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 = "FILNPTUVWXYZ".ToCharArray();
static int mQuestionNo = 1;
static char[, ,] mQuestionArr; //問題の初期盤面
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;
internal int PieceCnt;
}
//問題を定義
static void QuestionDef()
{
if (mQuestionNo == 1) { UB_X = 5 - 1; UB_Y = 4 - 1; UB_Z = 3 - 1; }
if (mQuestionNo == 2) { UB_X = 6 - 1; UB_Y = 5 - 1; UB_Z = 2 - 1; }
if (mQuestionNo == 3) { UB_X = 10 - 1; UB_Y = 3 - 1; UB_Z = 2 - 1; }
if (mQuestionNo == 4) { UB_X = 7 - 1; UB_Y = 5 - 1; UB_Z = 3 - 1; }
if (mQuestionNo == 5) { UB_X = 12 - 1; UB_Y = 3 - 1; UB_Z = 2 - 1; }
if (mQuestionNo == 6) { UB_X = 5 - 1; UB_Y = 5 - 1; UB_Z = 2 - 1; }
if (mQuestionNo == 7) { UB_X = 3 - 1; UB_Y = 3 - 1; UB_Z = 3 - 1; }
mQuestionArr = 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++)
mQuestionArr[X, Y, Z] = ' ';
if (mQuestionNo == 4) {
for (int X = 1; X <= 5; X++)
for (int Y = 1; Y <= 3; Y++)
for (int Z = 0; Z <= UB_Z; Z++)
mQuestionArr[X, Y, Z] = '*';
}
if (mQuestionNo == 5) {
for (int X = 0; X <= UB_X; X++)
mQuestionArr[X, 2, 1] = '*';
}
}
static void Main()
{
var sw = System.Diagnostics.Stopwatch.StartNew();
//問題を定義
QuestionDef();
foreach (char EachPiece in PieceNameArr) {
HaitiKouhoListDict[EachPiece] = DeriveHaitiKouhoList(EachPiece);
HaitiKouhoListDict[EachPiece].RemoveAll(A => A.GetUpperBound(0) > UB_X);
HaitiKouhoListDict[EachPiece].RemoveAll(A => A.GetUpperBound(1) > UB_Y);
HaitiKouhoListDict[EachPiece].RemoveAll(A => A.GetUpperBound(2) > UB_Z);
}
var Stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArr = mQuestionArr;
WillPush.CurrX = WillPush.CurrY = WillPush.CurrZ = 0;
WillPush.PieceCnt = 0;
Stk.Push(WillPush);
while (Stk.Count > 0) {
JyoutaiDef Popped = Stk.Pop();
//クリア判定
if (mQuestionNo <= 5 && Popped.PieceCnt == 12
|| mQuestionNo == 6 && Popped.PieceCnt == 10
|| mQuestionNo == 7 && Popped.PieceCnt == 5) {
Console.WriteLine("解を発見。経過時間={0}", sw.Elapsed);
PrintBan(Popped.BanArr);
break;
}
//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) {
Popped.CurrX = 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 EachPiece in PieceNameArr) {
if (Array.IndexOf(UsedPieceArr, EachPiece) >= 0) continue;
//回転解の除外
if (EachPiece == 'F') {
if (Popped.CurrX > UB_X / 2) continue;
if (mQuestionNo != 5 && Popped.CurrY > UB_Y / 2) continue;
if (mQuestionNo != 5 && Popped.CurrZ > UB_Z / 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, 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[, ,] EachPieceMap in HaitiKouhoList) {
WillPush.BanArr = (char[, ,])Popped.BanArr.Clone();
WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
WillPush.PieceCnt = Popped.PieceCnt + 1;
for (int X = 0; X <= EachPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= EachPieceMap.GetUpperBound(1); Y++) {
for (int Z = 0; Z <= EachPieceMap.GetUpperBound(2); Z++) {
if (EachPieceMap[X, Y, Z] == false) continue;
WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y, Popped.CurrZ + Z]
= EachPiece;
}
}
}
if (WillEdakiri(WillPush.BanArr)) continue;
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 (mQuestionNo == 7
|| Popped.BanArr[Popped.CurrX, Popped.CurrY, Popped.CurrZ] != ' ') {
WillPush.BanArr = Popped.BanArr;
WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY + 1;
WillPush.CurrZ = Popped.CurrZ;
WillPush.PieceCnt = Popped.PieceCnt;
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[1, 0, 0] = wkArr[2, 0, 0] = true;
wkArr[0, 1, 0] = wkArr[1, 1, 0] = true;
wkArr[1, 2, 0] = true;
}
//■
//■
//■
//■
//■
if (pPieceName == 'I') {
wkArr = new bool[1, 5, 1];
wkArr[0, 0, 0] = true;
wkArr[0, 1, 0] = true;
wkArr[0, 2, 0] = true;
wkArr[0, 3, 0] = true;
wkArr[0, 4, 0] = true;
}
//■
//■
//■
//■■
if (pPieceName == 'L') {
wkArr = new bool[2, 4, 1];
wkArr[0, 0, 0] = true;
wkArr[0, 1, 0] = true;
wkArr[0, 2, 0] = true;
wkArr[0, 3, 0] = wkArr[1, 3, 0] = true;
}
// ■
// ■
//■■
//■
if (pPieceName == 'N') {
wkArr = new bool[2, 4, 1];
wkArr[1, 0, 0] = true;
wkArr[1, 1, 0] = true;
wkArr[0, 2, 0] = wkArr[1, 2, 0] = true;
wkArr[0, 3, 0] = true;
}
//■■
//■■
//■
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;
}
//■■■
// ■
// ■
if (pPieceName == 'T') {
wkArr = new bool[3, 3, 1];
wkArr[0, 0, 0] = wkArr[1, 0, 0] = wkArr[2, 0, 0] = true;
wkArr[1, 1, 0] = true;
wkArr[1, 2, 0] = true;
}
//■ ■
//■■■
if (pPieceName == 'U') {
wkArr = new bool[3, 2, 1];
wkArr[0, 0, 0] = 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[0, 1, 0] = true;
wkArr[0, 2, 0] = wkArr[1, 2, 0] = wkArr[2, 2, 0] = true;
}
//■
//■■
// ■■
if (pPieceName == 'W') {
wkArr = new bool[3, 3, 1];
wkArr[0, 0, 0] = true;
wkArr[0, 1, 0] = wkArr[1, 1, 0] = true;
wkArr[1, 2, 0] = wkArr[2, 2, 0] = true;
}
// ■
//■■■
// ■
if (pPieceName == 'X') {
wkArr = new bool[3, 3, 1];
wkArr[1, 0, 0] = true;
wkArr[0, 1, 0] = wkArr[1, 1, 0] = wkArr[2, 1, 0] = true;
wkArr[1, 2, 0] = true;
}
// ■
//■■
// ■
// ■
if (pPieceName == 'Y') {
wkArr = new bool[2, 4, 1];
wkArr[1, 0, 0] = true;
wkArr[0, 1, 0] = wkArr[1, 1, 0] = true;
wkArr[1, 2, 0] = true;
wkArr[1, 3, 0] = true;
}
//■■
// ■
// ■■
if (pPieceName == 'Z') {
wkArr = new bool[3, 3, 1];
wkArr[0, 0, 0] = wkArr[1, 0, 0] = true;
wkArr[1, 1, 0] = true;
wkArr[1, 2, 0] = wkArr[2, 2, 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;
}
//空白マスからUnionFindして5の倍数でなかったら枝切り
static bool WillEdakiri(char[, ,] pBanArr)
{
if (mQuestionNo == 7) return false;
var SpaceSetList = new List<HashSet<int>>();
for (int X = 0; X <= UB_X; X++) {
for (int Y = 0; Y <= UB_Y; Y++) {
for (int Z = 0; Z <= UB_Z; Z++) {
if (pBanArr[X, Y, Z] != ' ') continue;
int CurrHash = GetHash(X, Y, Z);
bool IsExist = false;
foreach (var EachSet in SpaceSetList) {
if (EachSet.Contains(CurrHash)) {
IsExist = true;
break;
}
}
if (IsExist) continue;
//始点を引数として、連結した空白マスのHashSetを返す
HashSet<int> wkSet = ExecUnionFind(pBanArr, X, Y, Z);
//5の倍数でなかったら枝切り
if (wkSet.Count % 5 > 0) return true;
SpaceSetList.Add(wkSet);
}
}
}
return false;
}
//UnionFindで島のチェック用
struct JyoutaiDefUnionFind
{
internal int CurrX;
internal int CurrY;
internal int CurrZ;
}
//始点を引数として、連結した空白マスのHashSetを返す
static HashSet<int> ExecUnionFind(char[, ,] pBanArr, int pStaX, int pStaY, int pStaZ)
{
var Stk = new Stack<JyoutaiDefUnionFind>();
JyoutaiDefUnionFind WillPush;
WillPush.CurrX = pStaX;
WillPush.CurrY = pStaY;
WillPush.CurrZ = pStaZ;
Stk.Push(WillPush);
var VisitedSet = new HashSet<int>();
VisitedSet.Add(GetHash(pStaX, pStaY, pStaZ));
while (Stk.Count > 0) {
JyoutaiDefUnionFind Popped = Stk.Pop();
Action<int, int, int> PushSyori = (pNewX, pNewY, pNewZ) =>
{
if (pNewX < 0 || UB_X < pNewX) return;
if (pNewY < 0 || UB_Y < pNewY) return;
if (pNewZ < 0 || UB_Z < pNewZ) return;
if (pBanArr[pNewX, pNewY, pNewZ] != ' ') return;
int wkHash = GetHash(pNewX, pNewY, pNewZ);
if (VisitedSet.Add(wkHash) == false) return;
WillPush.CurrX = pNewX;
WillPush.CurrY = pNewY;
WillPush.CurrZ = pNewZ;
Stk.Push(WillPush);
};
PushSyori(Popped.CurrX, Popped.CurrY, Popped.CurrZ - 1);
PushSyori(Popped.CurrX, Popped.CurrY, Popped.CurrZ + 1);
PushSyori(Popped.CurrX, Popped.CurrY - 1, Popped.CurrZ);
PushSyori(Popped.CurrX, Popped.CurrY + 1, Popped.CurrZ);
PushSyori(Popped.CurrX - 1, Popped.CurrY, Popped.CurrZ);
PushSyori(Popped.CurrX + 1, Popped.CurrY, Popped.CurrZ);
}
return VisitedSet;
}
static int GetHash(int pX, int pY, int pZ)
{
return pX * (UB_Y + 1) * (UB_Z + 1) + pY * (UB_Z + 1) + pZ;
}
//解を出力
static void PrintBan(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] == ' ' ? '/' : pBanArr[X, Y, Z]);
}
sb.AppendLine();
}
}
Console.WriteLine(sb.ToString());
}
}
問題1 ３×４×５を作る 問題2 ２×５×６を作る 問題3 ２×３×10を作る 問題4 下記の立体を作る (ユニーク解)
問題5 下記の立体を作る (ユニーク解)
問題6 ２×５×５を作る (使わないピースあり)
問題7 ３×３×３（すき間２単位）を作る (使わないピースあり)
