STPC2025(Div2) M Take K

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("2 4 5");
            WillReturn.Add("BWW#");
            WillReturn.Add("W#BB");
            //Yes
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 1 4");
            WillReturn.Add("B");
            WillReturn.Add("W");
            WillReturn.Add("W");
            //Yes
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("2 5 3");
            WillReturn.Add("BWW##");
            WillReturn.Add("##WWB");
            //No
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

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

    static int mK;

    static char[,] mBanArr;
    static int UB_X;
    static int UB_Y;

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] wkArr = GetSplitArr(InputList[0]);
        mK = wkArr[2];

        mBanArr = CreateBanArr(InputList.Skip(1));
        UB_X = mBanArr.GetUpperBound(0);
        UB_Y = mBanArr.GetUpperBound(1);

        bool IsOK = false;
        for (int Y = 0; Y <= UB_Y; Y++) {
            for (int X = 0; X <= UB_X; X++) {
                if (mBanArr[X, Y] == 'B') {
                    if (IsRinsetuW(X, Y)) {
                        IsOK = true;
                    }
                }
            }
        }

        if (IsOK == false) {
            Console.WriteLine("No");
            return;
        }

        // 場合1 K=2の場合
        if (mK == 2) {
            Console.WriteLine("Yes");
            return;
        }

        // 場合2 Kが4以上の偶数の場合
        if (mK % 2 == 0) {
            if (ExecDFS4()) {
                Console.WriteLine("Yes");
            }
            else {
                Console.WriteLine("No");
            }
            return;
        }

        // 場合3 Kが奇数の場合

        // レベルが奇数のときの最小レベル
        int?[,] OddEdakiriArr = new int?[UB_X + 1, UB_Y + 1];

        // レベルが偶数のときの最小レベル
        int?[,] EvenEdakiriArr = new int?[UB_X + 1, UB_Y + 1];

        var Que = new Queue<JyoutaiDef>();
        JyoutaiDef WillEnqueue;
        for (int Y = 0; Y <= UB_Y; Y++) {
            for (int X = 0; X <= UB_X; X++) {
                if (mBanArr[X, Y] == 'B') {
                    WillEnqueue.CurrX = X;
                    WillEnqueue.CurrY = Y;
                    WillEnqueue.Level = 0;
                    Que.Enqueue(WillEnqueue);
                }
            }
        }

        var OddLevelList = new List<int>();
        while (Que.Count > 0) {
            JyoutaiDef Dequeued = Que.Dequeue();
            int CurrX = Dequeued.CurrX;
            int CurrY = Dequeued.CurrY;
            int CurrLevel = Dequeued.Level;

            if (mBanArr[CurrX, CurrY] != 'B') {
                if (CurrLevel % 2 == 1) {
                    if (OddEdakiriArr[CurrX, CurrY].HasValue) {
                        if (OddEdakiriArr[CurrX, CurrY] <= Dequeued.Level) {
                            continue;
                        }
                    }
                    OddEdakiriArr[CurrX, CurrY] = Dequeued.Level;
                }

                if (CurrLevel % 2 == 0) {
                    if (EvenEdakiriArr[CurrX, CurrY].HasValue) {
                        if (EvenEdakiriArr[CurrX, CurrY] <= Dequeued.Level) {
                            continue;
                        }
                    }
                    EvenEdakiriArr[CurrX, CurrY] = Dequeued.Level;
                }
            }

            if (mBanArr[CurrX, CurrY] == 'B' && Dequeued.Level > 0) {
                if (Dequeued.Level % 2 == 1 && Dequeued.Level >= 3) {
                    OddLevelList.Add(Dequeued.Level);
                }
                continue;
            }

            Action<int, int> EnqueueAct = (pNewX, pNewY) =>
            {
                if (pNewX < 0 || UB_X < pNewX) return;
                if (pNewY < 0 || UB_Y < pNewY) return;

                WillEnqueue.CurrX = pNewX;
                WillEnqueue.CurrY = pNewY;
                WillEnqueue.Level = Dequeued.Level + 1;
                if (mBanArr[pNewX, pNewY] == '#') return;

                Que.Enqueue(WillEnqueue);
            };
            EnqueueAct(CurrX, CurrY - 1);
            EnqueueAct(CurrX, CurrY + 1);
            EnqueueAct(CurrX - 1, CurrY);
            EnqueueAct(CurrX + 1, CurrY);
        }

        if (OddLevelList.Count == 0) {
            Console.WriteLine("No");
            return;
        }

        if (OddLevelList.Min() <= mK) {
            Console.WriteLine("Yes");
        }
        else {
            Console.WriteLine("No");
        }
    }

    static bool IsRinsetuW(int pBaseX, int pBaseY)
    {
        if (pBaseX > 0) {
            if (mBanArr[pBaseX - 1, pBaseY] == 'W') return true;
        }
        if (pBaseX < UB_X) {
            if (mBanArr[pBaseX + 1, pBaseY] == 'W') return true;
        }

        if (pBaseY > 0) {
            if (mBanArr[pBaseX, pBaseY - 1] == 'W') return true;
        }
        if (pBaseY < UB_Y) {
            if (mBanArr[pBaseX, pBaseY + 1] == 'W') return true;
        }

        return false;
    }

    struct JyoutaiDef
    {
        internal int CurrX;
        internal int CurrY;
        internal int Level;
    }

    // 4手で黒マスにこれるかを判定
    static bool ExecDFS4()
    {
        var WillReturn = new List<JyoutaiDef>();

        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;

        for (int Y = 0; Y <= UB_Y; Y++) {
            for (int X = 0; X <= UB_X; X++) {
                if (mBanArr[X, Y] == 'B') {
                    WillPush.CurrX = X;
                    WillPush.CurrY = Y;
                    WillPush.Level = 0;
                    Stk.Push(WillPush);
                }
            }
        }

        while (Stk.Count > 0) {
            JyoutaiDef Popped = Stk.Pop();
            int CurrX = Popped.CurrX;
            int CurrY = Popped.CurrY;

            if (Popped.Level == 4) {
                if (mBanArr[CurrX, CurrY] == 'B') {
                    return true;
                }
                continue;
            }

            Action<int, int, int> PushAct = (pNewX, pNewY, pNewLevel) =>
            {
                if (pNewX < 0 || UB_X < pNewX) return;
                if (pNewY < 0 || UB_Y < pNewY) return;

                if (1 <= pNewLevel && pNewLevel <= 3) {
                    if (mBanArr[pNewX, pNewY] != 'W') return;
                }
                else {
                    if (mBanArr[pNewX, pNewY] != 'B') return;
                }

                WillPush.CurrX = pNewX;
                WillPush.CurrY = pNewY;
                WillPush.Level = pNewLevel;
                Stk.Push(WillPush);
            };
            PushAct(CurrX, CurrY - 1, Popped.Level + 1);
            PushAct(CurrX, CurrY + 1, Popped.Level + 1);
            PushAct(CurrX - 1, CurrY, Popped.Level + 1);
            PushAct(CurrX + 1, CurrY, Popped.Level + 1);
        }
        return false;
    }

    ////////////////////////////////////////////////////////////////
    // 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

E8さんの「アルゴリズム×数学」の204ページの類題で
場合に分けて考えます。

白に隣接した黒がなかったら、Kによらず不可です。
K=2の場合は上記で判定できます。
Kが4以上の偶数の場合は、レベルを4に制限したDFSで判定できます。

Kが奇数の場合は、{X,Y,レベルの偶奇}での最小レベルで枝切りしつつ、多始点BFSを行い、
K以下の奇数レベルで他の黒ノードまでのパスの有無で判定できます。

グリッドで、白と黒の問題なので、
ダイソーのオセロセットで考察すると解きやすいです。