Czech ACM Student Chapter
Czech Technical University in Prague
Charles University in Prague
Technical University of Ostrava
ˇ ´
Slovak University of Technology
Pavol Jozef Safarik University in Koˇice
University of Zilina
Masaryk University
Matej Bel University in Bansk´ Bystrica
University of West Bohemia
CTU Open Contest 2012
Mosquito Multiplication
mosquito.c, mosquito.cpp,
Have you ever wondered why there are so many mosquitos in wet environments? One of the
reasons is that adult female mosquitos can lay as many as hundreds of eggs. Even if most of them
do not (fortunately!) survive, it is said that a single pair of mosquitos can generate a population
of thousands in just a couple of weeks. Let us have a closer look at these numbers.
The mosquito life cycle includes four stages: egg, larva, pupa, and adult. For simplicity, we will
make several assumptions that are not quite true in the nature: The egg stage lasts less than
one day, and all the other stages are one week long. Each mosquito lives as a larva for the first
week, the second week "hibernates" in the form of a pupa, and finally, the third week lives as
an adult mosquito. At the end of its three-week life, each mosquito lays eggs and dies.
To simplify things even further, we will assume that the transformation from one life stage into
another always happens on Sunday. Each Sunday, the following things happen:
· An adult mosquito lays E eggs and dies. Within a day, one larva hatches from each egg.
· Some of the larvae hatched from egg the last Sunday were not strong enough and died or
got eaten. Only every R-th larva will transform into a pupa on Sunday.
· An adult mosquito emerges from every S-th pupa, all other pupae dry.
For example, if there are 5 pupae and every 3-rd of them survives, there will be 1 mosquito left.
Out of 6 pupae, two adult mosquitos emerge.
In the first week, there are M mosquitos, P pupae and L larvae. Calculate how many mosquitos
will there be after N Sunday transformations. Of course, we are counting only living adult
mosquitos, not the dry dead bodies.
Input Specification
The input consists of several instances, each instance per one line. Each line contains seven
integers M , P , L, E, R, S, N separated by space. M , P and L are the numbers of mosquitos,
pupae, and larvae, respectively, in the first week. You may assume that 0 M, P, L 100 000,
0 E 100, 1 R, S 10, and 1 N 1000. E is the number of eggs laid by one mosquito,
R and S specify the survival rates of larvae and pupae, and N is the number of weeks.
Output Specification
For each input instance, output a single line containing an integer number C , giving the count
of mosquitos after the N -th Sunday.
You may assume that the number of mosquitos during each of the first N weeks will not exceed
1 000 000.
Sample Input
10 20 40
4 2 2 10
144 55 8
10 10 10
10 20 40
86 9 9 999
Output for Sample Input