排序不等式

• 问题背景

有 n 个人排队到 11 个水龙头处打水，第 i 个人装满水桶所需的时间是 ti，请问如何安排他们的打水顺序才能使所有人的等待时间之和最小？

• 策略
  • 让用时长短的人先装

练习

01 排队打水

• 题目

• 题解

import java.io.*;
import java.util.*;

public class Main {
    public static final int N = 100010;
    public static int[] t = new int[N];
    public static int n;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
        n = Integer.parseInt(br.readLine());
        String[] str1 = br.readLine().split(" ");
        for (int i = 1; i <= n; i++) {
            t[i] = Integer.parseInt(str1[i - 1]);
        }

        Arrays.sort(t, 1, n + 1);
        long res = 0;
        for (int i = 1; i <= n; i++) {
            res += t[i] * (n - i);
        }
        pw.println(res);
        pw.close();
        br.close();
    }
}