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 pointsprint(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 divisionprint(1000000002/2)# Gives wrong outputprint(int(((10 ** 17) + 2)/2))# Gives Correct outputprint(((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 = 10000000000000000000006if 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 = 10000000000s1 = int(n * (n + 1) / 2)s2 = n * (n + 1) // 2print("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.
