学步园

Marsha and Bill own a collection of marbles. They want to split the collection among themselves so that both receive an equal share of the marbles. This would be easy if all the marbles had the same value, because then they could
just split the collection in half. But unfortunately, some of the marbles are larger, or more beautiful than others. So, Marsha and Bill start by assigning a value, a natural number between one and six, to each marble. Now they want to divide the marbles so
that each of them gets the same total value.
Unfortunately, they realize that it might be impossible to divide the marbles in this way (even if the total value of all marbles is even). For example, if there are one marble of value 1, one of value 3 and two of value 4, then they cannot be split into sets
of equal value. So, they ask you to write a program that checks whether there is a fair partition of the marbles.

Each line in the input describes one collection of marbles to be divided. The lines consist of six non-negative integers n1, n2, ..., n6, where ni is the number of marbles of value i. So, the example from above would be described
by the input-line ``1 0 1 2 0 0''. The maximum total number of marbles will be 20000.

The last line of the input file will be ``0 0 0 0 0 0''; do not process this line.

For each colletcion, output ``Collection #k:'', where k is the number of the test case, and then either ``Can be divided.'' or ``Can't be divided.''.

Output a blank line after each test case.

1 0 1 2 0 0
1 0 0 0 1 1
0 0 0 0 0 0

Collection #1:
Can't be divided.

Collection #2:
Can be divided.
多重背包：由01背包和完全背包组合而成，只不过在用01背包时数值作了变换。
#include<stdio.h>
#include<string.h>
#define N 100010
int dp[N],Vect;
int max(int a,int b){return a>b?a:b;}
void zeroonepack(int use,int weight)//（01背包）
{
    for(int v=Vect;v>=use;v--)//递减开始，为了防止背包里重复放当前同一物品
    dp[v]=max(dp[v],dp[v-use]+weight);
}
void complexepack(int use,int weight)//完全背包
{
    for(int v=use;v<=Vect;v++)//递增开始，背包中可以放多个当前同一物品
    dp[v]=max(dp[v],dp[v-use]+weight);
}
void miltpack(int use,int weight,int n)//n为当前物品的数量（多重背包）
{
    if(n*use>=Vect)//当超出背包空间时，变成完全背包
        complexepack(use,weight);
    else//当没有超出，则为01背包
    {
        int k=1;
        while(k<n)//把当前物品分成多种类型
        {
            zeroonepack(k*use,k*weight);
            n-=k;
            k*=2;
        }
        zeroonepack(n*use,n*weight);//剩下作为一种
    }
}
int main()
{
    int nn[8],c=0;
    while(1)
    {
        Vect=0;
        for(int i=1;i<=6;i++)
        {
            scanf("%d",&nn[i]);
            Vect+=nn[i]*i;
        }
        if(Vect==0)break;
        if(Vect%2!=0)
            printf("Collection #%d:\nCan't be divided.\n\n",++c);
        else
        {
            Vect/=2;
            for(int i=0;i<=Vect;i++)
                dp[i]=0;
            for(int i=1;i<=6;i++)
            if(nn[i])
            miltpack(i,i,nn[i]);
            if(dp[Vect]==Vect)
                printf("Collection #%d:\nCan be divided.\n\n",++c);
            else
                printf("Collection #%d:\nCan't be divided.\n\n",++c);
        }
    }
}