ABC360-E Random Swaps of Balls

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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("2 1");
            //499122178
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 2");
            //554580198
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("4 4");
            //592707587
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    const long Hou = 998244353;

    static void Main()
    {
        List<string> InputList = GetInputList();
        long[] wkArr = InputList[0].Split(' ').Select(pX => long.Parse(pX)).ToArray();
        long MasuCnt = wkArr[0];
        long TryCnt = wkArr[1];

        if (MasuCnt == 1) {
            Console.WriteLine(1);
            return;
        }

        // 確率[1番左に黒玉があるか？]
        long[] PrevDP = new long[2];
        PrevDP[1] = 1;

        long AllPatternCnt = MasuCnt * MasuCnt;
        AllPatternCnt %= Hou;

        for (long I = 1; I <= TryCnt; I++) {
            long[] CurrDP = new long[2];
            for (long J = 0; J <= 1; J++) {
                if (PrevDP[J] == 0) continue;

                if (J == 0) {
                    long ChangeProb = 2 * DeriveGyakugen(AllPatternCnt);
                    ChangeProb %= Hou;
                    CurrDP[1] += PrevDP[J] * ChangeProb;
                    CurrDP[1] %= Hou;
                    CurrDP[0] += PrevDP[J] * (1 - ChangeProb);
                    CurrDP[0] %= Hou;
                    if (CurrDP[0] < 0) {
                        CurrDP[0] += Hou;
                    }
                }
                if (J == 1) {
                    long ChangeProb = 2 * (MasuCnt - 1);
                    ChangeProb %= Hou;
                    ChangeProb *= DeriveGyakugen(AllPatternCnt);
                    ChangeProb %= Hou;
                    CurrDP[0] += PrevDP[J] * ChangeProb;
                    CurrDP[0] %= Hou;
                    CurrDP[1] += PrevDP[J] * (1 - ChangeProb);
                    CurrDP[1] %= Hou;
                    if (CurrDP[1] < 0) {
                        CurrDP[1] += Hou;
                    }
                }
            }
            PrevDP = CurrDP;
        }

        long Answer = 0;
        Answer += PrevDP[1];

        long SuuretuSum = MasuCnt * (MasuCnt + 1);
        SuuretuSum %= Hou;
        SuuretuSum *= DeriveGyakugen(2);
        SuuretuSum %= Hou;
        SuuretuSum--;
        if (SuuretuSum < 0) SuuretuSum += Hou;
        SuuretuSum *= DeriveGyakugen(MasuCnt - 1);
        SuuretuSum %= Hou;

        Answer += PrevDP[0] * SuuretuSum;
        Answer %= Hou;

        Console.WriteLine(Answer);
    }

    // 引数の逆元を求める
    static Dictionary<long, long> mMemoGyakugen = new Dictionary<long, long>();
    static long DeriveGyakugen(long pLong)
    {
        if (mMemoGyakugen.ContainsKey(pLong)) {
            return mMemoGyakugen[pLong];
        }
        return mMemoGyakugen[pLong] = DeriveBekijyou(pLong, Hou - 2, Hou);
    }

    // 繰り返し2乗法で、(NのP乗) Mod Mを求める
    static long DeriveBekijyou(long pN, long pP, long pM)
    {
        long CurrJyousuu = pN % pM;
        long CurrShisuu = 1;
        long WillReturn = 1;

        while (true) {
            // 対象ビットが立っている場合
            if ((pP & CurrShisuu) > 0) {
                WillReturn = (WillReturn * CurrJyousuu) % pM;
            }

            CurrShisuu *= 2;
            if (CurrShisuu > pP) return WillReturn;
            CurrJyousuu = (CurrJyousuu * CurrJyousuu) % pM;
        }
    }
}

解説

確率[1番左に黒玉があるか？]
で確率DPし、最後に期待値を求めてます。