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-7

using 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;
	else
		return false;
}

void mainwork()
{
	double l=eps,r=inf-eps,mid;
	while(l+eps<r)
	{
		mid=(l+r)/2.0;
		if(jug(mid))
			l=mid;
		else
			r=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。