In [1]:
%load_ext watermark
%watermark -a 'Sebastian Raschka' -u -d -v
I don't want to get into the details about sorting algorithms here, but there is a great report
"Sorting in the Presence of Branch Prediction and Caches - Fast Sorting on Modern Computers" written by Paul Biggar and David Gregg, where they describe and analyze elementary sorting algorithms in very nice detail (see chapter 4).
And for a quick reference, this website has a nice animation of this algorithm.
A long story short: The "worst-case" complexity of the Bubble sort algorithm (i.e., "Big-O")
$\Rightarrow \pmb O(n^2)$
In [4]:
def python_bubblesort(a_list):
""" Bubblesort in Python for list objects (sorts in place)."""
length = len(a_list)
for i in range(length):
for j in range(1, length):
if a_list[j] < a_list[j-1]:
a_list[j-1], a_list[j] = a_list[j], a_list[j-1]
return a_list
Below is a improved version that quits early if no further swap is needed.
In [5]:
def python_bubblesort_improved(a_list):
""" Bubblesort in Python for list objects (sorts in place)."""
length = len(a_list)
swapped = 1
for i in range(length):
if swapped:
swapped = 0
for ele in range(length-i-1):
if a_list[ele] > a_list[ele + 1]:
temp = a_list[ele + 1]
a_list[ele + 1] = a_list[ele]
a_list[ele] = temp
swapped = 1
return a_list
In [6]:
import random
import copy
random.seed(4354353)
l = [random.randint(1,1000) for num in range(1, 1000)]
l_sorted = sorted(l)
for f in [python_bubblesort, python_bubblesort_improved]:
assert(l_sorted == f(copy.copy(l)))
print('Bubblesort works correctly')
In [7]:
# small list
l_small = [random.randint(1,100) for num in range(1, 100)]
l_small_cp = copy.copy(l_small)
%timeit python_bubblesort(l_small)
%timeit python_bubblesort_improved(l_small_cp)
In [8]:
# larger list
l_small = [random.randint(1,10000) for num in range(1, 10000)]
l_small_cp = copy.copy(l_small)
%timeit python_bubblesort(l_small)
%timeit python_bubblesort_improved(l_small_cp)