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20-033 ユニークキューブ2(立体)

問題

小田原充宏さんのユニークキューブの2の立体問題を解きます。

  
 

6つ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 解数は1
3*3*3の立方体

Q2 解数は1


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 = "PUVnto".ToCharArray();

    static int mQuestionNo = 2;
    static char[, ,] mQuestionArr; //問題の初期盤面

    static int UB_X;
    static int UB_Y;
    static int UB_Z;

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

    //問題を定義
    static void QuestionDef()
    {
        if (mQuestionNo == 1) { UB_X = UB_Y = UB_Z = 3 - 1; }
        if (mQuestionNo == 2) { UB_X = 5 - 1; UB_Y = 3 - 1; UB_Z = 3 - 1; }

        mQuestionArr = new char[UB_X + 1, UB_Y + 1, UB_Z + 1];
        for (int X = 0; X <= UB_X; X++)
            for (int Y = 0; Y <= UB_Y; Y++)
                for (int Z = 0; Z <= UB_Z; Z++)
                    mQuestionArr[X, Y, Z] = ' ';

        if (mQuestionNo == 2) {
            mQuestionArr[1, 1, 1] = mQuestionArr[2, 1, 1] = mQuestionArr[3, 1, 1] = '*';
            mQuestionArr[1, 2, 1] = mQuestionArr[2, 2, 1] = mQuestionArr[3, 2, 1] = '*';

            mQuestionArr[0, 0, 2] = mQuestionArr[4, 0, 2] = '*';

            for (int X = 0; X <= UB_X; X++)
                for (int Y = 1; Y <= UB_Y; Y++)
                    mQuestionArr[X, Y, 2] = '*';
        }
    }

    static void Main()
    {
        //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 = WillPush.CurrZ = 0;
        WillPush.PieceCnt = 0;
        Stk.Push(WillPush);

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

            //クリア判定
            if (Popped.PieceCnt == 6) {
                Console.WriteLine("解を発見");
                PrintBan(Popped.BanArr);
                break;
            }

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

            //最終行を超えた場合
            if (Popped.CurrY > UB_Y) {
                Popped.CurrY = 0;

                //最終高さを超えた場合
                if (++Popped.CurrZ > UB_Z) 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, Popped.CurrZ] == ' ') {
                    HaitiKouhoList.RemoveAll(X => X[0, 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.CurrZ, 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();
                    WillPush.CurrX = Popped.CurrX;
                    WillPush.CurrY = Popped.CurrY;
                    WillPush.CurrZ = Popped.CurrZ;
                    WillPush.PieceCnt = Popped.PieceCnt + 1;

                    for (int X = 0; X <= EachPieceMap.GetUpperBound(0); X++) {
                        for (int Y = 0; Y <= EachPieceMap.GetUpperBound(1); Y++) {
                            for (int Z = 0; Z <= EachPieceMap.GetUpperBound(2); Z++) {
                                if (EachPieceMap[X, Y, Z] == false) continue;
                                WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y, Popped.CurrZ + Z]
                                    = EachPiece;
                            }
                        }
                    }
                    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, Popped.CurrZ] != ' ') {
                WillPush.BanArr = Popped.BanArr;
                WillPush.CurrX = Popped.CurrX + 1;
                WillPush.CurrY = Popped.CurrY;
                WillPush.CurrZ = Popped.CurrZ;
                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 == 'P') {
            wkArr = new bool[2, 3, 1];
            wkArr[0, 0, 0] = wkArr[1, 0, 0] = true;
            wkArr[0, 1, 0] = wkArr[1, 1, 0] = true;
            wkArr[0, 2, 0] = true;
        }

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

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

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

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

        //■■
        //■■
        if (pPieceName == 'o') {
            wkArr = new bool[2, 2, 1];
            wkArr[0, 0, 0] = wkArr[1, 0, 0] = true;
            wkArr[0, 1, 0] = wkArr[1, 1, 0] = 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 BaseUB_X = pBaseArr.GetUpperBound(0);
        int BaseUB_Y = pBaseArr.GetUpperBound(1);
        int BaseUB_Z = pBaseArr.GetUpperBound(2);

        for (int I = 1; I <= 48; I++) KaitenArrList.Add(null);
        for (int P = 0; P <= 7; P++) KaitenArrList[P] = new bool[BaseUB_X + 1, BaseUB_Y + 1, BaseUB_Z + 1];
        for (int P = 8; P <= 15; P++) KaitenArrList[P] = new bool[BaseUB_X + 1, BaseUB_Z + 1, BaseUB_Y + 1];
        for (int P = 16; P <= 23; P++) KaitenArrList[P] = new bool[BaseUB_Y + 1, BaseUB_X + 1, BaseUB_Z + 1];
        for (int P = 24; P <= 31; P++) KaitenArrList[P] = new bool[BaseUB_Y + 1, BaseUB_Z + 1, BaseUB_X + 1];
        for (int P = 32; P <= 39; P++) KaitenArrList[P] = new bool[BaseUB_Z + 1, BaseUB_X + 1, BaseUB_Y + 1];
        for (int P = 40; P <= 47; P++) KaitenArrList[P] = new bool[BaseUB_Z + 1, BaseUB_Y + 1, BaseUB_X + 1];

        for (int X = 0; X <= BaseUB_X; X++) {
            for (int Y = 0; Y <= BaseUB_Y; Y++) {
                for (int Z = 0; Z <= BaseUB_Z; Z++) {
                    bool SetVal = pBaseArr[X, Y, Z];
                    KaitenArrList[0][X, Y, Z] = SetVal;
                    KaitenArrList[1][X, Y, BaseUB_Z - Z] = SetVal;
                    KaitenArrList[2][X, BaseUB_Y - Y, Z] = SetVal;
                    KaitenArrList[3][X, BaseUB_Y - Y, BaseUB_Z - Z] = SetVal;
                    KaitenArrList[4][BaseUB_X - X, Y, Z] = SetVal;
                    KaitenArrList[5][BaseUB_X - X, Y, BaseUB_Z - Z] = SetVal;
                    KaitenArrList[6][BaseUB_X - X, BaseUB_Y - Y, Z] = SetVal;
                    KaitenArrList[7][BaseUB_X - X, BaseUB_Y - Y, BaseUB_Z - Z] = SetVal;

                    KaitenArrList[8][X, Z, Y] = SetVal;
                    KaitenArrList[9][X, Z, BaseUB_Y - Y] = SetVal;
                    KaitenArrList[10][X, BaseUB_Z - Z, Y] = SetVal;
                    KaitenArrList[11][X, BaseUB_Z - Z, BaseUB_Y - Y] = SetVal;
                    KaitenArrList[12][BaseUB_X - X, Z, Y] = SetVal;
                    KaitenArrList[13][BaseUB_X - X, Z, BaseUB_Y - Y] = SetVal;
                    KaitenArrList[14][BaseUB_X - X, BaseUB_Z - Z, Y] = SetVal;
                    KaitenArrList[15][BaseUB_X - X, BaseUB_Z - Z, BaseUB_Y - Y] = SetVal;

                    KaitenArrList[16][Y, X, Z] = SetVal;
                    KaitenArrList[17][Y, X, BaseUB_Z - Z] = SetVal;
                    KaitenArrList[18][Y, BaseUB_X - X, Z] = SetVal;
                    KaitenArrList[19][Y, BaseUB_X - X, BaseUB_Z - Z] = SetVal;
                    KaitenArrList[20][BaseUB_Y - Y, X, Z] = SetVal;
                    KaitenArrList[21][BaseUB_Y - Y, X, BaseUB_Z - Z] = SetVal;
                    KaitenArrList[22][BaseUB_Y - Y, BaseUB_X - X, Z] = SetVal;
                    KaitenArrList[23][BaseUB_Y - Y, BaseUB_X - X, BaseUB_Z - Z] = SetVal;

                    KaitenArrList[24][Y, Z, X] = SetVal;
                    KaitenArrList[25][Y, Z, BaseUB_X - X] = SetVal;
                    KaitenArrList[26][Y, BaseUB_Z - Z, X] = SetVal;
                    KaitenArrList[27][Y, BaseUB_Z - Z, BaseUB_X - X] = SetVal;
                    KaitenArrList[28][BaseUB_Y - Y, Z, X] = SetVal;
                    KaitenArrList[29][BaseUB_Y - Y, Z, BaseUB_X - X] = SetVal;
                    KaitenArrList[30][BaseUB_Y - Y, BaseUB_Z - Z, X] = SetVal;
                    KaitenArrList[31][BaseUB_Y - Y, BaseUB_Z - Z, BaseUB_X - X] = SetVal;

                    KaitenArrList[32][Z, X, Y] = SetVal;
                    KaitenArrList[33][Z, X, BaseUB_Y - Y] = SetVal;
                    KaitenArrList[34][Z, BaseUB_X - X, Y] = SetVal;
                    KaitenArrList[35][Z, BaseUB_X - X, BaseUB_Y - Y] = SetVal;
                    KaitenArrList[36][BaseUB_Z - Z, X, Y] = SetVal;
                    KaitenArrList[37][BaseUB_Z - Z, X, BaseUB_Y - Y] = SetVal;
                    KaitenArrList[38][BaseUB_Z - Z, BaseUB_X - X, Y] = SetVal;
                    KaitenArrList[39][BaseUB_Z - Z, BaseUB_X - X, BaseUB_Y - Y] = SetVal;

                    KaitenArrList[40][Z, Y, X] = SetVal;
                    KaitenArrList[41][Z, Y, BaseUB_X - X] = SetVal;
                    KaitenArrList[42][Z, BaseUB_Y - Y, X] = SetVal;
                    KaitenArrList[43][Z, BaseUB_Y - Y, BaseUB_X - X] = SetVal;
                    KaitenArrList[44][BaseUB_Z - Z, Y, X] = SetVal;
                    KaitenArrList[45][BaseUB_Z - Z, Y, BaseUB_X - X] = SetVal;
                    KaitenArrList[46][BaseUB_Z - Z, BaseUB_Y - Y, X] = SetVal;
                    KaitenArrList[47][BaseUB_Z - Z, BaseUB_Y - Y, BaseUB_X - X] = SetVal;
                }
            }
        }

        //Distinctする
        for (int I = KaitenArrList.Count - 1; 0 <= I; I--) {
            for (int J = 0; J <= I - 1; J++) {
                //UBが違う場合は、同一でない
                if (KaitenArrList[I].GetUpperBound(0) != KaitenArrList[J].GetUpperBound(0)) continue;
                if (KaitenArrList[I].GetUpperBound(1) != KaitenArrList[J].GetUpperBound(1)) continue;
                if (KaitenArrList[I].GetUpperBound(2) != KaitenArrList[J].GetUpperBound(2)) 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, int pTargetZ, char[, ,] pBanArr)
    {
        if (pTargetX + pPieceMap.GetUpperBound(0) > UB_X) return false;
        if (pTargetY + pPieceMap.GetUpperBound(1) > UB_Y) return false;
        if (pTargetZ + pPieceMap.GetUpperBound(2) > UB_Z) return false;

        for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
            for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
                for (int Z = 0; Z <= pPieceMap.GetUpperBound(2); Z++) {
                    if (pPieceMap[X, Y, Z]
                     && pBanArr[pTargetX + X, pTargetY + Y, pTargetZ + Z] != ' ')
                        return false;
                }
            }
        }
        return true;
    }

    //解を出力
    static void PrintBan(char[, ,] pBanArr)
    {
        var sb = new System.Text.StringBuilder();

        for (int Z = 0; Z <= UB_Z; Z++) {
            sb.AppendFormat("Z={0}の平面", Z);
            sb.AppendLine();
            for (int Y = 0; Y <= UB_Y; Y++) {
                for (int X = 0; X <= UB_X; X++) {
                    sb.Append(pBanArr[X, Y, Z]);
                }
                sb.AppendLine();
            }
        }
        Console.WriteLine(sb.ToString());
    }
}


実行結果

解を発見
Z=0の平面
nVPtU
oVttt
oVVVU
Z=1の平面
nnPPU
o***U
o***U
Z=2の平面
*nPP*
*****
*****


解説

深さ優先探索でピースを敷き詰めてます。