using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
//Yペントミノの回転リスト
static List<bool[, ,]> PentominoKaitenList = new List<bool[, ,]>();
static int UB_X;
static int UB_Y;
static int UB_Z;
struct JyoutaiDef
{
internal char[, ,] BanArr;
internal int PentominoCnt;
internal int CurrX;
internal int CurrY;
internal int CurrZ;
}
static void Main()
{
var sw = System.Diagnostics.Stopwatch.StartNew();
//直方体を作成する
Func<int, int, int, int[, ,]> wkFunc = (pLen_X, pLen_Y, pLen_Z) =>
{
int[, ,] WillReturnArr = new int[pLen_X, pLen_Y, pLen_Z];
for (int X = 0; X <= WillReturnArr.GetUpperBound(0); X++)
for (int Y = 0; Y <= WillReturnArr.GetUpperBound(1); Y++)
for (int Z = 0; Z <= WillReturnArr.GetUpperBound(2); Z++)
WillReturnArr[X, Y, Z] = 1;
return WillReturnArr;
};
int[, ,] Q02Arr = wkFunc(2, 5, 6);
int[, ,] Q03Arr = wkFunc(3, 4, 5);
int[, ,] Q04Arr = wkFunc(2, 4, 10);
int[, ,] Q05Arr = wkFunc(2, 5, 8);
int[, ,] Q06Arr = wkFunc(4, 4, 5);
int[, ,] Q07Arr = wkFunc(4, 5, 5);
int[, ,] Q08Arr = wkFunc(2, 5, 11);
int[, ,] Q09Arr = wkFunc(2, 4, 15);
int[, ,] Q10Arr = wkFunc(5, 5, 5);
int[, ,] Q11Arr = wkFunc(5, 5, 5);
for (int Z = 0; Z <= 4; Z++) Q11Arr[2, 2, Z] = 0;
int[, ,] QuestionArr = Q02Arr;
UB_X = QuestionArr.GetUpperBound(0);
UB_Y = QuestionArr.GetUpperBound(1);
UB_Z = QuestionArr.GetUpperBound(2);
//Yペントミノを回転させた配置のListを返す
PentominoKaitenList = DerivePentominoKaitenList();
var stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArr = 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++)
WillPush.BanArr[X, Y, Z] = (QuestionArr[X, Y, Z] == 1 ? ' ' : '*');
WillPush.PentominoCnt = 0;
WillPush.CurrX = WillPush.CurrY = WillPush.CurrZ = 0;
stk.Push(WillPush);
int PopCnt = 0;
while (stk.Count > 0) {
JyoutaiDef Popped = stk.Pop();
if (++PopCnt % 100000 == 0) {
Console.WriteLine("{0}回目のPop。経過時間={1}", PopCnt, sw.Elapsed);
}
//クリア判定
if (Popped.BanArr.Cast<char>().All(X => X != ' ')) {
Console.WriteLine("解を発見。経過時間={0}", sw.Elapsed);
PrintAnswer(Popped.BanArr);
return;
}
//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;
}
//Yペントミノの配置候補リスト
List<bool[, ,]> HaitiKouhoList = new List<bool[, ,]>();
HaitiKouhoList.AddRange(PentominoKaitenList);
//Push後にX座標をインクリメントできるか？
bool CanIncrement = true;
//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);
CanIncrement = false;
}
//マス目にYペントミノを埋めれない候補をRemove
HaitiKouhoList.RemoveAll(X =>
CanFillPiece(X, Popped.CurrX, Popped.CurrY, Popped.CurrZ, Popped.BanArr) == false);
//10進数をchar型に変換
Func<int, char> DecToStr = (pInt) =>
{
if (pInt < 10) return (char)((int)'1' + pInt - 1);
return (char)((int)'A' + pInt - 10);
};
//Yペントミノを配置する経路のPush
foreach (bool[, ,] AnyPieceMap in HaitiKouhoList) {
WillPush.BanArr = (char[, ,])Popped.BanArr.Clone();
WillPush.PentominoCnt = Popped.PentominoCnt + 1;
WillPush.CurrX = Popped.CurrX;
if (CanIncrement) WillPush.CurrX++;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
for (int X = 0; X <= AnyPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= AnyPieceMap.GetUpperBound(1); Y++) {
for (int Z = 0; Z <= AnyPieceMap.GetUpperBound(2); Z++) {
if (AnyPieceMap[X, Y, Z] == false) continue;
WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y, Popped.CurrZ + Z]
= DecToStr(WillPush.PentominoCnt);
}
}
}
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.PentominoCnt = Popped.PentominoCnt;
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
stk.Push(WillPush);
}
}
}
//Yペントミノを回転させた配置のListを返す
static List<bool[, ,]> DerivePentominoKaitenList()
{
var WillReturn = new List<bool[, ,]>();
bool[, ,] wkArr = null;
// ■
//■■■■
wkArr = new bool[4, 2, 1];
wkArr[0, 0, 0] = false; wkArr[1, 0, 0] = true; wkArr[2, 0, 0] = wkArr[3, 0, 0] = false;
wkArr[0, 1, 0] = wkArr[1, 1, 0] = wkArr[2, 1, 0] = wkArr[3, 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 PrintAnswer(char[, ,] pBanArr)
{
char[, ,] wkBanArr = ArrBoundAscSort(pBanArr);
var sb = new System.Text.StringBuilder();
for (int Z = 0; Z <= wkBanArr.GetUpperBound(2); Z++) {
sb.AppendFormat("Z={0}の平面", Z);
sb.AppendLine();
for (int Y = 0; Y <= wkBanArr.GetUpperBound(1); Y++) {
for (int X = 0; X <= wkBanArr.GetUpperBound(0); X++) {
sb.Append(wkBanArr[X, Y, Z]);
}
sb.AppendLine();
}
}
Console.WriteLine(sb.ToString());
}
//配列の次元の長さがZ軸、X軸、Y軸で昇順になるように変換
static char[, ,] ArrBoundAscSort(char[, ,] pBanArr)
{
var LengthDict = new Dictionary<char, int>();
LengthDict['X'] = pBanArr.GetUpperBound(0);
LengthDict['Y'] = pBanArr.GetUpperBound(1);
LengthDict['Z'] = pBanArr.GetUpperBound(2);
IEnumerable<int> wkValues = LengthDict.Values.OrderByDescending(X => X);
char[, ,] WillReturnArr = new char[wkValues.ElementAt(0) + 1,
wkValues.ElementAt(1) + 1,
wkValues.ElementAt(2) + 1];
IEnumerable<char> wkKeys = LengthDict.OrderByDescending(X => X.Value).Select(X => X.Key);
for (int X = 0; X <= pBanArr.GetUpperBound(0); X++) {
for (int Y = 0; Y <= pBanArr.GetUpperBound(1); Y++) {
for (int Z = 0; Z <= pBanArr.GetUpperBound(2); Z++) {
char SetVal = pBanArr[X, Y, Z];
if (wkKeys.SequenceEqual(new char[] { 'Z', 'Y', 'X' }))
WillReturnArr[Z, Y, X] = SetVal;
if (wkKeys.SequenceEqual(new char[] { 'Z', 'X', 'Y' }))
WillReturnArr[Z, X, Y] = SetVal;
if (wkKeys.SequenceEqual(new char[] { 'Y', 'Z', 'X' }))
WillReturnArr[Y, Z, X] = SetVal;
if (wkKeys.SequenceEqual(new char[] { 'Y', 'X', 'Z' }))
WillReturnArr[Y, X, Z] = SetVal;
if (wkKeys.SequenceEqual(new char[] { 'X', 'Y', 'Z' }))
WillReturnArr[X, Y, Z] = SetVal;
if (wkKeys.SequenceEqual(new char[] { 'X', 'Z', 'Y' }))
WillReturnArr[X, Z, Y] = SetVal;
}
}
}
return WillReturnArr;
}
}
ピースは下記となります。ピースは回転や裏返しても使えます。
Q2 ２×５×６の直方体
Q3 ３×４×５の直方体
Q4 ２×４×１０の直方体
Q5 ２×５×８の直方体
Q6 ４×４×５の直方体
Q7 ４×５×５の直方体
Q8 ２×５×１１の直方体
Q9 ２×４×１５の直方体
Q10 ５×５×５の立方体
Q11 ５×５×５−５
