1257 背包问题 V3——分数规划

#include<cstdio>
#include<cstring>
#include<algorithm>
#define LL long long
using namespace std;
const int M=50007;
int read(){
    int ans=0,f=1,c=getchar();
    while(c<‘0‘||c>‘9‘){if(c==‘-‘) f=-1; c=getchar();}
    while(c>=‘0‘&&c<=‘9‘){ans=ans*10+(c-‘0‘); c=getchar();}
    return ans*f;
}
int n,k;
int c[M],w[M];
LL sumx,sumy,ansx,ansy;
LL gcd(LL x,LL y){
    while(y){
        LL p=x%y;
        x=y;
        y=p;
    } 
    return x;
}
struct node{double v; int pos;}e[M];
bool cmp(node a,node b){return a.v-b.v>1e-6;}
bool check(double mid){
    for(int i=1;i<=n;i++) e[i].v=1.0*w[i]-1.0*c[i]*mid,e[i].pos=i; 
    sort(e+1,e+1+n,cmp);
    double sum=0; sumx=0; sumy=0;
    for(int i=1;i<=k;i++){
        sum+=e[i].v;
        sumx+=w[e[i].pos];
        sumy+=c[e[i].pos];
    }
    return sum>=0;
}
int main()
{
    n=read(); k=read();
    for(int i=1;i<=n;i++) c[i]=read(),w[i]=read();
    double l=0,r=50000;
    while(r-l>1e-6){
        double mid=(l+r)/2;
        if(check(mid)) l=mid,ansx=sumx,ansy=sumy;
        else r=mid;
    }
    LL d=gcd(ansx,ansy);
    printf("%lld/%lld\n",ansx/d,ansy/d);
    return 0;
}