Basic ------ 13. Merge detection

topic:

The new crown epidemic is caused by the new crown virus. It has recently spread in country A. In order to control the epidemic as soon as possible, country A is preparing to conduct virus nucleic acid testing for a large number of people.

However, kits for testing are in short supply. In order to solve this difficulty, scientists thought of a way: combined detection. That is, samples collected from multiple people (k) are put into the same kit for detection. If the result is negative, it means that all k people are negative, and the detection of k people has been completed with one kit. If the result is positive, it means that at least one person is positive, and all samples of these k individuals need to be re-tested independently (theoretically, if all k−1 individuals are negative before the test, it can be inferred that the kth individual is positive, but In actual operation, this inference will not be used, but k individuals will be tested independently), plus the initial combined detection, a total of k + 1 kits will be used to complete the detection of k individuals.

Country A estimates that the infection rate of the people tested is about 1%, which is evenly distributed. May I ask how much k can save the most kits?

analyze:

The collected samples of k individuals are placed in one kit, and the infection rate of the people tested is about 1%, one in 100 people is infected

1) If the box is Yin, k people are Yin.
2) If the box is Yang, at least one of the k people is Yang. Retest k people independently

Assume that
k is 100 people
1) The number of people tested is just greater than the number of people tested by the kit: 
if(k%i==0) k/i + infected people *i
2) The number of people tested is greater than the number of people tested by the kit
k/i + 1 + infected people *i

import java.util.Scanner;

public class _1_13 {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int k = s.nextInt();        //检测人数
        int gan, people=0, usehe;     //感染数 使用人数 使用盒子数
        int maxhe = k;          //使用最多盒为一人一检
        if(k%100==0)
            gan = (int)(0.01*k); //每100人中感染数
        else
            gan= (int)(0.01*k)+1;     //检测人数不能被100整除

        for(int i=2; i<100; i++){
            if(k%i==0)
                usehe = k/i + gan*i;
            else
                usehe = k/i + 1 + gan*i;
            if(maxhe>usehe)
            {
                maxhe = usehe;
                people= i;
            }
        }
        System.out.println("每"+people+"人使用最节省");
    }
}