acm培训专题规划书_动态规划.doc

ACM-ICPC（重邮赛区）参赛队培训专题计划 培训专题及其所占比例： 有哪些信誉好的足球投注网站：10% 动态规划：15% 贪心算法：约5% 构造：约5% 图论：约10% 计算几何：约5% 纯数学问题：约20% 数据结构：约5% 其它：约25% 第二次专题——动态规划 （1）Jury Compromise Description In 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 randomly from 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 satisfactory to both parties. We will now make this more precise: given a pool of n potential jurors and two values di (the defences value) and pi (the prosecutions 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. Input The 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