Back to Intermediate Math
Input: standard input
Output: standard output
Time
Limit: 1 second
Umm! So, you claim yourself as an intelligent one? Let me check. As, computer science students always insist on optimization whenever possible, I give you an elementary problem of math to optimize.
You
are trying to cross a river of width d meters. You are given
that, the river flows at v ms-1 and you know
that you can speed up the boat in u ms-1.
There may be two goals how to cross the river: One goal (called fastest path) is
to cross it in fastest time, and it does not matter how far the flow of the
river takes the boat. The other goal (called shortest path) is to steer the boat
in a direction so that the flow of the river doesn't take the boat away, and the
boat passes the river in a line perpendicular to the boarder of the river.
Is it always possible to have two different paths, one to pass at shortest time
and the other at shortest path? If possible then, what is the difference (Let P
s) between the times needed to
cross the river in the different ways?
Input
The first line in the input file is an integer representing
the number of test cases. Each of the test cases follows below. Each case
consists three real numbers (all are nonnegative, d is positive) denoting the value of d, v
and u respectively.
For each test case, first print the serial number of the case, a colon, an space and then print "can't determine" (without the quotes) if it is not possible to find different paths as stated above, else print the value of P corrected to three digits after decimal point. Check the sample input & output.
Sample
Input
3
8 5 6
1 2 3
1 5 6
Sample Output
Case 1: 1.079
Case 2: 0.114
Case 3: 0.135
Problem setter: Anupam Bhattacharjee, CSE, BUET
Thanks to Adrian for alternate solution and clarification