gpa——01分数规划

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

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

题解：

感想：

这道题就是0，1分数规划的应用。

代码：

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
  
const double inf = 1e-6;
const int maxn = 1e5+5;
double a[maxn];
double b[maxn];
double f[maxn];
  
int solve(double x,int n,int k)
{
    for(int i = 0; i < n; i++)
        f[i] = a[i]*b[i]-x*a[i];
    sort(f, f+n);
    double ans = 0;
    for(int i = n-1; i > k-1; i--)
        ans += f[i];
    if(ans >= 0)
        return 1;
    return 0;
}
  
int main()
{
    int t;
    int n, k ;
    cin >> n >> k;
    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));
    memset(f, 0, sizeof(f));
    double maxx = 0;
    for(int i = 0; i < n; i++)
        scanf("%lf", &a[i]);
    for(int i = 0; i < n; i++)
    {
        scanf("%lf", &b[i]);
        maxx = max(maxx, b[i]);
    }
    double l = 0;
    double r = maxx;
    while(r-l > inf)
    {
        double m = (r+l)/2;
        if(solve(m, n, k))
            l = m;
        else
            r = m;
    }
    printf("%.6lf\n", l);
    return 0;
}

关于01分数规划具体解释可参考：http://www.cnblogs.com/perseawe/archive/2012/05/03/01fsgh.html