# POJ 2976 Dropping tests

• 2018-08-08
• 26
• 0

## 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.

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

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).

### 题目链接

01分数规划题目。给出n个物品，每个物品有两个属性ab，删除k个物品，求剩下物品\frac{\sum a_{i}}{\sum b_{i}}的最大值(显然的错误算法——贪心)。

\therefore \sum a_{i}=x\times \sum b_{i}

\therefore \sum a_{i}-x\times \sum b_{i}=0