集训第五周 动态规划 K题 背包

K - 背包

Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

Submit Status

Description

Now you are asked to measure a dose of medicine with a balance and a number of weights. Certainly it is not always achievable. So you should find out the qualities which cannot be measured from the range [1,S]. S is the total quality of all the weights. 

 

Input

The input consists of multiple test cases, and each case begins with a single positive integer N (1<=N<=100) on a line by itself indicating the number of weights you have. Followed by N integers Ai (1<=i<=N), indicating the quality of each weight where 1<=Ai<=100. 

 

Output

For each input set, you should first print a line specifying the number of qualities which cannot be measured. Then print another line which consists all the irrealizable qualities if the number is not zero. 

 

Sample Input

3 1 2 4 3 9 2 1

 

Sample Output

0 2 4 5

 

 

这道题可以使用DP做，dp（i）代表i这个数字是否可称，dp（i）=(( dp(j)==1 && 1<j<sum )     j==i + || - 新加入的数字 ?)

 

#include"iostream"
#include"algorithm"
#include"cstring"
using namespace std;

const int maxn=;

int dp[maxn],ok[maxn],ans[maxn];

int main()
{
    int sum,n,temp;

    while(cin>>n)
    {
        memset(dp,,sizeof(dp));
        dp[]=;
        sum=;
        for(int i=;i<=n;i++)
        {
            cin>>temp;
            memset(ok,,sizeof(ok));
            sum+=temp;
            for(int j=;j<=sum;j++) if(dp[j])
            {
                ok[j+temp]=;
                ok[abs(j-temp)]=;
            }
            for(int j=;j<=sum;j++) if(ok[j])
            dp[j]=;
        }
        int top=;
        for(int i=;i<=sum;i++)
        {
            if(dp[i]==) ans[top++]=i;
        }
        cout<<top<<endl;
        if(top)
        {
        for(int j=;j<top-;j++) cout<<ans[j]<<" ";
        cout<<ans[top-]<<endl;
        }
    }
    return ;
}

你好