HDU3535AreYouBusy[混合背包 分组背包]

AreYouBusy

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3985    Accepted Submission(s):
1580

Problem Description

Happy New Term!
As having become a junior, xiaoA
recognizes that there is not much time for her to AC problems, because there are
some other things for her to do, which makes her nearly mad.
What's more, her
boss tells her that for some sets of duties, she must choose at least one job to
do, but for some sets of things, she can only choose at most one to do, which is
meaningless to the boss. And for others, she can do of her will. We just define
the things that she can choose as "jobs". A job takes time , and gives xiaoA
some points of happiness (which means that she is always willing to do the
jobs).So can you choose the best sets of them to give her the maximum points of
happiness and also to be a good junior(which means that she should follow the
boss's advice)?

 

Input

There are several test cases, each test case begins
with two integers n and T (0<=n,T<=100) , n sets of jobs for you to choose
and T minutes for her to do them. Follows are n sets of description, each of
which starts with two integers m and s (0<m<=100), there are m jobs in
this set , and the set type is s, (0 stands for the sets that should choose at
least 1 job to do, 1 for the sets that should choose at most 1 , and 2 for the
one you can choose freely).then m pairs of integers ci,gi follows
(0<=ci,gi<=100), means the ith job cost ci minutes to finish and gi points
of happiness can be gained by finishing it. One job can be done only once.

 

Output

One line for each test case contains the maximum points
of happiness we can choose from all jobs .if she can’t finish what her boss
want, just output -1 .

 

Sample Input

3 3
2 1
2 5
3 8
2 0
1 0
2 1
3 2
4 3
2 1
1 1

3 4
2 1
2 5
3 8
2 0
1 1
2 8
3 2
4 4
2 1
1 1

1 1
1 0
2 1

5 3
2 0
1 0
2 1
2 0
2 2
1 1
2 0
3 2
2 1
2 1
1 5
2 8
3 2
3 8
4 9
5 10

 

Sample Output

5
13
-1
-1

 

Author

hphp

 

Source

2010
ACM-ICPC Multi-University Training Contest（10）——Host by HEU

---

题意：n组，每组m个物品，有三种类型：至少选一个，至多选一个，随便选

 

---

d[i][j]表示前i组体积j的最大值

至少选一个：d[i][j]=-INF，保证了至少一个

　　　　　　d[i][j]=max(d[i][j],max(d[i][j-v[x]]+w[x],d[i-1][j-v[x]]+w[x])) 因为可以选多个 【WARN：不能分成两次max，因为保证至少选一个-INF】

至多选一个：d[i][j]=d[i-1][j]，d[i][j]=max(d[i][j],d[i-1][j-v[x]]+w[x]) 可以不选，普通分组背包

随便：d[i][j]=d[i-1][j]，d[i][j]=max(d[i][j],d[i][j-v[x]]+w[x]); 可以不选，也可以选多个

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
const int N=,INF=1e9;
int read(){
    char c=getchar();int x=,f=;
    while(c<''||c>''){if(c=='-')f=-; c=getchar();}
    while(c>=''&&c<=''){x=x*+c-''; c=getchar();}
    return x*f;
}
int n,t,m,s,v[N],w[N];
int d[N][N];
int main(){
    while(cin>>n>>t){
        memset(d,,sizeof(d));
        for(int i=;i<=n;i++){
            m=read();s=read();
            for(int x=;x<=m;x++){
                v[x]=read();w[x]=read();
            }
            if(s==){
                for(int j=;j<=t;j++) d[i][j]=-INF;
                for(int x=;x<=m;x++)
                    for(int j=t;j>=v[x];j--)
                        d[i][j]=max(d[i][j],max(d[i][j-v[x]]+w[x],d[i-][j-v[x]]+w[x]));
            }
            else if(s==){
                for(int j=;j<=t;j++) d[i][j]=d[i-][j];
                for(int x=;x<=m;x++)
                    for(int j=t;j>=v[x];j--)
                        d[i][j]=max(d[i][j],d[i-][j-v[x]]+w[x]);
            }
            else if(s==){
                for(int j=;j<=t;j++) d[i][j]=d[i-][j];
                for(int x=;x<=m;x++)
                    for(int j=t;j>=v[x];j--)
                        d[i][j]=max(d[i][j],d[i][j-v[x]]+w[x]);
            }
        }
        printf("%d\n",max(d[n][t],-));
    }
}