PROBLEM LINK:
Practice
Contest: Division 1
Contest: Division 2
Contest: Division 3
Contest: Division 4
Author: pd_codes
Tester: yash_daga
Editorialist: iceknight1093
DIFFICULTY:
TBD
PREREQUISITES:
None
PROBLEM:
There are N episodes, numbered starting from 1.
The even-numbered episodes are A minutes long each, while the odd-numbered ones are B minutes long.
How many minutes will it take to watch all N episodes?
EXPLANATION:
Since the constraints are small, it’s possible to simply run a loop from 1 to N and add either A or B to the answer, depending on whether the current episode is odd- or even-numbered.
There’s also a solution in \mathcal{O}(1) by noting that the number of even episodes is exactly \lfloor \frac N2 \rfloor and the number of odd episodes is \lceil \frac N2 \rceil. Hence the answer is
where \lfloor \ \rfloor and \lceil \ \rceil denote the floor and ceiling functions, respectively.
TIME COMPLEXITY
\mathcal{O}(1) per test case.
CODE:
Editorialist's code (Python)
for _ in range(int(input())):
n, a, b = map(int, input().split())
print(a*(n//2) + b*(n - n//2))