ELECTION1 - Editorial

PROBLEM LINK:

Practice
Contest: Division 1
Contest: Division 2
Contest: Division 3
Contest: Division 4

Author: raysh07
Tester: sushil2006
Editorialist: iceknight1093

DIFFICULTY:

Cakewalk

PREREQUISITES:

None

PROBLEM:

A party is contesting an election with N seats, and has won K of them.
How many more additional seats do they need in order to get a strict majority?

EXPLANATION:

Let R = \left\lfloor \frac{N}{2} \right\rfloor + 1 denote the number of seats required for a strict majority.
This is the smallest integer that’s larger than half of N.

If K \ge R, then the party already has enough seats, and doesn’t need any more.
The answer in this case is 0.

If K \lt R, then the party needs additional seats.
We’re looking to minimize the number of additional seats, so clearly it’s optimal to reach exactly R.
This requires (R - K) additional seats, which is the answer in this case.

TIME COMPLEXITY:

\mathcal{O}(1) per testcase.

CODE:

Editorialist's code (PyPy3)
n, k = map(int, input().split())
req = n//2 + 1
if k >= req: print(0)
else: print(req - k)