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  • 【POJ 2976 Dropping tests】

    Time Limit: 1000MS
    Memory Limit: 65536K

    Total Submissions: 13849
    Accepted: 4851

    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 ≤ aibi ≤ 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).

    【翻译】给出n个物品,每个物品有两个值a和b,选择n-k个元素,询问sum{ai}/sum{bi}的最大值。

    题解:

            ①题目要求求出Sigma式子的最大值,可以考虑单个式子ai/bi的最大值,然后将它们合起来。

            ②但是直接计算是不方便转化的,因为Sigma和单个式子还是有区别的。

            ③由于具有取值上的单调性,因此考虑二分,二分最大值x,那么则有:

                     ∑ai/∑bi>=x      移项得到:   ∑ai>=x*∑bi ——> ∑ai-x*∑bi>=0

            ④所以就二分啊,使得x不断变大,大到使得∑ai-x*∑bi几乎等于0,就是最有解了。

    #include<stdio.h>
    #include<algorithm>
    #define go(i,a,b) for(int i=a;i<=b;i++)
    #define ro(i,a,b) for(int i=a;i>=b;i--)
    int n,k,a[4001],b[4001];
    double T[4001],res,l,r,M;
    bool check(double x)
    {
        go(i,1,n)T[i]=a[i]-x*b[i];std::sort(T+1,T+1+n);res=0;
        go(i,k+1,n)res+=T[i];return res>=0;
    }
    int main()
    {
        while(scanf("%d%d",&n,&k),n|k)
        {
        	go(i,1,n)scanf("%d",a+i);l=0;
        	go(i,1,n)scanf("%d",b+i);r=1;
        	while(r-l>1e-6)M=(l+r)/2,check(M)?l=M:r=M;printf("%.0f
    ",l*100);
        }
    }//Paul_Gudeiran

     

    希望你把我记住你流浪的孩子,无论在何时何地我都想念着你。————汪峰《我爱你中国》

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  • 原文地址:https://www.cnblogs.com/Damitu/p/7665507.html
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