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20-087 アソートキューブ(2片決め編)

問題

小田原充宏さんのアソートキューブ(2片決め編)を解きます。

15個のピースは下記となります。
各ピースは回転や裏返しても使えます。



Q1 bとdのピースの位置を下記に決めて、残りのピースを敷き詰める


Q2 bとdのピースの位置を下記に決めて、残りのピースを敷き詰める


ソース

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    //ピースごとの配置候補
    static Dictionary<char, List<bool[,]>> HaitiKouhoListDict =
        new Dictionary<char, List<bool[,]>>();

    static char[] PieceNameArr = "FPTUVWXZlnotabd".ToCharArray();

    static int mQuestionNo = 1;
    static char[,] mQuestionArr; //問題の初期盤面

    const int UB = 7;

    struct JyoutaiDef
    {
        internal char[,] BanArr;
        internal int CurrX;
        internal int CurrY;
        internal int PieceCnt;
    }

    //問題を定義
    static void QuestionDef()
    {
        mQuestionArr = new char[UB + 1, UB + 1];
        for (int X = 0; X <= UB; X++)
            for (int Y = 0; Y <= UB; Y++)
                mQuestionArr[X, Y] = ' ';

        if (mQuestionNo == 1) {
            mQuestionArr[0, 0] = 'b';
            mQuestionArr[1, 0] = 'b';
            mQuestionArr[0, 1] = 'b';
            mQuestionArr[7, 6] = 'd';
            mQuestionArr[7, 7] = 'd';
        }
        if (mQuestionNo == 2) {
            mQuestionArr[3, 6] = 'b';
            mQuestionArr[3, 7] = 'b';
            mQuestionArr[4, 6] = 'b';
            mQuestionArr[7, 5] = 'd';
            mQuestionArr[7, 6] = 'd';
        }
    }

    static void Main()
    {
        var sw = System.Diagnostics.Stopwatch.StartNew();

        //問題を定義
        QuestionDef();

        foreach (char EachPiece in PieceNameArr) {
            HaitiKouhoListDict[EachPiece] = DeriveHaitiKouhoList(EachPiece);
        }

        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.BanArr = mQuestionArr;
        WillPush.CurrX = WillPush.CurrY = 0;
        WillPush.PieceCnt = 0;
        Stk.Push(WillPush);

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

            //クリア判定
            if (Popped.PieceCnt == 15 - 2) {
                Console.WriteLine("解を発見。経過時間={0}", sw.Elapsed);
                PrintBan(Popped.BanArr);
                break;
            }

            //X座標の繰上げ処理
            if (Popped.CurrX > UB) {
                Popped.CurrX = 0;
                Popped.CurrY++;
            }

            //最終行を超えた場合
            if (Popped.CurrY > UB) continue;

            //使用済のピース名の配列
            char[] UsedPieceArr = Popped.BanArr.Cast<char>().Distinct().ToArray();

            foreach (char EachPiece in PieceNameArr) {
                if (Array.IndexOf(UsedPieceArr, EachPiece) >= 0) continue;

                //ピースの配置候補リスト
                List<bool[,]> HaitiKouhoList = new List<bool[,]>();
                HaitiKouhoList.AddRange(HaitiKouhoListDict[EachPiece]);

                //現在のマス目が空白の場合は、マス目を埋める必要あり
                if (Popped.BanArr[Popped.CurrX, Popped.CurrY] == ' ') {
                    HaitiKouhoList.RemoveAll(X => X[0, 0] == false);
                }

                //マス目にピースを埋めれない候補をRemove
                HaitiKouhoList.RemoveAll(X =>
                    CanFillPiece(X, Popped.CurrX, Popped.CurrY, Popped.BanArr) == false);

                //ピースを配置する経路のPush処理
                foreach (bool[,] EachPieceMap in HaitiKouhoList) {
                    WillPush.BanArr = (char[,])Popped.BanArr.Clone();

                    if (EachPiece == 'P' || EachPiece == 'U'
                     || EachPiece == 'X' || EachPiece == 'n'
                     || EachPiece == 't' || EachPiece == 'a')
                        WillPush.CurrX = Popped.CurrX + 1;
                    else WillPush.CurrX = Popped.CurrX;

                    WillPush.CurrY = Popped.CurrY;
                    WillPush.PieceCnt = Popped.PieceCnt + 1;

                    for (int X = 0; X <= EachPieceMap.GetUpperBound(0); X++) {
                        for (int Y = 0; Y <= EachPieceMap.GetUpperBound(1); Y++) {
                            if (EachPieceMap[X, Y] == false) continue;
                            WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y] = EachPiece;
                        }
                    }
                    if (WillEdakiri(WillPush.BanArr)) continue;
                    Stk.Push(WillPush);
                }
            }

            //現在のマス目が空白でない場合は、ピースを配置しない経路のPush
            if (Popped.BanArr[Popped.CurrX, Popped.CurrY] != ' ') {
                WillPush.BanArr = Popped.BanArr;
                WillPush.CurrX = Popped.CurrX + 1;
                WillPush.CurrY = Popped.CurrY;
                WillPush.PieceCnt = Popped.PieceCnt;
                Stk.Push(WillPush);
            }
        }
    }

    //ピース名を引数として、回転させた配置のListを返す
    static List<bool[,]> DeriveHaitiKouhoList(char pPieceName)
    {
        bool[,] wkArr = null;

        // ■■
        //■■
        // ■
        if (pPieceName == 'F') {
            wkArr = new bool[3, 3];
            wkArr[1, 0] = wkArr[2, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
            wkArr[1, 2] = true;
        }

        //■■
        //■■
        //■
        if (pPieceName == 'P') {
            wkArr = new bool[2, 3];
            wkArr[0, 0] = wkArr[1, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
            wkArr[0, 2] = true;
        }

        //■■■
        // ■
        // ■
        if (pPieceName == 'T') {
            wkArr = new bool[3, 3];
            wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
            wkArr[1, 1] = true;
            wkArr[1, 2] = true;
        }

        //■ ■
        //■■■
        if (pPieceName == 'U') {
            wkArr = new bool[3, 2];
            wkArr[0, 0] = wkArr[2, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = true;
        }

        //■
        //■
        //■■■
        if (pPieceName == 'V') {
            wkArr = new bool[3, 3];
            wkArr[0, 0] = true;
            wkArr[0, 1] = true;
            wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
        }

        //■
        //■■
        // ■■
        if (pPieceName == 'W') {
            wkArr = new bool[3, 3];
            wkArr[0, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
            wkArr[1, 2] = wkArr[2, 2] = true;
        }

        // ■
        //■■■
        // ■
        if (pPieceName == 'X') {
            wkArr = new bool[3, 3];
            wkArr[1, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = true;
            wkArr[1, 2] = true;
        }

        //■■
        // ■
        // ■■
        if (pPieceName == 'Z') {
            wkArr = new bool[3, 3];
            wkArr[0, 0] = wkArr[1, 0] = true;
            wkArr[1, 1] = true;
            wkArr[1, 2] = wkArr[2, 2] = true;
        }

        //■
        //■
        //■■
        if (pPieceName == 'l') {
            wkArr = new bool[2, 3];
            wkArr[0, 0] = true;
            wkArr[0, 1] = true;
            wkArr[0, 2] = wkArr[1, 2] = true;
        }

        // ■
        //■■
        //■
        if (pPieceName == 'n') {
            wkArr = new bool[2, 3];
            wkArr[1, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
            wkArr[0, 2] = true;
        }

        //■■
        //■■
        if (pPieceName == 'o') {
            wkArr = new bool[2, 2];
            wkArr[0, 0] = wkArr[1, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
        }

        //■■■
        // ■
        if (pPieceName == 't') {
            wkArr = new bool[3, 2];
            wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
            wkArr[1, 1] = true;
        }

        //■
        //■
        //■
        if (pPieceName == 'a') {
            wkArr = new bool[1, 3];
            wkArr[0, 0] = true;
            wkArr[0, 1] = true;
            wkArr[0, 2] = true;
        }

        //■
        //■■
        if (pPieceName == 'b') {
            wkArr = new bool[2, 2];
            wkArr[0, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
        }

        //■
        //■
        if (pPieceName == 'd') {
            wkArr = new bool[1, 2];
            wkArr[0, 0] = true;
            wkArr[0, 1] = true;
        }

        return DeriveKaitenArrList(wkArr);
    }

    //配列を引数として、回転させた配列のリストをDistinctして返す
    static List<bool[,]> DeriveKaitenArrList(bool[,] pBaseArr)
    {
        var KaitenArrList = new List<bool[,]>();

        int BaseArrUB_X = pBaseArr.GetUpperBound(0);
        int BaseArrUB_Y = pBaseArr.GetUpperBound(1);

        for (int I = 1; I <= 8; I++) KaitenArrList.Add(null);
        for (int P = 0; P <= 6; P += 2) KaitenArrList[P] = new bool[BaseArrUB_X + 1, BaseArrUB_Y + 1];
        for (int P = 1; P <= 7; P += 2) KaitenArrList[P] = new bool[BaseArrUB_Y + 1, BaseArrUB_X + 1];

        for (int X = 0; X <= BaseArrUB_X; X++) {
            for (int Y = 0; Y <= BaseArrUB_Y; Y++) {
                bool SetVal = pBaseArr[X, Y];
                KaitenArrList[0][X, Y] = SetVal;
                KaitenArrList[1][Y, BaseArrUB_X - X] = SetVal;
                KaitenArrList[2][BaseArrUB_X - X, BaseArrUB_Y - Y] = SetVal;
                KaitenArrList[3][BaseArrUB_Y - Y, X] = SetVal;

                KaitenArrList[4][X, BaseArrUB_Y - Y] = SetVal;
                KaitenArrList[5][BaseArrUB_Y - Y, BaseArrUB_X - X] = SetVal;
                KaitenArrList[6][BaseArrUB_X - X, Y] = SetVal;
                KaitenArrList[7][Y, X] = SetVal;
            }
        }

        //Distinctする
        for (int I = KaitenArrList.Count - 1; 0 <= I; I--) {
            for (int J = 0; J <= I - 1; J++) {
                if (KaitenArrList[I].GetUpperBound(0) !=
                    KaitenArrList[J].GetUpperBound(0)) continue;
                if (KaitenArrList[I].GetUpperBound(1) !=
                    KaitenArrList[J].GetUpperBound(1)) continue;

                IEnumerable<bool> wkEnum1 = KaitenArrList[I].Cast<bool>();
                IEnumerable<bool> wkEnum2 = KaitenArrList[J].Cast<bool>();
                if (wkEnum1.SequenceEqual(wkEnum2) == false) continue;

                KaitenArrList.RemoveAt(I);
                break;
            }
        }
        return KaitenArrList;
    }

    //マス目にピースを埋めれるか
    static bool CanFillPiece(bool[,] pPieceMap, int pTargetX, int pTargetY, char[,] pBanArr)
    {
        if (pTargetX + pPieceMap.GetUpperBound(0) > UB) return false;
        if (pTargetY + pPieceMap.GetUpperBound(1) > UB) return false;

        for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
            for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
                if (pPieceMap[X, Y] && pBanArr[pTargetX + X, pTargetY + Y] != ' ')
                    return false;
            }
        }
        return true;
    }

    //空白マスからUnionFindして面積が2以下なら枝切り
    static bool WillEdakiri(char[,] pBanArr)
    {
        var SpaceSetList = new List<HashSet<int>>();
        for (int X = 0; X <= UB; X++) {
            for (int Y = 0; Y <= UB; Y++) {
                if (pBanArr[X, Y] != ' ') continue;

                int CurrHash = GetHash(X, Y);
                bool IsExist = false;
                foreach (var EachSet in SpaceSetList) {
                    if (EachSet.Contains(CurrHash)) {
                        IsExist = true;
                        break;
                    }
                }
                if (IsExist) continue;

                //始点を引数として、連結した空白マスのHashSetを返す
                HashSet<int> wkSet = ExecUnionFind(pBanArr, X, Y);

                //面積が2以下なら枝切り
                if (wkSet.Count <= 2) return true;

                SpaceSetList.Add(wkSet);
            }
        }
        return false;
    }

    //UnionFindで島のチェック用
    struct JyoutaiDefUnionFind
    {
        internal int CurrX;
        internal int CurrY;
    }

    //始点を引数として、連結した空白マスのHashSetを返す
    static HashSet<int> ExecUnionFind(char[,] pBanArr, int pStaX, int pStaY)
    {
        var Stk = new Stack<JyoutaiDefUnionFind>();
        JyoutaiDefUnionFind WillPush;

        WillPush.CurrX = pStaX;
        WillPush.CurrY = pStaY;
        Stk.Push(WillPush);

        var VisitedSet = new HashSet<int>();
        VisitedSet.Add(GetHash(pStaX, pStaY));

        while (Stk.Count > 0) {
            JyoutaiDefUnionFind Popped = Stk.Pop();

            Action<int, int> PushSyori = (pNewX, pNewY) =>
            {
                if (pNewX < 0 || UB < pNewX) return;
                if (pNewY < 0 || UB < pNewY) return;

                if (pBanArr[pNewX, pNewY] != ' ') return;
                int wkHash = GetHash(pNewX, pNewY);
                if (VisitedSet.Add(wkHash) == false) return;

                WillPush.CurrX = pNewX;
                WillPush.CurrY = pNewY;
                Stk.Push(WillPush);
            };

            PushSyori(Popped.CurrX, Popped.CurrY - 1);
            PushSyori(Popped.CurrX, Popped.CurrY + 1);
            PushSyori(Popped.CurrX - 1, Popped.CurrY);
            PushSyori(Popped.CurrX + 1, Popped.CurrY);
        }
        return VisitedSet;
    }

    static int GetHash(int pX, int pY)
    {
        return pX * (UB + 1) + pY;
    }

    //盤面を出力
    static void PrintBan(char[,] pBanArr)
    {
        var sb = new System.Text.StringBuilder();
        for (int Y = 0; Y <= UB; Y++) {
            for (int X = 0; X <= UB; X++) {
                sb.Append(pBanArr[X, Y] == ' ' ? '/' : pBanArr[X, Y]);
            }
            sb.AppendLine();
        }
        Console.WriteLine(sb.ToString());
    }
}


実行結果

解を発見。経過時間=00:00:00.0669786
bbaaatll
booZZttl
VooTZtnl
VTTTZZnn
VVVTWWXn
UUFWWXXX
UFFWPPXd
UUFFPPPd


解説

空白を連結した島が存在し、面積が2以下だったら、
枝切りしてます。