Python Bisect - Binary Search

1. bisect.bisect_left() Overview
2. Applications of bisect_left()
3. bisect.bisect_right() Overview
4. Applications of bisect_right()

In this article, we will see how to use Python built-in 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

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 i - 1
    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

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[i - 1] == x:
        return i - 1
    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