Python Tutorial Part 1  >  Dictionaries

The compound types you have learned about'strings, lists, and tuples'use integers
as indices. If you try to use any other type as an index, you get an error.
Dictionaries are similar to other compound types except that they can use any
immutable type as an index. As an example, we will create a dictionary to translate
English words into Spanish. For this dictionary, the indices are strings.
One way to create a dictionary is to start with the empty dictionary and add
elements. The empty dictionary is denoted {}:
>>> eng2sp = {}
>>> eng2sp['one'] = 'uno'
>>> eng2sp['two'] = 'dos'
The first assignment creates a dictionary named eng2sp; the other assignments
add new elements to the dictionary. We can print the current value of the dictionary
in the usual way:
>>> print eng2sp
{'one': 'uno', 'two': 'dos'}
The elements of a dictionary appear in a comma-separated list. Each entry contains
an index and a value separated by a colon. In a dictionary, the indices are
called keys, so the elements are called key-value pairs.
Another way to create a dictionary is to provide a list of key-value pairs using the
same syntax as the previous output:
>>> eng2sp = {'one': 'uno', 'two': 'dos', 'three': 'tres'}

If we print the value of eng2sp again, we get a surprise:
>>> print eng2sp
{'one': 'uno', 'three': 'tres', 'two': 'dos'}
The key-value pairs are not in order! Fortunately, there is no reason to care about
the order, since the elements of a dictionary are never indexed with integer indices.
Instead, we use the keys to look up the corresponding values:
>>> print eng2sp['two']
The key 'two' yields the value 'dos' even though it appears in the third key-value

Dictionary operations
The del statement removes a key-value pair from a dictionary. For example, the
following dictionary contains the names of various fruits and the number of each
fruit in stock:
>>> inventory = {'apples': 430, 'bananas': 312, 'oranges': 525,
'pears': 217}
>>> print inventory
{'oranges': 525, 'apples': 430, 'pears': 217, 'bananas': 312}
If someone buys all of the pears, we can remove the entry from the dictionary:
>>> del inventory['pears']
>>> print inventory
{'oranges': 525, 'apples': 430, 'bananas': 312}
Or if we're expecting more pears soon, we might just change the value associated
with pears:
>>> inventory['pears'] = 0
>>> print inventory
{'oranges': 525, 'apples': 430, 'pears': 0, 'bananas': 312}
The len function also works on dictionaries; it returns the number of key-value
>>> len(inventory)

Dictionary methods
A method is similar to a function'it takes arguments and returns a value'
but the syntax is different. For example, the keys method takes a dictionary
and returns a list of the keys that appear, but instead of the function syntax
keys(eng2sp), we use the method syntax eng2sp.keys().
>>> eng2sp.keys()
['one', 'three', 'two']
This form of dot notation specifies the name of the function, keys, and the name
of the object to apply the function to, eng2sp. The parentheses indicate that this
method has no parameters.
A method call is called an invocation; in this case, we would say that we are
invoking keys on the object eng2sp.
The values method is similar; it returns a list of the values in the dictionary:
>>> eng2sp.values()
['uno', 'tres', 'dos']
The items method returns both, in the form of a list of tuples'one for each
key-value pair:
>>> eng2sp.items()
[('one','uno'), ('three', 'tres'), ('two', 'dos')]
The syntax provides useful type information. The square brackets indicate that
this is a list. The parentheses indicate that the elements of the list are tuples.
If a method takes an argument, it uses the same syntax as a function call. For
example, the method has key takes a key and returns true (1) if the key appears
in the dictionary:
>>> eng2sp.has_key('one')
>>> eng2sp.has_key('deux')
If you try to call a method without specifying an object, you get an error. In this
case, the error message is not very helpful:
>>> has_key('one')
NameError: has_key

Aliasing and copying
Because dictionaries are mutable, you need to be aware of aliasing. Whenever two
variables refer to the same object, changes to one affect the other.
If you want to modify a dictionary and keep a copy of the original, use the copy
method. For example, opposites is a dictionary that contains pairs of opposites:
>>> opposites = {'up': 'down', 'right': 'wrong', 'true': 'false'}
>>> alias = opposites
>>> copy = opposites.copy()
alias and opposites refer to the same object; copy refers to a fresh copy of the
same dictionary. If we modify alias, opposites is also changed:
>>> alias['right'] = 'left'
>>> opposites['right']
If we modify copy, opposites is unchanged:
>>> copy['right'] = 'privilege'
>>> opposites['right']

Sparse matrices
In the Lists page, we used a list of lists to represent a matrix. That is a good choice
for a matrix with mostly nonzero values, but consider a sparse matrix like this
0 2 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 3 0
0 0 0 0 0
The list representation contains a lot of zeroes:
matrix = [ [0,0,0,1,0],
[0,0,0,3,0] ]

An alternative is to use a dictionary. For the keys, we can use tuples that contain
the row and column numbers. Here is the dictionary representation of the same
matrix = {(0,3): 1, (2, 1): 2, (4, 3): 3}
We only need three key-value pairs, one for each nonzero element of the matrix.
Each key is a tuple, and each value is an integer.
To access an element of the matrix, we could use the [] operator:
Notice that the syntax for the dictionary representation is not the same as the
syntax for the nested list representation. Instead of two integer indices, we use
one index, which is a tuple of integers.
There is one problem. If we specify an element that is zero, we get an error,
because there is no entry in the dictionary with that key:
>>> matrix[1,3]
KeyError: (1, 3)
The get method solves this problem:
>>> matrix.get((0,3), 0)
The first argument is the key; the second argument is the value get should return
if the key is not in the dictionary:
>>> matrix.get((1,3), 0)
get definitely improves the semantics of accessing a sparse matrix. Shame about
the syntax.

If you played around with the fibonacci function from Section 5.7, you might
have noticed that the bigger the argument you provide, the longer the function
takes to run. Furthermore, the run time increases very quickly. On one of our
machines, fibonacci(20) finishes instantly, fibonacci(30) takes about a second,
and fibonacci(40) takes roughly forever.

To understand why, consider this call graph for fibonacci with n=4:
n 4
n 3
n 2
n 0
n 1
n 1
n 2
n 0
n 1
A call graph shows a set function frames, with lines connecting each frame to the
frames of the functions it calls. At the top of the graph, fibonacci with n=4 calls
fibonacci with n=3 and n=2. In turn, fibonacci with n=3 calls fibonacci with
n=2 and n=1. And so on.
Count how many times fibonacci(0) and fibonacci(1) are called. This is an
inefficient solution to the problem, and it gets far worse as the argument gets
A good solution is to keep track of values that have already been computed by
storing them in a dictionary. A previously computed value that is stored for later
use is called a hint. Here is an implementation of fibonacci using hints:
previous = {0:1, 1:1}
def fibonacci(n):
if previous.has_key(n):
return previous[n]
newValue = fibonacci(n-1) + fibonacci(n-2)
previous[n] = newValue
return newValue
The dictionary named previous keeps track of the Fibonacci numbers we already
know. We start with only two pairs: 0 maps to 1; and 1 maps to 1.
Whenever fibonacci is called, it checks the dictionary to determine if it contains
the result. If it's there, the function can return immediately without making any
more recursive calls. If not, it has to compute the new value. The new value is
added to the dictionary before the function returns.

Using this version of fibonacci, our machines can compute fibonacci(40) in
an eyeblink. But when we try to compute fibonacci(50), we see the following:
>>> fibonacci(50)
The L at the end of the result indicates that the answer +(20,365,011,074) is too
big to fit into a Python integer. Python has automatically converted the result to
a long integer.

Long integers
Python provides a type called long that can handle any size integer. There are
two ways to create a long value. One is to write an integer with a capital L at
the end:
>>> type(1L)
<type 'long'>
The other is to use the long function to convert a value to a long. long can
accept any numerical type and even strings of digits:
>>> long(1)
>>> long(3.9)
>>> long('57')
All of the math operations work on longs, so in general any code that works with
integers will also work with long integers. Any time the result of a computation is
too big to be represented with an integer, Python detects the overflow and returns
the result as a long integer. For example:
>>> 1000 * 1000
>>> 100000 * 100000
In the first case the result has type int; in the second case it is long.

Counting letters
In Strings page, we wrote a function that counted the number of occurrences of a
letter in a string. A more general version of this problem is to form a histogram
of the letters in the string, that is, how many times each letter appears.
Such a histogram might be useful for compressing a text file. Because different
letters appear with different frequencies, we can compress a file by using shorter
codes for common letters and longer codes for letters that appear less frequently.
Dictionaries provide an elegant way to generate a histogram:
>>> letterCounts = {}
>>> for letter in "Mississippi":
... letterCounts[letter] = letterCounts.get (letter, 0) + 1
>>> letterCounts
{'M': 1, 's': 4, 'p': 2, 'i': 4}
We start with an empty dictionary. For each letter in the string, we find the current
count (possibly zero) and increment it. At the end, the dictionary contains pairs
of letters and their frequencies.
It might be more appealing to display the histogram in alphabetical order. We
can do that with the items and sort methods:
>>> letterItems = letterCounts.items()
>>> letterItems.sort()
>>> print letterItems
[('M', 1), ('i', 4), ('p', 2), ('s', 4)]
You have seen the items method before, but sort is the first method you have
encountered that applies to lists. There are several other list methods, including
append, extend, and reverse. Consult the Python documentation for details.