using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
//ピースごとの配置候補
static List<bool[, ,]> HaitiKouhoList;
const int UB = 3;
struct JyoutaiDef
{
internal char[, ,] BanArr;
internal int CurrX;
internal int CurrY;
internal int CurrZ;
internal int PieceCnt;
internal int PassCnt;
}
static void Main()
{
var sw = System.Diagnostics.Stopwatch.StartNew();
HaitiKouhoList = DeriveHaitiKouhoList();
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.PassCnt = 0;
Stk.Push(WillPush);
while (Stk.Count > 0) {
JyoutaiDef Popped = Stk.Pop();
//クリア判定
if (Popped.PieceCnt == 11) {
Console.WriteLine("解を発見。経過時間={0}", sw.Elapsed);
PrintBan(Popped.BanArr);
break;
}
//X座標の繰上げ処理
if (Popped.CurrX > UB) {
Popped.CurrX = 0;
Popped.CurrY++;
//特殊枝切り1
if (Popped.CurrY == 1 && Popped.CurrZ == 0) {
int LeftCnt = 0;
for (int X = 0; X <= 1; X++)
if (Popped.BanArr[X, 0, 0] == ' ')
LeftCnt++;
int RightCnt = 0;
for (int X = 2; X <= 3; X++)
if (Popped.BanArr[X, 0, 0] == ' ')
RightCnt++;
if (LeftCnt > RightCnt) continue;
}
//解に到達しない場合は枝切り
if (Popped.CurrX >= 0 && Popped.CurrY == 3 && Popped.CurrZ == UB) {
continue;
}
}
//最終列を超えた場合
if (Popped.CurrY > UB) {
Popped.CurrY = 0;
Popped.CurrZ++;
//特殊枝切り2
if (Popped.CurrX == 0 && Popped.CurrY == 0 && Popped.CurrZ == 2)
if (Popped.PieceCnt < 6) continue;
}
//ピースの配置候補リスト
List<bool[, ,]> wkHaitiKouhoList = new List<bool[, ,]>();
wkHaitiKouhoList.AddRange(HaitiKouhoList);
//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);
//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);
};
//ピースを配置する経路のPush処理
foreach (bool[, ,] EachPieceMap in wkHaitiKouhoList) {
WillPush.BanArr = (char[, ,])Popped.BanArr.Clone();
WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
WillPush.PieceCnt = Popped.PieceCnt + 1;
WillPush.PassCnt = Popped.PassCnt;
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]
= DecToStr(WillPush.PieceCnt);
}
}
}
if (WillEdakiri(WillPush.BanArr, WillPush.PieceCnt) == false)
Stk.Push(WillPush);
}
//ピースを配置しない経路のPush
WillPush.BanArr = Popped.BanArr;
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.CurrZ = Popped.CurrZ;
WillPush.PieceCnt = Popped.PieceCnt;
WillPush.PassCnt = Popped.PassCnt;
if (WillPush.BanArr[Popped.CurrX, Popped.CurrY, Popped.CurrZ] == ' ')
WillPush.PassCnt++;
if (WillPush.PassCnt <= 9)
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()
{
bool[, ,] wkArr = null;
Action<int, int> SetAct = (pX, pY) => wkArr[pX, pY, 0] = true;
// ■■
//■■
// ■
wkArr = new bool[3, 3, 1];
SetAct(1, 0); SetAct(2, 0);
SetAct(0, 1); SetAct(1, 1);
SetAct(1, 2);
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) return false;
if (pTargetY + pPieceMap.GetUpperBound(1) > UB) return false;
if (pTargetZ + pPieceMap.GetUpperBound(2) > UB) 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、枝切り判定
static bool WillEdakiri(char[, ,] pBanArr, int pPieceCnt)
{
var SpaceSetList = new List<HashSet<int>>();
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] != ' ') 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);
SpaceSetList.Add(wkSet);
}
}
}
int RestSum = SpaceSetList.Sum(A => A.Count / 5);
return pPieceCnt + RestSum < 11;
}
//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 < pNewX) return;
if (pNewY < 0 || UB < pNewY) return;
if (pNewZ < 0 || UB < 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 + 1) * (UB + 1) + pY * (UB + 1) + pZ;
}
//解を出力
static void PrintBan(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] == ' ' ? '/' : pBanArr[X, Y, Z]);
}
sb.AppendLine();
}
}
Console.WriteLine(sb.ToString());
}
}
問題1 ４×４×４の立方形 (すき間9単位)
