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20-057 2004年年賀パズル(問題2)

問題

小田原充宏さんの2004年年賀パズルの問題2を解きます。

問題2．
　問題1で見つかったすべての解の、和が2004ではない方のピースをすべて集め、
裏返しなしで、すきまのない長方形にすべて納めてください。

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 = "123456789ABCDEF".ToCharArray();

    static int UB_X, UB_Y;

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

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

        int Menseki = 0;
        foreach (char EachPiece in PieceNameArr) {
            Menseki += HaitiKouhoListDict[EachPiece][0].Cast<bool>().Count(A => A);
        }
        DeriveXYArr(Menseki);

        foreach (XYDef EachXYZ in mXYArr) {
            Console.WriteLine("横={0,2},縦={1}の長方形で、解を検証中", EachXYZ.X, EachXYZ.Y);

            UB_X = EachXYZ.X - 1;
            UB_Y = EachXYZ.Y - 1;
            if (ExecDFS()) break;
        }
        Console.WriteLine("経過時間={0}", sw.Elapsed);
    }

    struct XYDef
    {
        internal int X;
        internal int Y;
    }
    static XYDef[] mXYArr;

    //直方体のXYZの候補の配列を求める
    static void DeriveXYArr(int pMenseki)
    {
        var XYList = new List<XYDef>();

        for (int Y = 1; Y <= pMenseki; Y++) {
            for (int X = Y; X <= pMenseki; X++) {
                if (X * Y != pMenseki) continue;

                //ピース2があるので3以上必要
                if (Y < 3) continue;

                XYDef WillAdd;
                WillAdd.X = X;
                WillAdd.Y = Y;
                XYList.Add(WillAdd);
            }
        }
        mXYArr = XYList.ToArray();
    }

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

    //深さ優先探索を行い、解の有無を返す
    static bool ExecDFS()
    {
        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;

        WillPush.BanArr = new char[UB_X + 1, UB_Y + 1];
        for (int X = 0; X <= UB_X; X++)
            for (int Y = 0; Y <= UB_Y; Y++)
                WillPush.BanArr[X, Y] = ' ';

        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) {
                Console.WriteLine("解を発見");
                PrintBan(Popped.BanArr);
                return true;
            }

            //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) 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 == '1') {
                    if (Popped.CurrX > UB_X / 2) continue;
                    if (Popped.CurrY > UB_Y / 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] == ' ') {
                    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();
                    WillPush.CurrX = Popped.CurrX;

                    if (EachPiece == '1' || EachPiece == '2' || EachPiece == '5'
                     || EachPiece == '7' || EachPiece == 'B' || EachPiece == 'C'
                     || EachPiece == 'D' || EachPiece == 'E')
                        WillPush.CurrY = Popped.CurrY;
                    else WillPush.CurrY = Popped.CurrY + 1;

                    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;
                        }
                    }
                    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;
                WillPush.CurrY = Popped.CurrY + 1;
                WillPush.PieceCnt = Popped.PieceCnt;
                Stk.Push(WillPush);
            }
        }
        return false;
    }

    //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 == '1') {
            wkArr = new bool[8, 2];
            for (int X = 0; X <= 7; X++) wkArr[X, 0] = true;
            wkArr[3, 1] = wkArr[7, 1] = true;
        }

        //■■■■■■
        //■
        //■
        if (pPieceName == '2') {
            wkArr = new bool[6, 3];
            for (int X = 0; X <= 5; X++) wkArr[X, 0] = true;
            wkArr[0, 1] = true;
            wkArr[0, 2] = true;
        }

        //■■■■■
        //　■　　■
        if (pPieceName == '3') {
            wkArr = new bool[5, 2];
            for (int X = 0; X <= 4; X++) wkArr[X, 0] = true;
            wkArr[1, 1] = wkArr[4, 1] = true;
        }

        //■■■■■
        //　　■■
        if (pPieceName == '4') {
            wkArr = new bool[5, 2];
            for (int X = 0; X <= 4; X++) wkArr[X, 0] = true;
            wkArr[2, 1] = wkArr[3, 1] = true;
        }

        //■■■■■■■
        //　　　■　　■
        if (pPieceName == '5') {
            wkArr = new bool[7, 2];
            for (int X = 0; X <= 6; X++) wkArr[X, 0] = true;
            wkArr[3, 1] = wkArr[6, 1] = true;
        }

        //■■■■
        //　■　■
        if (pPieceName == '6') {
            wkArr = new bool[4, 2];
            for (int X = 0; X <= 3; X++) wkArr[X, 0] = true;
            wkArr[1, 1] = wkArr[3, 1] = true;
        }

        //■■■■■■
        //　　　　■■
        if (pPieceName == '7') {
            wkArr = new bool[6, 2];
            for (int X = 0; X <= 5; X++) wkArr[X, 0] = true;
            wkArr[4, 1] = wkArr[5, 1] = true;
        }

        //　■■■
        //■■
        if (pPieceName == '8') {
            wkArr = new bool[4, 2];
            for (int X = 1; X <= 3; X++) wkArr[X, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
        }

        //■■
        //■■
        if (pPieceName == '9') {
            wkArr = new bool[2, 2];
            wkArr[0, 0] = wkArr[1, 0] = true;
            wkArr[0, 1] = wkArr[1, 1] = true;
        }

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

        //■■■
        //　　■
        //　　■
        //　　■
        //　　■
        //　　■
        if (pPieceName == 'B') {
            wkArr = new bool[3, 6];
            wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
            wkArr[2, 1] = true;
            wkArr[2, 2] = true;
            wkArr[2, 3] = true;
            wkArr[2, 4] = true;
            wkArr[2, 5] = true;
        }

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

        //■■
        //　■
        //　■
        //　■
        if (pPieceName == 'D') {
            wkArr = new bool[2, 4];
            wkArr[0, 0] = wkArr[1, 0] = true;
            wkArr[1, 1] = true;
            wkArr[1, 2] = true;
            wkArr[1, 3] = true;
        }

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

        //■■
        //　■
        //　■
        if (pPieceName == 'F') {
            wkArr = new bool[2, 3];
            wkArr[0, 0] = wkArr[1, 0] = true;
            wkArr[1, 1] = true;
            wkArr[1, 2] = 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 <= 4; I++) KaitenArrList.Add(null);
        for (int P = 0; P <= 2; P += 2) KaitenArrList[P] = new bool[BaseArrUB_X + 1, BaseArrUB_Y + 1];
        for (int P = 1; P <= 3; 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;
            }
        }

        //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_X) return false;
        if (pTargetY + pPieceMap.GetUpperBound(1) > UB_Y) 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;
    }

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

実行結果

横=30,縦=3の長方形で、解を検証中
解を発見
BBBBBB8882222227777776666DDDDF
BAA44889921EEE1CCC3773656D5FFF
BA4444499211111111333335555555

経過時間=00:03:05.8151195

解説

長方形の、横、縦の組み合わせごとに深さ優先探索してます。