Jury Compromise
| Time Limit: 1000MS | Memory Limit: 65536K | |||
| Total Submissions: 27314 | Accepted: 7208 | Special Judge | ||
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 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.
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 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.
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 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.
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.
Output
For 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.
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
双塔DP
法庭要选择若干个陪审团成员，是的二者和的差最小，并且在差最小的时候选择和最大的
差不多是这个意思。
可以用三维DP dp[i][j][p]表示第i个人已经选择了j个人差值为p的最大和
最后枚举P，选择p最小的且存在的
由于要输出路径，所以还要一个三维数组记录路径
#include <iostream> #include <algorithm> #include <string.h> #include <stdlib.h> #include <math.h> #include <stdio.h> using namespace std; int a[205]; int b[205]; int dp[205][25][805]; int ans[25]; struct Node { int i,j,k,value; }pre[205][25][805]; int n,m; int main() { int cas=0; while(scanf("%d%d",&n,&m)!=EOF) { if(n==0&&m==0) break; for(int i=1;i<=n;i++) { scanf("%d%d",&a[i],&b[i]); } memset(dp,-1,sizeof(dp)); dp[0][0][0+400]=0; pre[0][0][400].value=-1; for(int i=1;i<=n;i++) { //memcpy(dp[i],dp[i-1],sizeof(dp[i-1])); for(int j=0;j<=m;j++) { for(int k=-400;k<=400;k++) { //不选择 if(dp[i-1][j][k+400]!=-1) { if(dp[i][j][k+400]<dp[i-1][j][k+400]) { dp[i][j][k+400]=dp[i-1][j][k+400];pre[i][j][k+400].i=i-1; pre[i][j][k+400].j=j; pre[i][j][k+400].k=k+400; pre[i][j][k+400].value=pre[i-1][j][k+400].value; } } //选择 if(j==0||dp[i-1][j-1][k+400]==-1) continue; if(dp[i][j][k+400+a[i]-b[i]]<dp[i-1][j-1][k+400]+a[i]+b[i]) { dp[i][j][k+400+a[i]-b[i]]=dp[i-1][j-1][k+400]+a[i]+b[i]; pre[i][j][k+400+a[i]-b[i]].i=i-1; pre[i][j][k+400+a[i]-b[i]].j=j-1; pre[i][j][k+400+a[i]-b[i]].k=k+400; pre[i][j][k+400+a[i]-b[i]].value=i; } } } } int k=400; int j=k; int z=-1; while(k>=0&&j<=800) { if(dp[n][m][k]!=-1) z=k; if(dp[n][m][j]!=-1) if(dp[n][m][k]<dp[n][m][j]) z=j; if(z!=-1) break; k--; j++; } int x=n,y=m; int cnt=0; while(pre[x][y][z].value!=-1) { //cout<<dp[x][y][z]<<endl; if(pre[x][y][z].value!=ans[cnt-1]||cnt==0) ans[cnt++]=pre[x][y][z].value; int xx,yy,zz; xx=pre[x][y][z].i; yy=pre[x][y][z].j; zz=pre[x][y][z].k; x=xx;y=yy;z=zz; } sort(ans,ans+cnt); int res1=0,res2=0; for(int i=0;i<cnt;i++) res1+=a[ans[i]],res2+=b[ans[i]]; printf("Jury #%d ",++cas); printf("Best jury has value %d for prosecution and value %d for defence: ",res1,res2); for(int i=0;i<cnt;i++) printf(" %d",ans[i]); cout<<endl<<endl; } return 0; }