POJ-2976:Dropping tests【01分数规划】

本文介绍了一个算法问题,即如何通过放弃部分考试成绩来最大化累计平均分。通过使用01分数规划的方法解决了这一问题,并详细解释了算法实现过程及注意事项。

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Dropping tests
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 12059 Accepted: 4212

Description

In a certain course, you take n tests. If you get ai out of bi questions correct on test i, your cumulative average is defined to be

.

Given your test scores and a positive integer k, determine how high you can make your cumulative average if you are allowed to drop any k of your test scores.

Suppose you take 3 tests with scores of 5/5, 0/1, and 2/6. Without dropping any tests, your cumulative average is . However, if you drop the third test, your cumulative average becomes .

Input

The input test file will contain multiple test cases, each containing exactly three lines. The first line contains two integers, 1 ≤ n ≤ 1000 and 0 ≤ k < n. The second line contains n integers indicating ai for all i. The third line contains n positive integers indicating bi for all i. It is guaranteed that 0 ≤ ai ≤ bi ≤ 1, 000, 000, 000. The end-of-file is marked by a test case with n = k = 0 and should not be processed.

Output

For each test case, write a single line with the highest cumulative average possible after dropping k of the given test scores. The average should be rounded to the nearest integer.

Sample Input

3 1
5 0 2
5 1 6
4 2
1 2 7 9
5 6 7 9
0 0

Sample Output

83
100

Hint

To avoid ambiguities due to rounding errors, the judge tests have been constructed so that all answers are at least 0.001 away from a decision boundary (i.e., you can assume that the average is never 83.4997).


题意:从n对(a,b)中选择其中的n-k对,使(Σa[i]/Σb[i])*100的值最大。

分析:01分数规划,注意精度问题,如果写成ans=l=mid,输出printf("%.0f\n",ans*100);是错的……wrong了很多次,才找到这里有问题。要写成l=mid,输出是l*100就可以了。

#include<stdio.h>
#include<algorithm>
#define eps 1e-9
using namespace std;
const int maxn=1111;
int n,k;
double a[maxn],b[maxn];
double x[maxn];
int cmp(double a,double b)
{
    return a>b;
}
int check(double l)
{
    for(int i=0;i<n;i++)
        x[i]=a[i]-l*b[i];
    sort(x,x+n,cmp);
    double sum=0;
    for(int i=0;i<n-k;i++)
        sum+=x[i];
    return sum>=0;
}
int main()
{
    while(scanf("%d%d",&n,&k),n+k)
    {
        for(int i=0;i<n;i++)
            scanf("%lf",&a[i]);
        for(int i=0;i<n;i++)
            scanf("%lf",&b[i]);
        double l=0,r=1.0;
        while(r-l>=eps)
        {
            double mid=(l+r)/2.0;
            if(check(mid))
                l=mid;
            else
                r=mid;
        }
        printf("%.0f\n",l*100);
    }
    return 0;
}


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