# Data Structures¶

This chapter describes some things you’ve learned about already in more detail, and adds some new things as well.

## More on Lists¶

The list data type has some more methods. Here are all of the methods of list objects:

list.append(x)
Add an item to the end of the list; equivalent to a[len(a):] = [x].
list.extend(L)
Extend the list by appending all the items in the given list; equivalent to a[len(a):] = L.
list.insert(i, x)
Insert an item at a given position. The first argument is the index of the element before which to insert, so a.insert(0, x) inserts at the front of the list, and a.insert(len(a), x) is equivalent to a.append(x).
list.remove(x)
Remove the first item from the list whose value is x. It is an error if there is no such item.
list.pop([i])
Remove the item at the given position in the list, and return it. If no index is specified, a.pop() 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.)
list.index(x)
Return the index in the list of the first item whose value is x. It is an error if there is no such item.
list.count(x)
Return the number of times x appears in the list.
list.sort()
Sort the items of the list, in place.
list.reverse()
Reverse the elements of the list, in place.

An example that uses most of the list methods:

```>>> a = [66.25, 333, 333, 1, 1234.5]
>>> print(a.count(333), a.count(66.25), a.count('x'))
2 1 0
>>> a.insert(2, -1)
>>> a.append(333)
>>> a
[66.25, 333, -1, 333, 1, 1234.5, 333]
>>> a.index(333)
1
>>> a.remove(333)
>>> a
[66.25, -1, 333, 1, 1234.5, 333]
>>> a.reverse()
>>> a
[333, 1234.5, 1, 333, -1, 66.25]
>>> a.sort()
>>> a
[-1, 1, 66.25, 333, 333, 1234.5]
```

### Using Lists as Stacks¶

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 append(). To retrieve an item from the top of the stack, use pop() without an explicit index. For example:

```>>> stack = [3, 4, 5]
>>> stack.append(6)
>>> stack.append(7)
>>> stack
[3, 4, 5, 6, 7]
>>> stack.pop()
7
>>> stack
[3, 4, 5, 6]
>>> stack.pop()
6
>>> stack.pop()
5
>>> stack
[3, 4]
```

### Using Lists as Queues¶

You can also use a list conveniently as a queue, where the first element added is the first element retrieved (“first-in, first-out”). To add an item to the back of the queue, use append(). To retrieve an item from the front of the queue, use pop() with 0 as the index. For example:

```>>> queue = ["Eric", "John", "Michael"]
>>> queue.append("Terry")           # Terry arrives
>>> queue.append("Graham")          # Graham arrives
>>> queue.pop(0)
'Eric'
>>> queue.pop(0)
'John'
>>> queue
['Michael', 'Terry', 'Graham']
```

### List Comprehensions¶

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

Each list comprehension consists of an expression followed by a for clause, then zero or more for or if clauses. The result will be a list resulting from evaluating the expression in the context of the for and if clauses which follow it. If the expression would evaluate to a tuple, it must be parenthesized.

Here we take a list of numbers and return a list of three times each number:

```>>> vec = [2, 4, 6]
>>> [3*x for x in vec]
[6, 12, 18]
```

Now we get a little fancier:

```>>> [[x, x**2] for x in vec]
[[2, 4], [4, 16], [6, 36]]
```

Here we apply a method call to each item in a sequence:

```>>> freshfruit = ['  banana', '  loganberry ', 'passion fruit  ']
>>> [weapon.strip() for weapon in freshfruit]
['banana', 'loganberry', 'passion fruit']
```

Using the if clause we can filter the stream:

```>>> [3*x for x in vec if x > 3]
[12, 18]
>>> [3*x for x in vec if x < 2]
[]
```

Tuples can often be created without their parentheses, but not here:

```>>> [x, x**2 for x in vec]  # error - parens required for tuples
File "<stdin>", line 1, in ?
[x, x**2 for x in vec]
^
SyntaxError: invalid syntax
>>> [(x, x**2) for x in vec]
[(2, 4), (4, 16), (6, 36)]
```

Here are some nested for loops and other fancy behavior:

```>>> vec1 = [2, 4, 6]
>>> vec2 = [4, 3, -9]
>>> [x*y for x in vec1 for y in vec2]
[8, 6, -18, 16, 12, -36, 24, 18, -54]
>>> [x+y for x in vec1 for y in vec2]
[6, 5, -7, 8, 7, -5, 10, 9, -3]
>>> [vec1[i]*vec2[i] for i in range(len(vec1))]
[8, 12, -54]
```

List comprehensions can be applied to complex expressions and nested functions:

```>>> [str(round(355/113, i)) for i in range(1, 6)]
['3.1', '3.14', '3.142', '3.1416', '3.14159']
```

### Nested List Comprehensions¶

If you’ve got the stomach for it, list comprehensions can be nested. They are a powerful tool but – like all powerful tools – they need to be used carefully, if at all.

Consider the following example of a 3x3 matrix held as a list containing three lists, one list per row:

```>>> mat = [
...        [1, 2, 3],
...        [4, 5, 6],
...        [7, 8, 9],
...       ]
```

Now, if you wanted to swap rows and columns, you could use a list comprehension:

```>>> print([[row[i] for row in mat] for i in [0, 1, 2]])
[[1, 4, 7], [2, 5, 8], [3, 6, 9]]
```

Special care has to be taken for the nested list comprehension:

To avoid apprehension when nesting list comprehensions, read from right to left.

A more verbose version of this snippet shows the flow explicitly:

```for i in [0, 1, 2]:
for row in mat:
print(row[i], end="")
print()
```

In real world, you should prefer builtin functions to complex flow statements. The zip() function would do a great job for this use case:

```>>> list(zip(*mat))
[(1, 4, 7), (2, 5, 8), (3, 6, 9)]
```

See Unpacking Argument Lists for details on the asterisk in this line.

## The del statement¶

There is a way to remove an item from a list given its index instead of its value: the del statement. This differs from the pop() method which returns a value. The del 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:

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

del can also be used to delete entire variables:

```>>> del a
```

Referencing the name a hereafter is an error (at least until another value is assigned to it). We’ll find other uses for del later.

## Tuples and Sequences¶

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 Sequence Types — str, bytes, bytearray, list, tuple, range). 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:

```>>> t = 12345, 54321, 'hello!'
>>> t[0]
12345
>>> t
(12345, 54321, 'hello!')
>>> # Tuples may be nested:
... u = t, (1, 2, 3, 4, 5)
>>> u
((12345, 54321, 'hello!'), (1, 2, 3, 4, 5))
```

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).

Tuples have many uses. For example: (x, y) coordinate pairs, employee records from a database, etc. Tuples, like strings, are immutable: it is not possible to assign to the individual items of a tuple (you can simulate much of the same effect with slicing and concatenation, though). It is also possible to create tuples which contain mutable objects, such as lists.

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:

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

The statement t = 12345, 54321, 'hello!' is an example of tuple packing: the values 12345, 54321 and 'hello!' are packed together in a tuple. The reverse operation is also possible:

```>>> x, y, z = t
```

This is called, appropriately enough, sequence unpacking. 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!

There is a small bit of asymmetry here: packing multiple values always creates a tuple, and unpacking works for any sequence.

## Sets¶

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 set() function can be use to create sets. Note: To create an empty set you have to use set(), not {}; the latter creates an empty dictionary, a data structure that we discuss in the next section.

Here is a brief demonstration:

```>>> basket = {'apple', 'orange', 'apple', 'pear', 'orange', 'banana'}
{'orange', 'banana', 'pear', 'apple'}
>>> fruit = ['apple', 'orange', 'apple', 'pear', 'orange', 'banana']
>>> fruit = set(basket)               # create a set without duplicates
>>> fruit
{'orange', 'pear', 'apple', 'banana'}
>>> fruit = {'orange', 'apple'}       # {} syntax is equivalent to [] for lists
>>> fruit
{'orange', 'apple'}
>>> 'orange' in fruit                 # fast membership testing
True
>>> 'crabgrass' in fruit
False

>>> # Demonstrate set operations on unique letters from two words
...
>>> b = set('alacazam')
>>> a                                  # unique letters in a
{'a', 'r', 'b', 'c', 'd'}
>>> a - b                              # letters in a but not in b
{'r', 'd', 'b'}
>>> a | b                              # letters in either a or b
{'a', 'c', 'r', 'd', 'b', 'm', 'z', 'l'}
>>> a & b                              # letters in both a and b
{'a', 'c'}
>>> a ^ b                              # letters in a or b but not both
{'r', 'd', 'b', 'm', 'z', 'l'}
```

Like for lists, there is a set comprehension syntax:

```>>> a = {x for x in 'abracadabra' if x not in 'abc'}
>>> a
{'r', 'd'}
```

## Dictionaries¶

Another useful data type built into Python is the dictionary (see Mapping Types — dict). 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 append() and extend().

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: {}. 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 del. 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 list(d.keys()) on a dictionary returns a list of all the keys used in the dictionary, in arbitrary order (if you want it sorted, just apply the sorted() function instead). To check whether a single key is in the dictionary, use the in keyword.

Here is a small example using a dictionary:

```>>> tel = {'jack': 4098, 'sape': 4139}
>>> tel['guido'] = 4127
>>> tel
{'sape': 4139, 'guido': 4127, 'jack': 4098}
>>> tel['jack']
4098
>>> del tel['sape']
>>> tel['irv'] = 4127
>>> tel
{'guido': 4127, 'irv': 4127, 'jack': 4098}
>>> list(tel.keys())
['irv', 'guido', 'jack']
>>> sorted(tel.keys())
['guido', 'irv', 'jack']
>>> 'guido' in tel
True
>>> 'jack' not in tel
False
```

The dict() constructor builds dictionaries directly from lists of key-value pairs stored as tuples. When the pairs form a pattern, list comprehensions can compactly specify the key-value list.

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

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

```>>> {x: x**2 for x in (2, 4, 6)}
{2: 4, 4: 16, 6: 36}
```

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

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

## Looping Techniques¶

When looping through dictionaries, the key and corresponding value can be retrieved at the same time using the items() method.

```>>> knights = {'gallahad': 'the pure', 'robin': 'the brave'}
>>> for k, v in knights.items():
...     print(k, v)
...
robin the brave
```

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

```>>> for i, v in enumerate(['tic', 'tac', 'toe']):
...     print(i, v)
...
0 tic
1 tac
2 toe
```

To loop over two or more sequences at the same time, the entries can be paired with the zip() function.

```>>> questions = ['name', 'quest', 'favorite color']
>>> answers = ['lancelot', 'the holy grail', 'blue']
>>> for q, a in zip(questions, answers):
...     print('What is your {0}?  It is {1}.'.format(q, a))
...
What is your name?  It is lancelot.
What is your quest?  It is the holy grail.
What is your favorite color?  It is blue.
```

To loop over a sequence in reverse, first specify the sequence in a forward direction and then call the reversed() function.

```>>> for i in reversed(range(1, 10, 2)):
...     print(i)
...
9
7
5
3
1
```

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

```>>> basket = ['apple', 'orange', 'apple', 'pear', 'orange', 'banana']
...     print(f)
...
apple
banana
orange
pear
```

## More on Conditions¶

The conditions used in while and if statements can contain any operators, not just comparisons.

The comparison operators in and not in check whether a value occurs (does not occur) in a sequence. The operators is and is not 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, a < b == c tests whether a is less than b and moreover b equals c.

Comparisons may be combined using the Boolean operators and and or, and the outcome of a comparison (or of any other Boolean expression) may be negated with not. These have lower priorities than comparison operators; between them, not has the highest priority and or the lowest, so that A and not B or C is equivalent to (A and (not B)) or C. As always, parentheses can be used to express the desired composition.

The Boolean operators and and or 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 A and C are true but B is false, A and B and C does not evaluate the expression C. 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,

```>>> string1, string2, string3 = '', 'Trondheim', 'Hammer Dance'
>>> non_null = string1 or string2 or string3
>>> non_null
'Trondheim'
```

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 = in an expression when == was intended.

## Comparing Sequences and Other Types¶

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:

```(1, 2, 3)              < (1, 2, 4)
[1, 2, 3]              < [1, 2, 4]
'ABC' < 'C' < 'Pascal' < 'Python'
(1, 2, 3, 4)           < (1, 2, 4)
(1, 2)                 < (1, 2, -1)
(1, 2, 3)             == (1.0, 2.0, 3.0)
(1, 2, ('aa', 'ab'))   < (1, 2, ('abc', 'a'), 4)
```

Note that comparing objects of different types with < or > is 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 TypeError exception.