Python Bisect  Binary Search

bisect.bisect_left()
Overview 
Applications of
bisect_left()

bisect.bisect_right()
Overview 
Applications of
bisect_right()
If you want to understand Binary Search in detail, then refer to the binary search algorithm article.
In this article, we will see how to use Python builtin modules to perform Binary Search. The bisect
module is based on the bisection method for finding the roots of functions. It consists of 6 functions: bisect()
, bisect_left()
, bisect_right()
, insort()
, insort_left()
, insort_right()
which allows us to find index of an element or insert element in right position in a list. It also helps to keep the list sorted after each insertion. But for them to work properly, we have to make sure that the array is already sorted.
bisect.bisect_left()
Overview
It is used to locate the leftmost insertion point of a number x
inside a sorted list. If x
is already present in the list, then new x
will be inserted in the leftmost position among all x
in the list.
Syntax
bisect_left(arr, x, lo = 0, hi = len(a))
Parameters
arr 
The input list 
x 
The element whose insertion point we are locating. 
lo 
It helps to specify the starting index of a subset of a list. The default value is 0 . 
hi 
It helps to specify the ending index of a subset of a list. The default value is len(arr) . 
Return
It returns an insertion point that partitions the array into two halves: the first with all values smaller than x
and the second with all values larger than x
.
Applications of bisect_left()
Find the first occurrence of an element
from bisect import bisect_left
def binary_search(a, x):
i = bisect_left(a, x)
if i != len(a) and a[i] == x:
return i
else:
return 1
a = [1, 2, 3, 3, 3]
x = int(3)
res = binary_search(a, x)
if res == 1:
print("Element not Found")
else:
print("First occurrence of", x, "is at index", res)
Output:
First occurrence of 3 is at index 2
Findthe greatest value smaller than x
from bisect import bisect_left
def binary_search(a, x):
i = bisect_left(a, x)
if i:
return (i1)
else:
return 1
# Driver code
a = [1, 2, 4, 4, 8]
x = int(7)
res = binary_search(a, x)
if res == 1:
print("There is no value smaller than", x)
else:
print("Largest value smaller than", x, " is at index", res)
Output:
Largest value smaller than 7 is at index 3
bisect.bisect_right()
Overview
It is used to return the rightmost insertion point of a number x
inside a sorted list. If x
is already present in the list, then new x
will be inserted in the rightmost position among all x
in the list.
Syntax
bisect_right(arr, x, lo = 0, hi = len(a))
Parameters
arr 
The input list 
x 
The element whose insertion point we are locating. 
lo 
It helps to specify the starting index of a subset of a list. The default value is 0 . 
hi 
It helps to specify the ending index of a subset of a list. The default value is len(arr) . 
Return
It returns an insertion point that partitions the array into two halves: the first with all values <= x
and the second with all values > x
.
Applications of bisect_right()
Find the last occurrence of an element
from bisect import bisect_right
def binary_search(a, x):
i = bisect_right(a, x)
if i != len(a)+1 and a[i1] == x:
return (i1)
else:
return 1
a = [1, 2, 4, 4]
x = int(4)
res = binary_search(a, x)
if res == 1:
print(x, "is absent")
else:
print("Last occurrence of", x, "is present at", res)
Output:
Last occurrence of 4 is present at 3