Pie
My birthday is coming up and traditionally I'm serving pie. Not just one pie, no, I have a number N of them, of various tastes and of various sizes. F of my friends are coming to my party and each of them gets a piece of pie. This should be one piece of one pie, not several small pieces since that looks messy. This piece can be one whole pie though.
My friends are very annoying and if one of them gets a bigger piece than the others, they start complaining. Therefore all of them should get equally sized (but not necessarily equally shaped) pieces, even if this leads to some pie getting spoiled (which is better than spoiling the party). Of course, I want a piece of pie for myself too, and that piece should also be of the same size.
What is the largest possible piece size all of us can get? All the pies are cylindrical in shape and they all have the same height 1, but the radii of the pies can be different.
InputOne line with a positive integer: the number of test cases. Then for each test case:My friends are very annoying and if one of them gets a bigger piece than the others, they start complaining. Therefore all of them should get equally sized (but not necessarily equally shaped) pieces, even if this leads to some pie getting spoiled (which is better than spoiling the party). Of course, I want a piece of pie for myself too, and that piece should also be of the same size.
What is the largest possible piece size all of us can get? All the pies are cylindrical in shape and they all have the same height 1, but the radii of the pies can be different.
---One line with two integers N and F with 1 <= N, F <= 10 000: the number of pies and the number of friends.
---One line with N integers ri with 1 <= ri <= 10 000: the radii of the pies.
OutputFor each test case, output one line with the largest possible volume V such that me and my friends can all get a pie piece of size V. The answer should be given as a floating point number with an absolute error of at most 10^(-3).Sample Input
3 3 3 4 3 3 1 24 5 10 5 1 4 2 3 4 5 6 5 4 2Sample Output
25.1327 3.1416 50.2655
by talk:分馅饼，馅饼高度都为1，所以馅饼的体积V=π*r*r*1=π*r*r;分到最大馅饼的体积是：所有馅饼体积之和/（F+1）；（为什么不能是直接所有馅饼之和/（F+1）呢？因为每人只能分到一块，如果讲究平均分的话，一个人分到的就是拼凑起来的“最大的体积”，一个人甚至可能得到超过一块馅饼）最小即为0，然后我们对这两个最大最小值采用二分方法，求出中间符合最大的体积。那么怎么判断那个值就是最大的体积呢？让每个馅饼的体积/能分到最大的体积=能分到的人数，然后将每个馅饼能分到的人数相加，将该人数与F+1做判断比较，然后就是熟悉的套路了。