 # ODDPAIRS - Editorial

Author: Abhinav Gupta
Testers: Nishank Suresh, Tejas Pandey
Editorialist: Nishank Suresh

1044

None

# PROBLEM:

Given N, count the number of pairs (A, B) such that 1 \leq A, B \leq N and A+B is odd.

# EXPLANATION:

For A+B to be odd, one of A must be odd and the other must be even. In fact, this is the only restriction.

So, to count the total number of pairs:

• Let the number of even numbers from 1 to N be E, and the number of odd numbers from 1 to N be O.
• If A is odd and B is even, we have O\cdot E choices for them (O for A and E for B)
• If A is even and B is odd, we have E\cdot O choices for them.
• So, the total number of choices is 2\cdot E \cdot O.

All that remains is to find E and O quickly. This is quite easy:

• O = \left\lceil \frac{N}{2}\right\rceil, which can be implemented in most languages as (N+1)/2, using integer division.
• E = \left\lfloor \frac{N}{2}\right\rfloor, which can be implemented in most languages as simply N/2 using integer division

Note that N \leq 10^9, so the answer can exceed the range of 32-bit integers. Make sure to use a 64-bit integer datatype.

# TIME COMPLEXITY

\mathcal{O}(1) per test case.

# CODE:

Editorialist's code (Python)
for _ in range(int(input())):
n = int(input())
odds, evens = (n+1)//2, n//2
print(2*odds*evens)


Is this question solvable using nodejs?
I tried many time. In submission also only one person solved it and if I am running his code that is also not running.
please tell if I should keep trying or i should leave this question