ABC212-E Safety Journey

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 1 4");
            WillReturn.Add("2 3");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 3 3");
            WillReturn.Add("1 2");
            WillReturn.Add("1 3");
            WillReturn.Add("2 3");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("5 3 100");
            WillReturn.Add("1 2");
            WillReturn.Add("4 5");
            WillReturn.Add("2 3");
            //428417047
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    const long Hou = 998244353;

    // 隣接リスト
    static Dictionary<long, List<long>> mToNodeListDict = new Dictionary<long, List<long>>();

    static void Main()
    {
        List<string> InputList = GetInputList();

        long[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(pX => long.Parse(pX)).ToArray();

        SplitAct(InputList[0]);
        long N = wkArr[0];
        long K = wkArr[2];
        long UB = N;

        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            long FromNode = wkArr[0];
            long ToNode = wkArr[1];

            if (mToNodeListDict.ContainsKey(FromNode) == false) {
                mToNodeListDict[FromNode] = new List<long>();
            }
            if (mToNodeListDict.ContainsKey(ToNode) == false) {
                mToNodeListDict[ToNode] = new List<long>();
            }
            mToNodeListDict[FromNode].Add(ToNode);
            mToNodeListDict[ToNode].Add(FromNode);
        }

        // 場合の数[現在位置]なDP表
        long[] PrevDP = new long[UB + 1];
        for (long I = 1; I <= UB; I++) {
            PrevDP[I] = 0;
        }
        PrevDP[1] = 1;
        long PrevDPSum = 1;

        for (int I = 1; I <= K; I++) {
            long[] CurrDP = new long[UB + 1];
            long CurrDPSum = 0;

            for (long J = 1; J <= UB; J++) {
                CurrDP[J] = PrevDPSum;
                CurrDP[J] %= Hou;

                // 自己ループは存在しない
                CurrDP[J] -= PrevDP[J];
                if (CurrDP[J] < 0) {
                    CurrDP[J] += Hou;
                }

                // NGな辺の分
                if (mToNodeListDict.ContainsKey(J)) {
                    foreach (long EachFromNode in mToNodeListDict[J]) {
                        CurrDP[J] -= PrevDP[EachFromNode];
                        if (CurrDP[J] < 0) {
                            CurrDP[J] += Hou;
                        }
                    }
                }

                CurrDPSum += CurrDP[J];
                CurrDPSum %= Hou;
            }
            PrevDP = CurrDP;
            PrevDPSum = CurrDPSum;
        }
        Console.WriteLine(PrevDP[1]);
    }
}

解説

完全グラフで、使えない辺があると考えて

場合の数[現在位置]なDP表を
貰うDPで更新してます。