YOGACLASS - Editorial

editorial
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1

PROBLEM LINK:

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

Author: notsoloud
Tester: airths
Editorialist: iceknight1093

DIFFICULTY:

TBD

PREREQUISITES:

None

PROBLEM:

Chef can teach a 1-hr class for X rupees, or a 2-hr class for Y rupees.
What’s the maximum amount of money Chef can earn in N hours?

EXPLANATION:

Note that if 2\cdot X \geq Y, Chef will earn more by holding two 1-hr classes rather than a single 2-hr class.

So,

  • If 2\cdot X \geq Y, Chef will never hold a 2-hr class.
    His total earnings will be N\cdot X.
  • If 2\cdot X \lt Y, it’s always better for Chef to hold a 2-hr class when possible.
    So,
    • If N is even, Chef will hold \frac{N}{2} 2-hr classes, earning Y\cdot \frac{N}{2} in total.
    • If N is odd, Chef will hold \left\lfloor\frac{N}{2}\right\rfloor 2-hr classes, and then a single 1-hr class, earning Y\cdot \left\lfloor\frac{N}{2}\right\rfloor + X in total.

TIME COMPLEXITY:

\mathcal{O}(1) per testcase.

CODE:

Editorialist's code (Python) 
for _ in range(int(input())):
    n, x, y = map(int, input().split())
    ans = x*(n%2) + (n//2)*max(y, 2*x)
    print(ans)
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