using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
//配置候補
static List<bool[, ,]> HaitiKouhoList;
static int UB_X;
static int UB_Y;
static int UB_Z;
struct JyoutaiDef
{
internal int Level;
internal char[, ,] BanArr;
internal int CurrX;
internal int CurrY;
internal int CurrZ;
}
static void Main()
{
for (int I = 1; I <= 10; I++) {
List<int[]> XYZArrList = DeriveXYZArrListFromTaiseki(I * 5);
Console.WriteLine("Nペンタキューブ{0}個分の体積でのXYZの組み合わせは、{1}通り",
I, XYZArrList.Count);
foreach (int[] EachArr in XYZArrList) {
Console.Write("X={0},Y={1},Z={2}の直方体を、", EachArr[0], EachArr[1], EachArr[2]);
Console.WriteLine("Nペンタキューブ{0}個で作成できるか検証中", I);
if (CanCreateTyokuhoutai(EachArr[0], EachArr[1], EachArr[2])) {
Console.WriteLine("直方体を作成できました。");
return;
}
Console.WriteLine("直方体を作成できません。");
}
Console.WriteLine();
}
}
//体積から直方体のX,Y,Zを列挙する。(X > Y > Z とする)
static List<int[]> DeriveXYZArrListFromTaiseki(int pTaiseki)
{
var XYZArrList = new List<int[]>();
for (int Z = 1; Z <= pTaiseki; Z++) {
for (int Y = Z; Y * Z <= pTaiseki; Y++) {
for (int X = Y; X * Y * Z <= pTaiseki; X++) {
if (X * Y * Z == pTaiseki)
XYZArrList.Add(new int[] { X, Y, Z });
}
}
}
return XYZArrList;
}
//X,Y,Zを引数として、直方体をYペンタキューブで作成可能かを返す
static bool CanCreateTyokuhoutai(int pX, int pY, int pZ)
{
int[, ,] QuestionArr = new int[pX, pY, pZ];
UB_X = QuestionArr.GetUpperBound(0);
UB_Y = QuestionArr.GetUpperBound(1);
UB_Z = QuestionArr.GetUpperBound(2);
HaitiKouhoList = DeriveHaitiKouhoList();
var stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.Level = 0;
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] = ' ';
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");
PrintAnswer(Popped.BanArr);
return true;
}
//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;
}
//ピースの配置候補リスト
List<bool[, ,]> wkHaitiKouhoList = new List<bool[, ,]>(HaitiKouhoList);
//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] == ' ') {
wkHaitiKouhoList.RemoveAll(X => X[0, 0, 0] == false);
}
//マス目にピースを埋めれない候補をRemove
wkHaitiKouhoList.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 wkHaitiKouhoList) {
WillPush.Level = Popped.Level + 1;
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]
= DecToStr(WillPush.Level);
}
}
}
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.Level = Popped.Level;
WillPush.BanArr = Popped.BanArr;
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
stk.Push(WillPush);
}
}
return false;
}
//10進数をchar型に変換
static char DecToStr(int pInt)
{
if (pInt < 10) return (char)((int)'1' + pInt - 1);
return (char)((int)'A' + pInt - 10);
}
//回転させた配置のListを返す
static List<bool[, ,]> DeriveHaitiKouhoList()
{
bool[, ,] wkArr = null;
//Uペンタキューブでの検証用
//■ ■
//■■■
//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;
//Nペンタキューブ
// ■
// ■
//■■
//■
wkArr = new bool[2, 4, 1];
wkArr[0, 0, 0] = false; wkArr[1, 0, 0] = true;
wkArr[0, 1, 0] = false; wkArr[1, 1, 0] = true;
wkArr[0, 2, 0] = wkArr[1, 2, 0] = true;
wkArr[0, 3, 0] = true; wkArr[1, 3, 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());
}
}
Fig.1(b) Nペンタキューブ
