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 = { 'F', 'P', 'U', 'V', 'l', 'n', 'o', 't' };
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;
}
static void Main()
{
var sw = System.Diagnostics.Stopwatch.StartNew();
int[, ,] Q13Arr = new int[3, 3, 3];
for (int X = 0; X <= Q13Arr.GetUpperBound(0); X++)
for (int Y = 0; Y <= Q13Arr.GetUpperBound(1); Y++)
for (int Z = 0; Z <= Q13Arr.GetUpperBound(2); Z++)
Q13Arr[X, Y, Z] = 1;
int[, ,] Q27Arr = Q13Arr;
int[, ,] Q28Arr = new int[4, 4, 2];
for (int X = 0; X <= Q28Arr.GetUpperBound(0); X++)
for (int Y = 0; Y <= Q28Arr.GetUpperBound(1); Y++)
for (int Z = 0; Z <= Q28Arr.GetUpperBound(2); Z++)
Q28Arr[X, Y, Z] = 1;
int[, ,] Q51Arr = new int[6, 3, 3];
for (int Z = 0; Z <= Q51Arr.GetUpperBound(2); Z++) {
int wk_UB_Y;
if (Z == 0) wk_UB_Y = 2;
else if (Z == 1) wk_UB_Y = 1;
else wk_UB_Y = 0;
for (int Y = 0; Y <= wk_UB_Y; Y++) {
for (int X = 0; X <= Q51Arr.GetUpperBound(0); X++) {
Q51Arr[X, Y, Z] = 1;
}
}
}
int[, ,] Ex1Arr = new int[6, 4, 2];
for (int Z = 0; Z <= Ex1Arr.GetUpperBound(2); Z++) {
for (int X = 0; X <= 3; X++)
for (int Y = 0; Y <= 1; Y++)
Ex1Arr[X, Y, Z] = 1;
for (int X = 2; X <= 5; X++)
for (int Y = 2; Y <= 3; Y++)
Ex1Arr[X, Y, Z] = 1;
}
int[, ,] QuestionArr = Q13Arr;
PieceNameArr = PieceNameArr.Where(X => X != 'F' && X != 'n').ToArray(); //Q13
//PieceNameArr = PieceNameArr.Where(X => X != 'P' && X != 'l').ToArray(); //Q27
//PieceNameArr = PieceNameArr.Where(X => X != 'o').ToArray(); //Q28
//PieceNameArr = PieceNameArr.Where(X => X != 'n').ToArray(); //Ex1
UB_X = QuestionArr.GetUpperBound(0);
UB_Y = QuestionArr.GetUpperBound(1);
UB_Z = QuestionArr.GetUpperBound(2);
foreach (char AnyPiece in PieceNameArr) {
HaitiKouhoListDict[AnyPiece] = DeriveHaitiKouhoList(AnyPiece);
}
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.CurrX = WillPush.CurrY = WillPush.CurrZ = 0;
stk.Push(WillPush);
while (stk.Count > 0) {
JyoutaiDef Popped = stk.Pop();
//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;
}
//使用済のピース名の配列
char[] UsedPieceArr = Popped.BanArr.Cast<char>().Distinct().ToArray();
foreach (char AnyPiece in PieceNameArr) {
if (Array.IndexOf(UsedPieceArr, AnyPiece) >= 0) continue;
//ピースの配置候補リスト
List<bool[, ,]> HaitiKouhoList = new List<bool[, ,]>();
HaitiKouhoList.AddRange(HaitiKouhoListDict[AnyPiece]);
//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[, ,] AnyPieceMap in HaitiKouhoList) {
WillPush.BanArr = (char[, ,])Popped.BanArr.Clone();
WillPush.CurrX = Popped.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]
= AnyPiece;
}
}
}
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;
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 == 'F') {
wkArr = new bool[3, 3, 1];
wkArr[0, 0, 0] = true; wkArr[1, 0, 0] = wkArr[2, 0, 0] = false;
wkArr[0, 1, 0] = wkArr[1, 1, 0] = wkArr[2, 1, 0] = true;
wkArr[0, 2, 0] = false; wkArr[1, 2, 0] = true; wkArr[2, 2, 0] = false;
}
//■■
//■■
//■
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; wkArr[1, 2, 0] = false;
}
//■ ■
//■■■
if (pPieceName == 'U') {
wkArr = new bool[3, 2, 1];
wkArr[0, 0, 0] = true; wkArr[1, 0, 0] = false; 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[1, 0, 0] = wkArr[2, 0, 0] = false;
wkArr[0, 1, 0] = true; wkArr[1, 1, 0] = wkArr[2, 1, 0] = false;
wkArr[0, 2, 0] = wkArr[1, 2, 0] = wkArr[2, 2, 0] = true;
}
//■
//■
//■■
if (pPieceName == 'l') {
wkArr = new bool[2, 3, 1];
wkArr[0, 0, 0] = true; wkArr[1, 0, 0] = false;
wkArr[0, 1, 0] = true; wkArr[1, 1, 0] = false;
wkArr[0, 2, 0] = wkArr[1, 2, 0] = true;
}
// ■
//■■
//■
if (pPieceName == 'n') {
wkArr = new bool[2, 3, 1];
wkArr[0, 0, 0] = false; wkArr[1, 0, 0] = true;
wkArr[0, 1, 0] = wkArr[1, 1, 0] = true;
wkArr[0, 2, 0] = true; wkArr[1, 2, 0] = false;
}
//■■
//■■
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;
}
//■■■
// ■
if (pPieceName == 't') {
wkArr = new bool[3, 2, 1];
wkArr[0, 0, 0] = wkArr[1, 0, 0] = wkArr[2, 0, 0] = true;
wkArr[0, 1, 0] = false; wkArr[1, 1, 0] = true; wkArr[2, 1, 0] = false;
}
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_X) return false;
for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
if (pTargetY + Y > UB_Y) return false;
for (int Z = 0; Z <= pPieceMap.GetUpperBound(2); Z++) {
if (pTargetZ + Z > UB_Z) 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; 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());
}
}
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13 Fとnのピースを除いた6つのピースで３×３×３の立方体を作ります。108解 問27 Pとlのピースを除いた6つのピースで３×３×３の立方体を作ります。ユニーク解
問28 oのピースを除いた7つのピースで２×４×４の直方体をつくります。6解
問51 8つのピース全部で下記の立体を作ります。
Ex1 nのピースを除いた7つのピースでnの2倍体の立体を作ります。4解
