2018牛客暑假多校A题GPA 01分数规划

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

gpa

时间限制：C/C++ 1秒，其他语言2秒
空间限制：C/C++ 262144K，其他语言524288K
Special Judge, 64bit IO Format: %lld

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

复制

3 1
1 2 3
3 2 1

输出

复制

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

题目：考虑01分数规划

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=100005;
const double eps=1.0e-6;
int n,k;
double a[maxn],b[maxn],s[maxn];
double d[maxn];
bool judge(double x)
{
 
    for(int i=1;i<=n;i++)
    {
        d[i]=a[i]-x*s[i];
    }
    sort(d+1,d+n+1);
    double sum=0;
    for(int i=k+1;i<=n;i++)
    {
        sum+=d[i];
    }
    return sum>=0.0;
}
int main()
{
    int i;
    scanf("%d%d",&n,&k);
    for(i=1;i<=n;i++)
        scanf("%lf",&s[i]);
    for(i=1;i<=n;i++)
        scanf("%lf",&b[i]);
    for(i=1;i<=n;i++)
        a[i]=s[i]*b[i];
    double l=0;
    double r=0x3f3f3f3f;
    while((r-l)>eps)
    {
        double mid=(l+r)/2;
        if(judge(mid))    l=mid;
        else r=mid;
    }
    printf("%.11f\n",l);
}