M-SOLUTIONSプロコン2020 D Road to Millionaire

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("7");
            WillReturn.Add("100 130 130 130 115 115 150");
            //1685
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("6");
            WillReturn.Add("200 180 160 140 120 100");
            //1000
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("2");
            WillReturn.Add("157 193");
            //1216
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

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

        // 最大の所持金[所持してる株数]なDP表
        var PrevDP = new Dictionary<long, long>();
        PrevDP[0] = 1000;

        foreach (long EachA in AArr) {
            var CurrDP = new Dictionary<long, long>(PrevDP);

            foreach (var EachPair in PrevDP) {
                Action<long, long> UpsertAct = (pNewKey, pNewVal) =>
                {
                    if (CurrDP.ContainsKey(pNewKey) == false ||
                        CurrDP[pNewKey] < pNewVal) {
                        CurrDP[pNewKey] = pNewVal;
                    }
                };

                // 株を全部売る経路
                if (EachPair.Key > 0) {
                    long NewKey = 0;
                    long NewVal = EachPair.Value + EachPair.Key * EachA;
                    UpsertAct(NewKey, NewVal);
                }

                // 株を買えるだけ買う経路
                long BuyCnt = EachPair.Value / EachA;
                if (BuyCnt > 0) {
                    long NewKey = BuyCnt;
                    long NewVal = EachPair.Value - BuyCnt * EachA;
                    UpsertAct(NewKey, NewVal);
                }
            }
            PrevDP = CurrDP;
        }
        Console.WriteLine(PrevDP.Values.Max());
    }
}

解説

株の売買で利益が出るのであれば、
買うときは、買えるだけ買って
売るときは、全部売るのが最適です。

これをふまえて、状態の遷移数を減らしつつ、
DPで解いてます。