【HDU 2126】Buy the souvenirs（01背包）

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When the winter holiday comes, a lot of people will have a trip. Generally, there are a lot of souvenirs to sell, and sometimes the travelers will buy some ones with pleasure. Not only can they give the souvenirs to their friends and families as gifts, but also can the souvenirs leave them good recollections. All in all, the prices of souvenirs are not very dear, and the souvenirs are also very lovable and interesting. But the money the people have is under the control. They can’t buy a lot, but only a few. So after they admire all the souvenirs, they decide to buy some ones, and they have many combinations to select, but there are no two ones with the same kind in any combination. Now there is a blank written by the names and prices of the souvenirs, as a top coder all around the world, you should calculate how many selections you have, and any selection owns the most kinds of different souvenirs. For instance:

And you have only 7 RMB, this time you can select any combination with 3 kinds of souvenirs at most, so the selections of 3 kinds of souvenirs are ABC (6), ABD (7). But if you have 8 RMB, the selections with the most kinds of souvenirs are ABC (6), ABD (7), ACD (8), and if you have 10 RMB, there is only one selection with the most kinds of souvenirs to you: ABCD (10).

Input

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For the first line, there is a T means the number cases, then T cases follow.

In each case, in the first line there are two integer n and m, n is the number of the souvenirs and m is the money you have. The second line contains n integers; each integer describes a kind of souvenir.

All the numbers and results are in the range of 32-signed integer, and 0<=m<=500, 0<n<=30, t<=500, and the prices are all positive integers. There is a blank line between two cases.

Output

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If you can buy some souvenirs, you should print the result with the same formation as “You have S selection(s) to buy with K kind(s) of souvenirs”, where the K means the most kinds of souvenirs you can buy, and S means the numbers of the combinations you can buy with the K kinds of souvenirs combination. But sometimes you can buy nothing, so you must print the result “Sorry, you can't buy anything.”

Sample Input

2
4 7
1 2 3 4
4 0
1 2 3 4

Sample Output

You have 2 selection(s) to buy with 3 kind(s) of souvenirs.
Sorry, you can't buy anything.

题解

求最大取得值显然是01背包，需要求方案数，只要再开一个数组在转移时记录即可

01背包转移方程为

dp[j]代表花费为j时的最大选择数
For i:1~n
   For j:m~a[i]
       dp[j]=max(dp[j],d[j-a[i]]+1);
f[j]代表花费为j时最大选择数的方案数
if(dp[j]==dp[j-a[i]]+1)
     f[j]+=f[j-a[i]]
if(dp[j]<dp[j-a[i]]+1)
     f[j]=f[j-a[i]];

#include <map>
#include <queue>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
#define inf 1000000000
#define PI acos(-1)
#define REP(i,x,n) for(int i=x;i<=n;i++)
#define DEP(i,n,x) for(int i=n;i>=x;i--)
#define mem(a,x) memset(a,x,sizeof(a))
using namespace std;
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-') f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
const int N=500+5;
int dp[N],f[N];
int a[35];
int main(){
    int T=read();
    while(T--){
      int n=read(),m=read();
      REP(i,1,n) a[i]=read();
      mem(dp,0);mem(f,0);
      REP(i,0,m) f[i]=1;
      REP(i,1,n) DEP(j,m,a[i]){
            if(dp[j]==dp[j-a[i]]+1)
                f[j]=f[j-a[i]]+f[j];
            else if(dp[j]<dp[j-a[i]]+1){
                dp[j]=dp[j-a[i]]+1;
                f[j]=f[j-a[i]];
            }
      }
      if (dp[m]!=0)
            printf("You have %d selection(s) to buy with %d kind(s) of souvenirs.\n"
                   , f[m], dp[m]);
      else
            printf("Sorry, you can't buy anything.\n");
    }
    return 0;
}