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20-067 フレミン(立体)

問題

小田原充宏さんのフレミンの立体問題を解きます。

8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。


問題4 ２×３×６に入れる(240解)

問題5 ３×３×４に入れる(3122解)

問題6〜14 ５単位のもの(Ｆ・Ｐ・Ｔ)と４単位のもの(ｌ・ｎ・ｔ)を
          それぞれ１ピースずつ除いた６ピースで３×３×３をつくる
          (６単位と３単位のものを除いた場合は解がありません)。

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;

    static int mQuestionNo = 4;
    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;
        internal int PassCnt;
    }

    //問題を定義
    static void QuestionDef()
    {
        if (mQuestionNo == 4) { UB_X = 6 - 1; UB_Y = 3 - 1; UB_Z = 2 - 1; }
        if (mQuestionNo == 5) { UB_X = 4 - 1; UB_Y = 3 - 1; UB_Z = 3 - 1; }
        if (mQuestionNo >= 6) { UB_X = 3 - 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 <= 5) {
            PieceNameArr = "AFPTlntb".ToCharArray();
        }
        if (mQuestionNo >= 6) {
            var KouhoPieceNameArrList = new List<char[]>();
            foreach (char wkChar1 in "FPT") {
                foreach (char wkChar2 in "lnt") {
                    var FullCharList = "AFPTlntb".ToCharArray().ToList();
                    FullCharList.Remove(wkChar1);
                    FullCharList.Remove(wkChar2);
                    KouhoPieceNameArrList.Add(FullCharList.ToArray());
                }
            }
            PieceNameArr = KouhoPieceNameArrList[mQuestionNo - 6];
        }
        Console.WriteLine("使用するピースは{0}です", new string(PieceNameArr));
    }

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

        //問題を定義
        QuestionDef();

        foreach (char EachPiece in PieceNameArr) {
            HaitiKouhoListDict[EachPiece] = DeriveHaitiKouhoList(EachPiece);
            HaitiKouhoListDict[EachPiece].RemoveAll(A => A.GetUpperBound(0) > UB_X);
            HaitiKouhoListDict[EachPiece].RemoveAll(A => A.GetUpperBound(1) > UB_Y);
            HaitiKouhoListDict[EachPiece].RemoveAll(A => A.GetUpperBound(2) > UB_Z);
        }

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

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

            //クリア判定
            if (mQuestionNo <= 5 && Popped.PieceCnt == 8
             || mQuestionNo >= 6 && Popped.PieceCnt == 6) {
                Console.WriteLine("解を発見。経過時間={0}", sw.Elapsed);
                PrintBan(Popped.BanArr);
                break;
            }

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

            //最終列を超えた場合
            if (Popped.CurrX > UB_X) {
                Popped.CurrX = 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;

                //回転解の除外
                if (EachPiece == 'A') {
                    if (Popped.CurrX > UB_X / 2) continue;
                    if (Popped.CurrY > UB_Y / 2) continue;
                    if (Popped.CurrZ > UB_Z / 2) 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;
                    WillPush.PassCnt = Popped.PassCnt;

                    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);
                }
            }

            //ピースを配置しない経路のPush
            WillPush.BanArr = Popped.BanArr;
            WillPush.CurrX = Popped.CurrX;
            WillPush.CurrY = Popped.CurrY + 1;
            WillPush.CurrZ = Popped.CurrZ;
            WillPush.PieceCnt = Popped.PieceCnt;
            WillPush.PassCnt = Popped.PassCnt;
            if (Popped.BanArr[Popped.CurrX, Popped.CurrY, Popped.CurrZ] == ' ')
                WillPush.PassCnt++;

            if (WillPush.PassCnt <= 1)
                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;

        Action<int, int> SetAct = (pX, pY) => wkArr[pX, pY, 0] = true;

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

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

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

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

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

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

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

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

        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] == ' ' ? '/' : pBanArr[X, Y, Z]);
                }
                sb.AppendLine();
            }
        }
        Console.WriteLine(sb.ToString());
    }
}

実行結果

使用するピースはAFPTlntbです
解を発見。経過時間=00:00:16.7153185
Z=0の平面
btAAll
bAAAln
PPPAln
Z=1の平面
tttFTn
bFFFTn
PPFTTT

解説

深さ優先探索でピースを敷き詰めてます。