01分数规划

\(\frac{\sum_{i=1}^N a_ix_i}{\sum_{i=1}^Nb_ix_i}=ans\)

\(\sum_{i=1}^N a_ix_i-ans\sum_{i=1}^N b_ix_i=0\)

二分答案ans即可

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

const int MAXN=1e5+5;
const double eps=1e-8;

int n,K;
double l=1e6+5,r,mid;
struct rpg{
	int a,b;
}a[MAXN];

bool cmp(rpg a,rpg b){return a.a-a.b*mid>b.a-b.b*mid;}

bool check()
{
	sort(a+1,a+n+1,cmp);
	double sum=0;
	int ct=1;
	while(sum+eps>0&&ct<=n){
		sum+=a[ct].a-a[ct].b*mid;
		++ct;
	}if(sum+eps<0) --ct;
	--ct;
	return ct>=K;
}

int main()
{
	scanf("%d%d",&n,&K);
	for(int i=1;i<=n;++i) scanf("%d",&a[i].a);
	for(int i=1;i<=n;++i) scanf("%d",&a[i].b),l=min(l,(double)a[i].a/a[i].b),r=max(r,(double)a[i].a/a[i].b);
	while(r-l>eps){
		mid=(l+r)/2;
		if(check()) l=mid;
		else r=mid;
	}printf("%.4lf\n",l);
	return 0;
}