CSU-ACM2017暑假集训比赛1 TD POJ3111

#include<cstdio>#include<cstring>#include<algorithm>#define maxl 100010#define inf 2000000001#define eps 1e-7using namespace std;int n,k;double ans;double v[maxl],w[maxl];struct node{double num;int pos;} a[maxl];void prework(){scanf("%d%d",&n,&k);for(int i=1;i<=n;i++)scanf("%lf%lf",&v[i],&w[i]);}bool cmp(const node &x,const node &y){return x.num>y.num;}bool jug(double x){for(int i=1;i<=n;i++)a[i].num=v[i]-w[i]*x,a[i].pos=i;sort(a+1,a+1+n,cmp);double sum=0;for(int i=1;i<=k;i++)sum+=a[i].num;if(sum>eps)return true;elsereturn false;}void mainwork(){double l=eps,r=inf-eps,mid;while(l+eps<r){mid=(l+r)/2.0;if(jug(mid))l=mid;elser=mid;}ans=l;}void print(){jug(ans);for(int i=1;i<=k;i++)printf("%d ",a[i].pos);}int main(){prework();mainwork();print();return 0;}

Demy has n jewels. Each of her jewels has some value v_i and weight w_i.

Since her husband John got broke after recent financial crises, Demy has decided to sell some jewels. She has decided that she would keep k best jewels for herself. She decided to keep such jewels that their specific value is as large as possible. That is, denote the specific value of some set of jewels S = {i₁, i₂, …, i_k} as

.

Demy would like to select such k jewels that their specific value is maximal possible. Help her to do so.

选出能使上式最大的k个珠子、

选出vi/wi最大的珠子无法满足vi之和/wi之和最大。于是我们二分这个最大值为x

然后 求一组(vi+vj....)/（wi+wj..）=x，移项得 (vi+vj...)-(wi+wj..)*x=0，而我们要求最大的x，所以只要(vi+vj...)-(wi+wj..)*x >= 0,这个x就是满足的。