In [1]:
from bisect import bisect_left, bisect_right # for binary search
import random
random.seed(77) # so that you and I get same random lists

In [2]:
a = [1, 2, 3, 3, 3, 4, 5]
bisect_left(a, 3), bisect_right(a, 3)

Out[2]:
(2, 5)
In [3]:
a = [2, 4, 6, 8, 10]
bisect_left(a, 5), bisect_right(a, 5)

Out[3]:
(2, 2)
In [4]:
# make a list of pseudo-random integers in [1, 99]
ls = [ random.randint(1, 99) for _ in range(30) ]
ls # show it

Out[4]:
[80,
33,
24,
82,
12,
48,
56,
61,
15,
63,
50,
85,
3,
95,
18,
81,
51,
83,
19,
32,
9,
78,
53,
21,
19,
9,
20,
56,
44,
70]
In [5]:
ls.sort() # sort the list in-place
ls # show the sorted list; note there are some repeated elements

Out[5]:
[3,
9,
9,
12,
15,
18,
19,
19,
20,
21,
24,
32,
33,
44,
48,
50,
51,
53,
56,
56,
61,
63,
70,
78,
80,
81,
82,
83,
85,
95]
In [6]:
# The number 40 is not in the sorted list.  If it were, where would it go?
bisect_left(ls, 40)

Out[6]:
13
In [7]:
# insert it
ls.insert(13, 40)
ls # show the new list

Out[7]:
[3,
9,
9,
12,
15,
18,
19,
19,
20,
21,
24,
32,
33,
40,
44,
48,
50,
51,
53,
56,
56,
61,
63,
70,
78,
80,
81,
82,
83,
85,
95]
In [8]:
# The number 19 appears in the list multiple times.
# Say we want a range [st, en) where st is the first element
# (inclusive) and en is last element (exclusive) that contains a 19
st, en = bisect_left(ls, 19), bisect_right(ls, 19)

In [9]:
st, en

Out[9]:
(6, 8)
In [10]:
ls[st:en]

Out[10]:
[19, 19]
In [11]:
# Of course, there also exists a total ordering over strings
# (lexicographical ordering), so we can do all the same things
# with strings
strls = ['a', 'awkward', 'awl', 'awls', 'axe', 'axes', 'bee']

In [12]:
strls == sorted(strls)

Out[12]:
True
In [13]:
# We want to get the range of elements that equal a query string:
st, en = bisect_left(strls, 'awl'), bisect_right(strls, 'awl')
st, en

Out[13]:
(2, 3)
In [14]:
# Say we want to get the range of elements that have some prefix,
# e.g. 'aw' and say that 'z' is the lexicographically greatest
# character in the alphabet.
st, en = bisect_left(strls, 'aw'), bisect_left(strls, 'ax')
st, en

Out[14]:
(1, 4)
In [15]:
strls[st:en]

Out[15]:
['awkward', 'awl', 'awls']
In [16]:
# If we can do it for any sorted list of strings, we can do it for
# a sorted list of suffixes
t = 'abaaba$' suffixes = sorted([t[i:] for i in range(len(t))]) suffixes  Out[16]: ['$', 'a$', 'aaba$', 'aba$', 'abaaba$', 'ba$', 'baaba$']
In [17]:
st, en = bisect_left(suffixes, 'aba'), bisect_left(suffixes, 'abb')
st, en

Out[17]:
(3, 5)