HDU 1059.Dividing【多重背包+筛选（DP）】【3月17】

Dividing

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 22051    Accepted Submission(s): 6208

Problem Description

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.

 

Input

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.

 

Output

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.

 

Sample Input

1 0 1 2 0 01 0 0 0 1 10 0 0 0 0 0

 

Sample Output

Collection #1:Can't be divided.Collection #2:Can be divided.

 

题目意思就是要把价值为1/2/3/4/5/6的若干个石头分成价值相等的两堆，问是否可以，具体操作看代码：

#include<iostream>#include<cstdio>#include<cstring>using namespace std;int main(){    int kase = 1, sum, MAXN;    int num[7], dp[60010];    while(1)    {        sum = 0;        for(int i = 1;i <= 6; ++i)        {            scanf("%d", &num[i]);            sum += num[i]*i;        }        if(sum == 0) break;        else if(sum%2 == 1)//总价值为奇数，肯定无法平分        {            printf("Collection #%d:\nCan't be divided.\n\n", kase++);            continue;        }        else        {            printf("Collection #%d:\n", kase++);            memset(dp, 0, sizeof(dp));            MAXN = sum/2;            //多重背包，这次我们不保存价值，而是看当前价值能否凑出来            for(int i = 0;i <= MAXN && i <= num[1]; ++i) dp[i] = 1;            for(int i = 2;i <= 6; ++i)            {                for(int j = MAXN; j >= 0; --j)                {                    if(dp[j] == 0) continue;                    for(int k = 1; k <= num[i]; ++k)                    {                        if(k*i+j > MAXN) break;//超范围                        if(dp[k*i+j] == 1) break;//去重                        dp[k*i+j] = 1;                    }                }            }            if(dp[MAXN]) cout <<"Can be divided.\n\n";            else cout <<"Can't be divided.\n\n";        }    }    return 0;}