Benefits of Double Division Operator over Single Division Operator in Python

The Double Division operator in Python returns the floor value for both integer and floating-point arguments after division. 

Python3

# A Python program to demonstrate use of
# "//" for both integers and floating points

print(5//2)
print(-5//2)
print(5.0//2)

Output:

2
-3
2.0

The time complexity of the program is O(1) as it contains only constant-time operations.

The auxiliary space used by the program is O(1) as it only uses a fixed amount of memory to store the variables and constant values used in the program.

The single division operator behaves abnormally generally for very large numbers. Consider the following example. Examples 1:

Python3

# single division
print(1000000002/2)

# Gives wrong output
print(int(((10 ** 17) + 2)/2))

# Gives Correct output
print(((10 ** 17) + 2)//2)

Output:

500000001.0
50000000000000000
50000000000000001

The time complexity of all three operations is constant time O(1) as they involve simple arithmetic operations.

The auxiliary space complexity of all three operations is also constant space O(1) as they do not use any extra memory that depends on the input size.

Example 2:

Python3

x = 10000000000000000000006
if int(x / 2) == x // 2:
    print("Hello")
else:
    print("World")

Output: 

World

The Output should have been Hello if the single division operator behaved normally because 2 properly divides x. But the output is World because The results after Single Division Operator and Double Division Operator ARE NOT THE SAME. This fact can be used for programs such as finding the sum of first n numbers for a large n. 

Python3

n = 10000000000

s1 = int(n * (n + 1) / 2)
s2 = n * (n + 1) // 2

print("Sum using single division operator : ", s1)
print("Sum using double division operator : ", s2)

Output: 

Sum using single division operator :  50000000005000003584
Sum using double division operator :  50000000005000000000

Thus the result found by using the single division operator is Wrong, while the result found by using the double division operator is Correct. This is a huge benefit of Double Division Operator over Single Division Operator in Python.

The time complexity of the code is O(1), as the code involves only simple arithmetic operations.

The auxiliary space used by the code is O(1), as the code does not involve any data structures whose size depends on the input size.