hdu 1709 普通母函数

最新推荐文章于 2019-10-10 16:49:51 发布

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#母函数

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本文介绍了一道关于天平原理的母函数问题，并提供了一段C++代码实现。该问题探讨如何通过一系列不同重量的砝码组合来测量特定范围内的所有可能重量。

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题目传送门：点击打开链接

这道题与别的母函数题不一样，利用了天平的原理，一开始只是盲目的套一下模版，但后来发现他们的重量不只是相加，也可以相减，但是我只是写出了一种相减的情况，就是利用的得出的重量减去第i种的重量，且没有写到第i种的重量减去得出的重量。。如果不懂可以看一下代码。

#include <iostream>
#include <cstring>
#include <vector>
using namespace std;
int n;int sum;
int c1[11000],c2[11000];
int w[110];
void init()
{
    sum=0;
    for(int i=1;i<=n;++i)
    {
        cin>>w[i];
        sum+=w[i];
    }
}
void solve()
{
    memset(c1,0,sizeof(c1));
    memset(c2,0,sizeof(c2));
    c1[w[1]]=1;c1[0]=1;
    for(int cnt=2;cnt<=n;++cnt)
    {
        int i=w[cnt];
        for(int j=0;j<=sum;++j)
        {
            if(c1[j])
            {
                for(int k=0;k<=i;k+=i)
                {
                    if(k+j<=sum)
                        c2[k+j]+=c1[j];
                    if(j-k>0)
                        c2[j-k]+=c1[j];
                    if(k>j)
                        ++c2[k-j];
                }
            }
        }
        memcpy(&c1,&c2,sizeof(c2));
        memset(c2,0,sizeof(c2));
    }
    vector<int> v;int num=0;
    for(int i=1;i<=sum;++i)
    {
        if(!c1[i])
        {
            ++num;
            v.push_back(i);
        }
    }
    cout<<num<<endl;
    if(num)
    {
        for(int i=0;i<num-1;++i)
            cout<<v[i]<<" ";
        cout<<v[num-1]<<endl;
    }
}
int main(int argc, const char * argv[])
{
    while(cin>>n)
    {
        init();
        solve();
    }
    return 0;
}
//4
//1 3 5 8
//answer:0

The Balance

Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 7623 Accepted Submission(s): 3167

Problem 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