牛客网暑期ACM多校训练营（第五场） A gpa (01分数规划）

题目链接：https://www.nowcoder.com/acm/contest/143/A
来源：牛客网
 

题目描述

Kanade selected n courses in the university. The academic credit of the i-th course is s[i] and the score of the i-th course is c[i].

At the university where she attended, the final score of her is 

Now she can delete at most k courses and she want to know what the highest final score that can get.

输入描述:

The first line has two positive integers n,k

The second line has n positive integers s[i]

The third line has n positive integers c[i]

输出描述:

Output the highest final score, your answer is correct if and only if the absolute error with the standard answer is no more than 10-5

示例1

输入

3 1
1 2 3
3 2 1

输出

2.33333333333

说明

Delete the third course and the final score is 

备注:

1≤ n≤ 105

0≤ k < n

1≤ s[i],c[i] ≤ 103

题意：就是从n个里面删除最多K个让那个值最大，01分数规划是选n-k个，不难发现删除的话删的越多数值越大(很难发现)，然后就套用01分数规划就行了。

#include<bits/stdc++.h>
using namespace std;
const int MAXN = 1e5+5;
const double eps = 1e-6;
int a[MAXN];
int b[MAXN];
double c[MAXN];
int n,k;
int check(double mid)
{
	for(int i=0;i<n;i++)
		c[i]=a[i]-mid*b[i];
	sort(c,c+n);
	double ans=0;
	for(int i=k;i<n;i++)
		ans=ans+c[i];
	return ans>=0;
}
void solve()
{
	double l=0;
	double r=1000000000;
	while(r-l>eps)
	{
		double mid = (l+r)/2;
		if(check(mid))
			l=mid;
		else
			r=mid;
	}
	printf("%.10lf\n",l);
}
int main()
{
	scanf("%d%d",&n,&k);
	for(int i=0;i<n;i++)
		scanf("%d",&a[i]);
	for(int i=0;i<n;i++)
		scanf("%d",&b[i]);
	for(int i=0;i<n;i++)
	{
		int t=a[i];
		a[i]=a[i]*b[i];
		b[i]=t;
	}
	solve();
	return 0;
}