Jury Compromise

DescriptionIn Frobnia, a far-away country, the verdicts in court trials are determined by a jury consisting of members of the general public. Every time a trial is set to begin, a jury has to be selected, which is done as follows. First, several people are drawn randomlyfrom the public. For each person in this pool, defence and prosecution assign a grade from 0 to 20 indicating their preference for this person. 0 means total dislike, 20 on the other hand means that this person is considered ideally suited for the jury. Based on the grades of the two parties, the judge selects the jury. In order to ensure a fair trial, the tendencies of the jury to favour either defence or prosecution should be as balanced as possible. The jury therefore has to be chosen in a way that is satisfactoryto both parties. We will now make this more precise: given a pool of n potential jurors and two values di (the defence's value) and pi (the prosecution's value) for each potential juror i, you are to select a jury of m persons. If J is a subset of {1,..., n} with m elements,then D(J ) = sum(dk) k belong to J and P(J) = sum(pk) k belong to J are the total values of this jury for defence and prosecution. For an optimal jury J , the value |D(J) - P(J)| must be minimal. If there are several jurys with minimal |D(J) - P(J)|, one which maximizes D(J) + P(J) should be selected since the jury should be as ideal as possible for both parties. You are to write a program that implements this jury selection process and chooses an optimal jury given a set of candidates.InputThe input file contains several jury selection rounds. Each round starts with a line containing two integers n and m. n is the number of candidates and m the number of jury members. These values will satisfy 1<=n<=200, 1<=m<=20 and of course m<=n. The following n lines contain the two integers pi and di for i = 1,...,n. A blank line separates each round from the next. The file ends with a round that has n = m = 0.OutputFor each round output a line containing the number of the jury selection round ('Jury #1', 'Jury #2', etc.). On the next line print the values D(J ) and P (J ) of your jury as shown below and on another line print the numbers of the m chosen candidates in ascending order. Output a blank before each individual candidate number. Output an empty line after each test case.Sample Input

4 2
1 2
2 3
4 1
6 2
0 0

Sample Output

Jury #1
Best jury has value 6 for prosecution and value 4 for defence: 

2 3

首先我想到的状态转移方程式：dp[i][k]:从前i个中选出k个，使得差距最小的差距值。但是这样根本没有办法用动态规划的策略，通过前面的状态推出后面的状态。改变思路：dp[i][k]:选出i个且差距为k时两者之和的最大值。这样的方法只要在每一次遍历一遍候选人，因此关键在于当前选的人不能再所依赖的决策中已选。又考虑到答案中本身要输出选择的人，因此用数组select[i][k]保存对应决策中选择的人。这样又可以用它来递推查找某人是否已经选了。初始化已经无意义量的处理略。还有就是因为差值可能有负，所以统一加上常量400。用400代替0。