ABC425-D Ulam-Warburton Automaton

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("9 9");
            WillReturn.Add(".........");
            WillReturn.Add(".........");
            WillReturn.Add(".........");
            WillReturn.Add(".........");
            WillReturn.Add("....#....");
            WillReturn.Add(".........");
            WillReturn.Add(".........");
            WillReturn.Add(".........");
            WillReturn.Add(".........");
            //57
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("2 2");
            WillReturn.Add("..");
            WillReturn.Add("..");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("10 10");
            WillReturn.Add("..........");
            WillReturn.Add("....#.....");
            WillReturn.Add("#.......#.");
            WillReturn.Add("......#...");
            WillReturn.Add(".......#..");
            WillReturn.Add(".....#....");
            WillReturn.Add("..........");
            WillReturn.Add("..........");
            WillReturn.Add("..#...#...");
            WillReturn.Add(".......#..");
            //64
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static long[] GetSplitArr(string pStr)
    {
        return (pStr == "" ? new string[0] : pStr.Split(' ')).Select(pX => long.Parse(pX)).ToArray();
    }

    struct PointDef
    {
        internal long X;
        internal long Y;
    }

    static long UB_X;
    static long UB_Y;
    static char[,] mBanArr;
    static long[,] mCntArr;

    static void Main()
    {
        List<string> InputList = GetInputList();
        mBanArr = CreateBanArr(InputList.Skip(1));
        UB_X = mBanArr.GetUpperBound(0);
        UB_Y = mBanArr.GetUpperBound(1);
        mCntArr = new long[UB_X + 1, UB_Y + 1];

        var KouhoQue = new Queue<PointDef>();
        var BlackSet = new HashSet<long>();

        for (long X = 0; X <= UB_X; X++) {
            for (long Y = 0; Y <= UB_Y; Y++) {
                if (mBanArr[X, Y] == '#') {
                    long Hash = GetHash(X, Y);
                    BlackSet.Add(Hash);

                    List<PointDef> KinbouPointList = DeriveKinbouPointList(X, Y);
                    foreach (PointDef EachKinbouPoint in KinbouPointList) {
                        KouhoQue.Enqueue(EachKinbouPoint);
                        mCntArr[EachKinbouPoint.X, EachKinbouPoint.Y]++;
                    }
                }
            }
        }

        if (BlackSet.Count == 0) {
            Console.WriteLine(0);
            return;
        }

        while (true) {
            bool WillContinue = false;

            // 一括操作なので、変更操作は遅延させる必要あり
            var NewKouhoList = new List<PointDef>();
            var LazyAddPointList = new List<PointDef>();

            while (KouhoQue.Count > 0) {
                PointDef EachKouho = KouhoQue.Dequeue();
                long KouhoX = EachKouho.X;
                long KouhoY = EachKouho.Y;

                if (mCntArr[KouhoX, KouhoY] != 1) {
                    continue;
                }

                long KouhoHash = GetHash(KouhoX, KouhoY);
                if (BlackSet.Add(KouhoHash) == false) continue;
                WillContinue = true;

                List<PointDef> KinbouPointList = DeriveKinbouPointList(KouhoX, KouhoY);
                foreach (PointDef EachKinbouPoint in KinbouPointList) {
                    long KinbouHash = GetHash(EachKinbouPoint.X, EachKinbouPoint.Y);
                    if (BlackSet.Contains(KinbouHash)) continue;

                    LazyAddPointList.Add(EachKinbouPoint);
                    NewKouhoList.Add(EachKinbouPoint);
                }
            }
            if (WillContinue) {
                NewKouhoList.ForEach(pX => KouhoQue.Enqueue(pX));
                LazyAddPointList.ForEach(pX => mCntArr[pX.X, pX.Y]++);
                continue;
            }
            break;
        }
        Console.WriteLine(BlackSet.Count);
    }

    // 座標を引数として、4近傍の座標のListを返す
    static List<PointDef> DeriveKinbouPointList(long pX, long pY)
    {
        var WillReturn = new List<PointDef>();

        Action<long, long> AddAct = (pTargetX, pTargetY) =>
        {
            if (pTargetX < 0 || UB_X < pTargetX) return;
            if (pTargetY < 0 || UB_Y < pTargetY) return;
            PointDef WillAdd;
            WillAdd.X = pTargetX;
            WillAdd.Y = pTargetY;
            WillReturn.Add(WillAdd);
        };
        AddAct(pX, pY - 1);
        AddAct(pX, pY + 1);
        AddAct(pX - 1, pY);
        AddAct(pX + 1, pY);
        return WillReturn;
    }

    // 座標のハッシュ値を返す
    static long GetHash(long pX, long pY)
    {
        return pX * 1000000 + pY;
    }

    ////////////////////////////////////////////////////////////////
    // IEnumerable<string>をcharの2次元配列に設定
    ////////////////////////////////////////////////////////////////
    static char[,] CreateBanArr(IEnumerable<string> pStrEnum)
    {
        var StrList = pStrEnum.ToList();
        if (StrList.Count == 0) {
            return new char[0, 0];
        }
        int UB_X = StrList[0].Length - 1;
        int UB_Y = StrList.Count - 1;

        char[,] WillReturn = new char[UB_X + 1, UB_Y + 1];

        for (int Y = 0; Y <= UB_Y; Y++) {
            for (int X = 0; X <= UB_X; X++) {
                WillReturn[X, Y] = StrList[Y][X];
            }
        }
        return WillReturn;
    }
}

解説

ダイソーの500円のオセロセットで考察すると、
新しく黒にしたマスの4近傍を
次に黒くするマスの候補にすることを繰り返せば良いと分かります。

実装では、
●4近傍の黒マスの件数を持つ2次元配列
●既に黒マスな座標のハッシュ値のHashSet
●次に黒マスにする候補のキュー
●今回の一括操作で、4近傍の黒マスの件数が増える座標のList
を持ってます。