Czech ACM Student Chapter
Czech Technical University in Prague
Charles University in Prague
Technical University of Ostrava
Slovak University of Technology
University of Zilina
Masaryk University
University of West Bohemia
CTU Open Contest 2017
Pond Cascade
cascade.c, cascade.cpp, cascade.c11,,
The cascade of water slides has been installed in the park recently and it has to be tested. The
cascade consists of some number of reservoirs, or "ponds" for short, which are linked into a single
sequence connected by water slides. Visitors are expected to start the journey in the topmost
pond, then to be washed into subsequent lower ponds, and finally end the journey in the last
pond of the cascade, which is also the lowest pond of the cascade. The journey spans all ponds
in the cascade.
To test the cascade, each pond has to be completely filled with water. Each pond is attached
to a pipe with a valve which, when opened, pours water into the pond. The sizes and capacities
of different ponds are different. Fortunately, at least the pipes and the valves are standardized.
Therefore, the rate at which water is poured through the valve into a pond is the same for all
When a pond is filled, water overflows and continues to flow into the next pond. If that pond is
also filled, water continues to the next subsequent pond, and so on, until it either reaches some
pond which has not been completely filled yet, or it overflows the lowest pond and sinks in the
drain at the bottom of the cascade. The time in which the overflowing water reaches the next
pond is considered to be negligible. The test starts at time 0 with all ponds being empty. Then,
all valves are opened simultaneously. The test stops and the valves are closed when all ponds
are filled by water.
The pond capacities and valves flow rate are known, you have to determine the moment when
the lowest pond starts to overflow and the first moment when all ponds are filled.
Input Specification
There are more test cases. Each test case consists of two lines. The first line contains two
integers N (1 N 105, 1 F 109 ) separated by space. N is the number of ponds, F is the
rate of water flow through each valve. We consider the flow to be expressed in litres per second.
The second line contains a sequence of N integers Ci (1 Ci 109) separated by spaces and
representing the pond capacities expressed in litres. The sequence reflects the order of ponds
from the topmost one to the lowest one.
Output Specification
For each test case, print a single line with two numbers separated by space. The first number
represents the time in which the lowest pond in the cascade starts to overflow. The second
number represents the duration of the test. Both times should be printed in seconds and should
be accurate within an absolute or relative error of 10-6.
Sample Input
10 7 3 2
Output for Sample Input
1.25 1.25
0.66666667 3.33333333