I am very confused by this problem, especially with the third test case.
http://mirror.codeforces.com/contest/127/problem/C
It says the answer is
76 54
I am wondering why isn't the answer
114 81
Both gives the same final temperature
(143*114 + 81 * 456)/(114 + 81)
273.015384615
(143 * 76 + 456 * 54) / (76 + 54)
273.015384615
Since the temperature is same i thought that the higher values for y1 and y2 should be chosen since that will fill up faster. So, i thought 114 and 81 should be the optimal answer. Please help with this dilemma. I appreciate it!!
In this case x1 = 110 then y1 can't be 114 since y1 <= x1.
Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2)You output y1 = 114, but 114 > 110 = x1.
You should divide y1 and y2 on gcd(y1, y2)
@Elise and @alexyz
114 < 117
if you read carefully
y1 flows through first tap and first tap is hot water top.
Hot water tap can transmit from 0 to x2 water units per second
in the test case
x2 is 117.
so is there still my misunderstanding or is the test case wrong? Thanks!
The statement is a little misleading. It actually never explicitly says that the hot water tap is the first, it just says that there are two taps and name the hot before the cold but that doesn't mean there is an order between them.
Furthermore, judging by the equation and numbers associated with t and x I think you can safely assume that the first tap is cold water tap.