py py-meth docutils literal notranslate">append()</code>. To retrieve an item from the
top of the stack, use <code class="xref py py-meth docutils literal notranslate">pop()</code> without an explicit index. For example:
<div class="highlight-python3 notranslate"><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 (“first-in, first-out”); 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"><code class="xref py py-class docutils literal notranslate">collections.deque</code></a> which was designed to
have fast appends and pops from both ends. For example:
<div class="highlight-python3 notranslate"><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="list-comprehensions">
<h3>5.1.3. 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-python3 notranslate"><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>
Note that this creates (or overwrites) a variable named <code class="docutils literal notranslate">x</code> that still exists
after the loop completes. We can calculate the list of squares without any
side effects using:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>squares = list(map(lambda x: x**2, range(10)))
</pre></div>
</div>
or, equivalently:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>squares = [x**2 for x in range(10)]
</pre></div>
</div>
which is 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"><code class="xref std std-keyword docutils literal notranslate">for</code></a> clause, then zero or more <a class="reference internal" href="../reference/compound_stmts.html#for"><code class="xref std std-keyword docutils literal notranslate">for</code></a> or <a class="reference internal" href="../reference/compound_stmts.html#if"><code class="xref std std-keyword docutils literal notranslate">if</code></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"><code class="xref std std-keyword docutils literal notranslate">for</code></a> and <a class="reference internal" href="../reference/compound_stmts.html#if"><code class="xref std std-keyword docutils literal notranslate">if</code></a> clauses which follow it.
For example, this listcomp combines the elements of two lists if they are not
equal:
<div class="highlight-python3 notranslate"><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’s equivalent to:
<div class="highlight-python3 notranslate"><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"><code class="xref std std-keyword docutils literal notranslate">for</code></a> and <a class="reference internal" href="../reference/compound_stmts.html#if"><code class="xref std std-keyword docutils literal notranslate">if</code></a> statements is the
same in both these snippets.
If the expression is a tuple (e.g. the <code class="docutils literal notranslate">(x, y)</code> in the previous example),
it must be parenthesized.
<div class="highlight-python3 notranslate"><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, in &lt;module&gt;
 [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-python3 notranslate"><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>
<div class="section" id="nested-list-comprehensions">
<h3>5.1.4. Nested List Comprehensions<a class="headerlink" href="#nested-list-comprehensions" title="Permalink to this headline">¶</a></h3>
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-python3 notranslate"><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-python3 notranslate"><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"><code class="xref std std-keyword docutils literal notranslate">for</code></a> that follows it, so this example is
equivalent to:
<div class="highlight-python3 notranslate"><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-python3 notranslate"><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"><code class="xref py py-func docutils literal notranslate">zip()</code></a> function would do a great job for this use case:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; list(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 class="section" id="the-del-statement">
<h2>5.2. The <a class="reference internal" href="../reference/simple_stmts.html#del"><code class="xref std std-keyword docutils literal notranslate">del</code></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"><code class="xref std std-keyword docutils literal notranslate">del</code></a> statement. This differs from the <code class="xref py py-meth docutils literal notranslate">pop()</code> method
which returns a value. The <a class="reference internal" href="../reference/simple_stmts.html#del"><code class="xref std std-keyword docutils literal notranslate">del</code></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-python3 notranslate"><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"><code class="xref std std-keyword docutils literal notranslate">del</code></a> can also be used to delete entire variables:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; del a
</pre></div>
</div>
Referencing the name <code class="docutils literal notranslate">a</code> hereafter is an error (at least until another value
is assigned to it). We’ll find other uses for <a class="reference internal" href="../reference/simple_stmts.html#del"><code class="xref std std-keyword docutils literal notranslate">del</code></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 — list, tuple, range</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-python3 notranslate"><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 a 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"><code class="xref py py-func docutils literal notranslate">namedtuples</code></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-python3 notranslate"><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 <code class="docutils literal notranslate">t = 12345, 54321, 'hello!'</code> is an example of tuple packing:
the values <code class="docutils literal notranslate">12345</code>, <code class="docutils literal notranslate">54321</code> and <code class="docutils literal notranslate">'hello!'</code> are packed together in a tuple.
The reverse operation is also possible:
<div class="highlight-python3 notranslate"><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 that there are as
many variables on the left side of the equals sign as there are elements in 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"><code class="xref py py-func docutils literal notranslate">set()</code></a> function can be used to create sets. Note: to
create an empty set you have to use <code class="docutils literal notranslate">set()</code>, not <code class="docutils literal notranslate">{}</code>; the latter creates an
empty dictionary, a data structure that we discuss in the next section.
Here is a brief demonstration:
<div class="highlight-python3 notranslate"><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; print(basket) # show that duplicates have been removed
{&#39;orange&#39;, &#39;banana&#39;, &#39;pear&#39;, &#39;apple&#39;}
&gt;&gt;&gt; &#39;orange&#39; in basket # fast membership testing
True
&gt;&gt;&gt; &#39;crabgrass&#39; in basket
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
{&#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
{&#39;r&#39;, &#39;d&#39;, &#39;b&#39;}
&gt;&gt;&gt; a | b # letters in a or b or both
{&#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
{&#39;a&#39;, &#39;c&#39;}
&gt;&gt;&gt; a ^ b # letters in a or b but not both
{&#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-python3 notranslate"><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
{&#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 — dict</a>). Dictionaries are sometimes found in other languages as
“associative memories” or “associative arrays”. Unlike sequences, which are
indexed by a range of numbers, dictionaries are indexed by keys, which can be
any immutable type; strings and numbers can always be keys. Tuples can be used
as keys if they contain only strings, numbers, or tuples; if a tuple contains
any mutable object either directly or indirectly, it cannot be used as a key.
You can’t use lists as keys, since lists can be modified in place using index
assignments, slice assignments, or methods like <code class="xref py py-meth docutils literal notranslate">append()</code> and
<code class="xref py py-meth docutils literal notranslate">extend()</code>.
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: <code class="docutils literal notranslate">{}</code>. 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 <code class="docutils literal notranslate">del</code>. 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.
Performing <code class="docutils literal notranslate">list(d.keys())</code> on a dictionary returns a list of all the keys
used in the dictionary, in arbitrary order (if you want it sorted, just use
<code class="docutils literal notranslate">sorted(d.keys())</code> instead). <a class="footnote-reference" href="#id4" id="id2">[2]</a> To check whether a single key is in the
dictionary, use the <a class="reference internal" href="../reference/expressions.html#in"><code class="xref std std-keyword docutils literal notranslate">in</code></a> keyword.
Here is a small example using a dictionary:
<div class="highlight-python3 notranslate"><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; list(tel.keys())
[&#39;irv&#39;, &#39;guido&#39;, &#39;jack&#39;]
&gt;&gt;&gt; sorted(tel.keys())
[&#39;guido&#39;, &#39;irv&#39;, &#39;jack&#39;]
&gt;&gt;&gt; &#39;guido&#39; in tel
True
&gt;&gt;&gt; &#39;jack&#39; not in tel
False
</pre></div>
</div>
The <a class="reference internal" href="../library/stdtypes.html#dict" title="dict"><code class="xref py py-func docutils literal notranslate">dict()</code></a> constructor builds dictionaries directly from sequences of
key-value pairs:
<div class="highlight-python3 notranslate"><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-python3 notranslate"><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-python3 notranslate"><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 dictionaries, the key and corresponding value can be
retrieved at the same time using the <code class="xref py py-meth docutils literal notranslate">items()</code> method.
<div class="highlight-python3 notranslate"><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.items():
... print(k, v)
...
gallahad the pure
robin the brave
</pre></div>
</div>
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"><code class="xref py py-func docutils literal notranslate">enumerate()</code></a> function.
<div class="highlight-python3 notranslate"><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"><code class="xref py py-func docutils literal notranslate">zip()</code></a> function.
<div class="highlight-python3 notranslate"><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"><code class="xref py py-func docutils literal notranslate">reversed()</code></a> function.
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; for i in reversed(range(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"><code class="xref py py-func docutils literal notranslate">sorted()</code></a> function which
returns a new sorted list while leaving the source unaltered.
<div class="highlight-python3 notranslate"><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>
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.
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import math
&gt;&gt;&gt; raw_data = [56.2, float(&#39;NaN&#39;), 51.7, 55.3, 52.5, float(&#39;NaN&#39;), 47.8]
&gt;&gt;&gt; filtered_data = []
&gt;&gt;&gt; for value in raw_data:
... if not math.isnan(value):
... filtered_data.append(value)
...
&gt;&gt;&gt; filtered_data
[56.2, 51.7, 55.3, 52.5, 47.8]
</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 <code class="docutils literal notranslate">while</code> and <code class="docutils literal notranslate">if</code> statements can contain any
operators, not just comparisons.
The comparison operators <code class="docutils literal notranslate">in</code> and <code class="docutils literal notranslate">not in</code> check whether a value occurs
(does not occur) in a sequence. The operators <code class="docutils literal notranslate">is</code> and <code class="docutils literal notranslate">is not</code> 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, <code class="docutils literal notranslate">a &lt; b == c</code> tests whether <code class="docutils literal notranslate">a</code> is
less than <code class="docutils literal notranslate">b</code> and moreover <code class="docutils literal notranslate">b</code> equals <code class="docutils literal notranslate">c</code>.
Comparisons may be combined using the Boolean operators <code class="docutils literal notranslate">and</code> and <code class="docutils literal notranslate">or</code>, and
the outcome of a comparison (or of any other Boolean expression) may be negated
with <code class="docutils literal notranslate">not</code>. These have lower priorities than comparison operators; between
them, <code class="docutils literal notranslate">not</code> has the highest priority and <code class="docutils literal notranslate">or</code> the lowest, so that <code class="docutils literal notranslate">A and
not B or C</code> is equivalent to <code class="docutils literal notranslate">(A and (not B)) or C</code>. As always, parentheses
can be used to express the desired composition.
The Boolean operators <code class="docutils literal notranslate">and</code> and <code class="docutils literal notranslate">or</code> 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 <code class="docutils literal notranslate">A</code> and <code class="docutils literal notranslate">C</code> are
true but <code class="docutils literal notranslate">B</code> is false, <code class="docutils literal notranslate">A and B and C</code> does not evaluate the expression
<code class="docutils literal notranslate">C</code>. 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-python3 notranslate"><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 <code class="docutils literal notranslate">=</code> in an expression when <code class="docutils literal notranslate">==</code> 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 Unicode
code point number to order individual characters. Some examples of comparisons
between sequences of the same type:
<div class="highlight-python3 notranslate"><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 with <code class="docutils literal notranslate">&lt;</code> or <code class="docutils literal notranslate">&gt;</code> is legal
provided that the objects have appropriate comparison methods. For example,
mixed numeric types are compared according to their numeric value, so 0 equals
0.0, etc. Otherwise, rather than providing an arbitrary ordering, the
interpreter will raise a <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate">TypeError</code></a> exception.
Footnotes
<table class="docutils footnote" frame="void" id="id3" 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>Other languages may return the mutated object, which allows method
chaining, such as <code class="docutils literal notranslate">d-&gt;insert(&quot;a&quot;)-&gt;remove(&quot;b&quot;)-&gt;sort();</code>.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id4" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[2]</a></td><td>Calling <code class="docutils literal notranslate">d.keys()</code> will return a dictionary view object. It
supports operations like membership test and iteration, but its contents
are not independent of the original dictionary – it is only a view.</td></tr>
</tbody>
</table>
</div>
</div>

</div>
 </div>
 </div>
 <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
 <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="#list-comprehensions">5.1.3. List Comprehensions</a></li>
<li><a class="reference internal" href="#nested-list-comprehensions">5.1.4. Nested List Comprehensions</a></li>
</ul>
</li>
<li><a class="reference internal" href="#the-del-statement">5.2. The <code class="docutils literal notranslate">del</code> 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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