2.7. Dictionaries¶
The second major Python data structure is the dictionary. As you
probably recall, dictionaries differ from lists in that you can access
items in a dictionary by a key rather than a position. Later in this
book you will see that there are many ways to implement a dictionary.
The thing that is most important to notice right now is that the get
item
and set item
operations on a dictionary are \(O(1)\). Another
important dictionary operation is the contains
operation. Checking to
see whether a key is in the dictionary or not is also \(O(1)\).
The efficiency of all dictionary operations is summarized in
Table 3. One important side note on dictionary performance
is that the efficiencies we provide in the table are for average
performance. In some rare cases the contains
, get item
, and set item
operations can degenerate into \(O(n)\) performance, but we will
get into that in Chapter 8 when we talk about the different ways
that a dictionary could be implemented.
Operation 
Big O Efficiency 


O(n) 

O(1) 

O(1) 

O(1) 

O(1) 

O(n) 
For our last performance experiment we will compare the performance of the contains operation between lists and dictionaries. In the process we will confirm that the contains operator for lists is \(O(n)\) and the contains operator for dictionaries is \(O(1)\). The experiment we will use to compare the two is simple: we’ll make a list with a range of numbers in it, then we will pick numbers at random and check to see if the numbers are in the list. If our performance tables are correct, the bigger the list, the longer it should take to determine if any one number is contained in the list.
We will repeat the same experiment for a dictionary that contains numbers as the keys. In this experiment we should see that determining whether or not a number is in the dictionary is not only much faster, but the time it takes to check should remain constant even as the dictionary grows larger.
Listing 6 implements this comparison. Notice that we are
performing exactly the same operation, number in container
. The
difference is that on line 8 x
is a list, and on line 10 x
is a
dictionary.
Listing 6
1import timeit
2import random
3
4print(f"{'n':10s}{'list':>10s}{'dict':>10s}")
5for i in range(10_000, 1_000_001, 20_000):
6 t = timeit.Timer(f"random.randrange({i}) in x",
7 "from __main__ import random, x")
8 x = list(range(i))
9 lst_time = t.timeit(number=1000)
10 x = {j: None for j in range(i)}
11 dict_time = t.timeit(number=1000)
12 print(f"{i:<10,}{lst_time:>10.3f}{dict_time:>10.3f}")
Figure 4 summarizes the results of running
Listing 6. You can see that the dictionary is consistently
faster. For the smallest list size of 10,000 elements a dictionary is
89.4 times faster than a list. For the largest list size of 990,000
elements the dictionary is 11,603 times faster! You can also see that
the time it takes for the contains
operator on the list grows linearly
with the size of the list. This verifies the assertion that the contains
operator on a list is \(O(n)\). It can also be seen that the time
for the contains
operator on a dictionary is constant even as the
dictionary size grows. In fact, for a dictionary size of 10,000 the
contains
operation took 0.004 milliseconds, and for the dictionary size
of 990,000 it also took 0.004 milliseconds.
Since Python is an evolving language, there are always changes going on behind the scenes. The latest information on the performance of Python data structures can be found on the Python website. As of this writing the Python wiki has a nice time complexity page that can be found at the Time Complexity Wiki.
Self Check
 a_list.pop(0)
 When you remove the first element of a list, all the other elements of the list must be shifted forward.
 a_list.pop()
 Removing an element from the end of the list is a constant operation.
 a_list.append()
 Appending to the end of the list is a constant operation
 a_list[10]
 Indexing a list is a constant operation
 all of the above are O(1)
 There is one operation that requires all other list elements to be moved.
Q1: Which of the list operations shown below is not O(1)?
 "x" in a_dict
 in is a constant operation for a dictionary because you do not have to iterate but there is a better answer.
 del a_dict["x"]
 deleting an element from a dictionary is a constant operation but there is a better answer.
 a_dict["x"] == 10
 Assignment to a dictionary key is constant but there is a better answer.
 a_dict["x"] = a_dict["x"] + 1
 Reassignment to a dictionary key is constant but there is a better answer.
 all of the above are O(1)
 The only dictionary operations that are not O(1) are those that require iteration.
Q2: Which of the dictionary operations shown below is O(1)?