ARC122-B Insurance

問題へのリンク

C#のソース

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3");
            WillReturn.Add("3 1 4");
            //1.83333333333333333333
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("10");
            WillReturn.Add("866111664 178537096 844917655 218662351 383133839 231371336 353498483 865935868 472381277 579910117");
            //362925658.10000000000000000000
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static double[] mAArr;

    static void Main()
    {
        List<string> InputList = GetInputList();
        mAArr = InputList[1].Split(' ').Select(pX => double.Parse(pX)).ToArray();

        double Result = ExecSanbuntansaku();
        Console.WriteLine(Result);
    }

    // 三分探索で極小値を求める
    static double ExecSanbuntansaku()
    {
        double L = 0;
        double R = mAArr.Max();

        var PairHashSet = new HashSet<string>();
        while (L + double.Epsilon < R) {
            double C1 = (L * 2 + R) / 3;
            double C2 = (L + R * 2) / 3;

            double C1Val = DeriveY(C1);
            double C2Val = DeriveY(C2);

            if (C1Val < C2Val) {
                R = C2;
            }
            else {
                L = C1;
            }

            string Hash = string.Format("{0},{1}", L, R);
            if (PairHashSet.Add(Hash) == false) {
                break;
            }
        }

        var MinKouhoList = new List<double>();
        MinKouhoList.Add(DeriveY(L));
        MinKouhoList.Add(DeriveY(R));
        return MinKouhoList.Min();
    }

    // Xの値を引数として、期待値を返す
    static double DeriveY(double pX)
    {
        double WillReturn = 0;
        foreach (double EachA in mAArr) {
            WillReturn += pX + EachA - Math.Min(EachA, pX * 2);
        }
        WillReturn /= mAArr.Length;
        return WillReturn;
    }
}

解説

下に凸なグラフなので三分探索してます。