I'm referring to this: http://docs.python.org/tutorial/datastructures.html
What would be the running time of list.index(x) function in terms of Big O notation?
6 Answers
It's O(n), also check out: http://wiki.python.org/moin/TimeComplexity
This page documents the time-complexity (aka "Big O" or "Big Oh") of various operations in current CPython. Other Python implementations (or older or still-under development versions of CPython) may have slightly different performance characteristics. However, it is generally safe to assume that they are not slower by more than a factor of O(log n)...
5 Comments
Krishna
just to add since the index algorithm can be applied on
list or other data structures, it is implement as linear search hence O(n).
bmiselis
Do you happen to know if there is a specific reason it has not been implemented as a binary search instead? It does not sound overly complex, yet would be way more efficient.
Vib
Theres no guarantee that the list is sorted so a binary search would not work
user7356972
The doc that you have shared, get item for list is O(1).
duhaime
It'd be great if
binary=True or sorted=True were an argument one could provideAccording to said documentation:
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.
Which implies searching. You're effectively doing x in s but rather than returning True or False you're returning the index of x. As such, I'd go with the listed time complexity of O(n).
Comments
Any list implementation is going to have an O(n) complexity for a linear search (e.g., list.index). Although maybe there are some wacky implementations out there that do worse...
You can improve lookup complexity by using different data structures, such as ordered lists or sets. These are usually implemented with binary trees. However, these data structures put constraints on the elements they contain. In the case of a binary tree, the elements need to be orderable, but the lookup cost goes down to O(log n).
As mentioned previously, look here for run time costs of standard Python data structures: http://wiki.python.org/moin/TimeComplexity
Comments
Try this code, it will help you to get your execution time taken by lis.index operator.
import timeit
lis=[11,22,33,44,55,66,77]
for i in lis:
t = timeit.Timer("lis.index(11)", "from main import lis")
TimeTaken= t.timeit(number=100000)
print (TimeTaken)
Comments
The documentation provided above did not cover list.index()
from my understanding, list.index is O(1) operation. Here is a link if you want to know more. https://www.ics.uci.edu/~pattis/ICS-33/lectures/complexitypython.txt
1 Comment
Mike Lane
You are mistaken. The "Index" that your link is talking about is the same as Get Item in the python.org wiki. You can see in the cpython source code that the index method is doing an O(n) search of the list.
Use the following code to check the timing. Its complexity is O(n).
import time
class TimeChecker:
def __init__(self, name):
self.name = name
def __enter__(self):
self.start = self.get_time_in_sec()
return self
def __exit__(self, exc_type, exc_val, exc_tb):
now = self.get_time_in_sec()
time_taken = now - self.start # in seconds
print("Time Taken by " + self.name + ": " + str(time_taken))
def get_time_in_sec(self):
return int(round(time.time() * 1000))
def test_list_index_func(range_num):
lis = [1,2,3,4,5]
with TimeChecker('Process 1') as tim:
for i in range(range_num):
lis.index(4)
test_list_index_func(1000)
test_list_index_func(10000)
test_list_index_func(100000)
test_list_index_func(1000000)
print("Time: O(n)")
2 Comments
Rohan
This code fails to prove that
list.index operates in linear time. It does not compare how long list.index takes to run on varying input sizes, but it simply runs list.index multiple times. Even if you were computing 1+1, if you compute 1+1 a thousand times it will take 1000x longer than computing it once. To ensure this is true, I tested your code with binary search, which should be O(log n), and with accessing an element of the list, which should be O(1). Both of them, naturally, took 10x longer with each call of test_list_index_func, which is linear growth, which is incorrect.
Z4-tier
This code makes no sense. Time complexity is usually expressed as a function of the input size. The inputs you are giving to
list.index never change, it's always the same list and the same search value. When you call test_list_index_func with increasing values, it isn't changing the input size to list.index, it's just changing the number of times that the exact same operation is performed. Doing that will always show a linear pattern, for any deterministic function called with the same inputs (which, again, is what you're doing here).
O(n).%%timeitsaid 2.2ns whereas fetching an attribute via an ORM (warm queryset) was 80ns.