HDu 1059 Dividing(dp+バイナリ最適化)

Dividing
Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 10438    Accepted Submission(s): 2918
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 0
1 0 0 0 1 1
0 0 0 0 0 0
   
   
   
   

 
Sample Output

   
   
   
   

    
    
    
    Collection #1:
Can't be divided.

Collection #2:
Can be divided.
   
   
   
   

 
Source
Mid-Central European Regional Contest 1999
 
Recommend
JGShining
 
構想:直接リュックサックの時間は6*N*Nで間違いなくTLEです.したがって、バイナリ最適化が必要です.
        for(int i=1;i<=6;i++)         for(int j=1;j<=v[i];j++)         for(int k=sum-i*j;k>=0;k--)         if(dp[k])dp[k+j*i]=1;   
しかし、このプロセスをよく考えて、手動でシミュレーションすると、多くの重複マークが見つかります.
したがって、バイナリを使用して、これらの重複タグを低減することができます. の手順に従います.1 2, 4 8 16...
具体的に手動で計算すれば、わかります.
for(int i=1;i<=6;i++)     { for(int j=1;j<=v[i];j*=2)       { v[i]-=j;         for(int k=sum-i*j;k>=0;k--)         {         if(dp[k])dp[k+j*i]=1;         }      }      if(v[i])      {        for(int k=sum-i*v[i];k>=0;k--)        if(dp[k])dp[k+i*v[i]]=1;      }     }                                           
 

#include<iostream>
#include<cstring>
using namespace std;
const int mm=620010;
int dp[mm];
int v[7];
int main()
{ int sum;
  int cas=0;
  while(1)
  { sum=0;++cas;
    for(int i=1;i<=6;i++)
    {
      cin>>v[i];
      sum+=v[i]*i;
    }
    if(!sum)break;
    cout<<"Collection #"<<cas<<":
";
    if(sum&1)
    {cout<<"Can't be divided.

";
     continue;
    }
    sum/=2;
    memset(dp,0,sizeof(dp));
    dp[0]=1;
    for(int i=1;i<=6;i++)
    { for(int j=1;j<=v[i];j*=2)
      { v[i]-=j;
        for(int k=sum-i*j;k>=0;k--)
        {
        if(dp[k])dp[k+j*i]=1;
        }
     }
     if(v[i])
     {
       for(int k=sum-i*v[i];k>=0;k--)
       if(dp[k])dp[k+i*v[i]]=1;
     }
    }
    if(dp[sum])cout<<"Can be divided.
";
    else cout<<"Can't be divided.
";
    cout<<"
";
  }
}