2024年蓝桥杯Java B组省赛真题超详解析-最优分组

审题：混合、再消耗；取值、最小

汇总：关键：期望

基础：特殊情况

注意：稍微理解

import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {

    static int N, ans;
    static double p, min = Double.MAX_VALUE / 2; // min是可能的最小期望
    static ArrayList<Integer> factors = new ArrayList<>();

    // 计算不同K值对应的期望
    static double calculateExpected(int K) {
        if (K == 1) return N; // 每一个都检测，所以直接是N的消耗
        double probabilityAllNegative = Math.pow(1 - p, K);
        double expectedTestsPerGroup = probabilityAllNegative * 1 + (1 - probabilityAllNegative) * (1 + K);
        return expectedTestsPerGroup * ((double) N / K);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        p = sc.nextDouble();

        // 计算所有的约数K
        for (int i = 1; i <= Math.sqrt(N); i++) {
            if (N % i == 0) {
                factors.add(i);
                if (N / i != i) {
                    factors.add(N / i);
                }
            }
        }

        // 对K进行升序
        Collections.sort(factors);

        // 枚举所有可能的约数K，寻找最小期望对应的K
        for (int K : factors) {
            double currentExpected = calculateExpected(K);
            if (currentExpected < min) {
                ans = K;
                min = currentExpected;
            }
        }

        System.out.println(ans);
    }
}