using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
//配置候補のList
static List<bool[, ,]> HaitiKouhoList;
static System.Diagnostics.Stopwatch sw = System.Diagnostics.Stopwatch.StartNew();
static void Main()
{
HaitiKouhoList = DeriveHaitiKouhoList();
for (int Depth = 16; Depth >= 1; Depth--) {
Console.WriteLine("ピースの数={0}の解を探索中", Depth);
if (ExecDES(Depth) == false) {
Console.WriteLine("ピースの数={0}の解は、ありません。", Depth);
break;
}
}
Console.WriteLine("経過時間={0}", sw.Elapsed);
}
static int UB = 4 - 1;
struct JyoutaiDef
{
internal char[, ,] BanArr;
internal int CurrX;
internal int CurrY;
internal int CurrZ;
internal int PieceCnt;
internal int SpaceCnt;
}
//深さを指定してDFSを行い、解の有無を返す
static bool ExecDES(int pDepth)
{
var stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArr = new char[UB + 1, UB + 1, UB + 1];
for (int X = 0; X <= UB; X++)
for (int Y = 0; Y <= UB; Y++)
for (int Z = 0; Z <= UB; Z++)
WillPush.BanArr[X, Y, Z] = ' ';
WillPush.CurrX = WillPush.CurrY = WillPush.CurrZ = 0;
WillPush.PieceCnt = 0;
WillPush.SpaceCnt = 0;
stk.Push(WillPush);
while (stk.Count > 0) {
JyoutaiDef Popped = stk.Pop();
//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) {
//スライド可能なピースがあれば枝切り
if (ExistCanSlidePiece(Popped.BanArr, Popped.PieceCnt)) continue;
Popped.CurrY = 0;
//最終高さを超えた場合
if (++Popped.CurrZ > UB) {
Console.WriteLine("解を発見。経過時間={0}", sw.Elapsed);
PrintAnswer(Popped.BanArr);
return true;
}
}
for (int I = 0; I <= HaitiKouhoList.Count - 1; I++) {
//ピース上限ならピースをセットできない
if (Popped.PieceCnt == pDepth) break;
//1個目のピースは回転させない
if (Popped.PieceCnt == 0 && 0 < I) break;
//マス目にピースを埋めれない場合
if (CanFillPiece(HaitiKouhoList[I], Popped.CurrX, Popped.CurrY, Popped.CurrZ,
Popped.BanArr) == false) continue;
//ピースを配置する経路のPush処理
WillPush.BanArr = (char[, ,])Popped.BanArr.Clone();
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
WillPush.PieceCnt = Popped.PieceCnt + 1;
WillPush.SpaceCnt = Popped.SpaceCnt;
bool[, ,] PieceMap = HaitiKouhoList[I];
for (int X = 0; X <= PieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= PieceMap.GetUpperBound(1); Y++) {
for (int Z = 0; Z <= PieceMap.GetUpperBound(2); Z++) {
if (PieceMap[X, Y, Z] == false) continue;
WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y, Popped.CurrZ + Z]
= (Char)('A' + WillPush.PieceCnt - 1);
}
}
}
stk.Push(WillPush);
}
//ピースを配置しない経路のPush
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
//ピースを配置済の場合
if (Popped.BanArr[Popped.CurrX, Popped.CurrY, Popped.CurrZ] != ' ') {
WillPush.BanArr = Popped.BanArr;
WillPush.SpaceCnt = Popped.SpaceCnt;
}
else { //確定空白の場合
//確定空白の上限を超えたら枝切り
WillPush.SpaceCnt = Popped.SpaceCnt + 1;
if (64 < WillPush.SpaceCnt + 4 * pDepth) continue;
WillPush.BanArr = (char[, ,])Popped.BanArr.Clone();
WillPush.BanArr[Popped.CurrX, Popped.CurrY, Popped.CurrZ] = '/';
}
WillPush.PieceCnt = Popped.PieceCnt;
stk.Push(WillPush);
}
return false;
}
//スライド可能なピースの有無を返す
static bool ExistCanSlidePiece(char[, ,] pBanArr, int pPieceCnt)
{
//ピースのループ
for (char LoopChar = 'A'; LoopChar <= 'A' + pPieceCnt - 1; LoopChar++) {
//各軸の移動可否
bool CanMoveXMinus = true;
bool CanMoveXPlus = true;
bool CanMoveYMinus = true;
bool CanMoveYPlus = true;
bool CanMoveZMinus = true;
bool CanMoveZPlus = true;
for (int X = 0; X <= UB; X++) {
for (int Y = 0; Y <= UB; Y++) {
for (int Z = 0; Z <= UB; Z++) {
if (pBanArr[X, Y, Z] != LoopChar) continue;
Predicate<char> wkPred = (pChar) =>
(pChar != LoopChar && pChar != '/');
if (X == 0 || wkPred(pBanArr[X - 1, Y, Z])) CanMoveXMinus = false;
if (X == UB || wkPred(pBanArr[X + 1, Y, Z])) CanMoveXPlus = false;
if (Y == 0 || wkPred(pBanArr[X, Y - 1, Z])) CanMoveYMinus = false;
if (Y == UB || wkPred(pBanArr[X, Y + 1, Z])) CanMoveYPlus = false;
if (Z == 0 || wkPred(pBanArr[X, Y, Z - 1])) CanMoveZMinus = false;
if (Z == UB || wkPred(pBanArr[X, Y, Z + 1])) CanMoveZPlus = false;
}
}
}
if (CanMoveXMinus || CanMoveXPlus) return true;
if (CanMoveYMinus || CanMoveYPlus) return true;
if (CanMoveZMinus || CanMoveZPlus) return true;
}
return false;
}
//回転させた配置のListを返す
static List<bool[, ,]> DeriveHaitiKouhoList()
{
bool[, ,] wkArr = null;
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)
{
for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
if (pTargetX + X > UB) return false;
for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
if (pTargetY + Y > UB) return false;
for (int Z = 0; Z <= pPieceMap.GetUpperBound(2); Z++) {
if (pTargetZ + Z > UB) return false;
if (pPieceMap[X, Y, Z]
&& pBanArr[pTargetX + X, pTargetY + Y, pTargetZ + Z] != ' ')
return false;
}
}
}
return true;
}
//解を出力
static void PrintAnswer(char[, ,] pBanArr)
{
var sb = new System.Text.StringBuilder();
for (int Z = 0; Z <= UB; Z++) {
sb.AppendFormat("Z={0}の平面", Z);
sb.AppendLine();
for (int Y = 0; Y <= UB; Y++) {
for (int X = 0; X <= UB; X++) {
sb.Append(pBanArr[X, Y, Z]);
}
sb.AppendLine();
}
}
Console.WriteLine(sb.ToString());
}
}
Fig2. 2×2×1のピース
