SRM657 DIV1 Problem Sets

原题链接:Problem Sets

Cat Snuke came up with some problems. He wants to construct as many problem sets as possible using those problems. Each problem set must contain exactly three problems: one for the Easy slot, one for the Medium slot, and one for the Hard slot. Each problem can only be assigned to a single slot in a single problem set. He came up with E + EM + M + MH + H problems in total. The distribution of the problems is as follows:

  • E problems can only be used in the Easy slot.
  • EM problems can be used either in the Easy slot or the Medium slot.
  • M problems can only be used in the Medium slot.
  • MH problems can be used either in the Medium slot or the Hard slot.
  • H problems can only be used in the Hard slot.

Return the maximal number of problem sets he can construct.


SRM656 DIV1 Random Pancake Stack


原题链接:Random Pancake Stack

Charlie has N pancakes. He wants to serve some of them for breakfast. We will number the pancakes 0 through N-1. For each i, pancake i has width i+1 and deliciousness d[i].

Charlie chooses the pancakes he is going to serve using the following randomized process: He starts by choosing the first pancake uniformly at random from all the pancakes he has. He places the chosen pancake onto a plate. This pancake now forms the bottom of a future stack of pancakes. Then, Charlie repeats the following procedure:

  1. If there are no more pancakes remaining, terminate.
  2. Choose a pancake uniformly at random from the pancakes that have not been chosen yet.
  3. If the width of this pancake is greater than the width of the pancake on top of the stack, terminate without taking it.
  4. Place the chosen pancake on top of the stack and go back to step 1.

You are given the vector d with N elements. The total deliciousness of a serving of pancakes is the sum of the deliciousness of all pancakes used in the serving. Compute and return the expected value of the total deliciousness of the pancakes chosen by Charlie.