MOVIE7 - Editorial

PROBLEM LINK:

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

Author: raysh07
Tester: sushil2006
Editorialist: iceknight1093

DIFFICULTY:

TBD

PREREQUISITES:

None

PROBLEM:

Chef will buy N movie tickets and M buckets of popcorn.
Each ticket costs A, each popcorn bucket costs B.
There’s also a combo of one ticket and one popcorn bucket for C.
It’s guaranteed that \max(A, B) \lt C \le A+B.

Find the minimum amount Chef needs to spend.

EXPLANATION:

Because of the condition \max(A, B) \lt C \le A+B, it’s always optimal to buy the combo when it’s possible to do so, i.e. when we need both a ticket and a bucket of popcorn.

So, let X = \min(N, M).
X denotes the largest number of combos we can buy.

The answer is hence obtained by summing the following:

  • X combos, costing C each.
    The total is X\cdot C.
  • N-X individual tickets, costing A each.
    The total is (N-X)\cdot A.
  • M-X individual buckets, costing B each.
    The total is (M-X)\cdot B.

Print their sum as the answer.

TIME COMPLEXITY:

\mathcal{O}(1) per testcase.

CODE:

Editorialist's code (PyPy3)
for _ in range(int(input())):
    n, m, a, b, c = map(int, input().split())
    x = min(n, m)
    print(x*c + (n-x)*a + (m-x)*b)