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 = "FPTUVWXZlnotabd".ToCharArray();
static int mQuestionNo = 1;
static List<char[,]> mQuestionArrList = new List<char[,]>(); //問題の初期盤面
static int UB_X;
static int UB_Y;
struct JyoutaiDef
{
internal List<char[,]> BanArrList;
internal int CurrBanInd;
internal int CurrX;
internal int CurrY;
internal HashSet<char> UsedPieceSet;
}
//問題を定義
static void QuestionDef()
{
if (mQuestionNo == 1) {
UB_X = UB_Y = 8 - 1;
char[,] wkArr = new char[UB_X + 1, UB_Y + 1];
for (int X = 0; X <= UB_X; X++)
for (int Y = 0; Y <= UB_Y; Y++)
wkArr[X, Y] = ' ';
mQuestionArrList.Add(wkArr);
}
if (mQuestionNo == 2) {
UB_X = 4 - 1;
UB_Y = 5 - 1;
char[,] wkArr = new char[UB_X + 1, UB_Y + 1];
for (int X = 0; X <= UB_X; X++)
for (int Y = 0; Y <= UB_Y; Y++)
wkArr[X, Y] = ' ';
for (int I = 1; I <= 3; I++)
mQuestionArrList.Add(wkArr);
}
}
static void Main()
{
//問題を定義
QuestionDef();
foreach (char EachPiece in PieceNameArr) {
HaitiKouhoListDict[EachPiece] = DeriveHaitiKouhoList(EachPiece);
}
var Stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArrList = mQuestionArrList;
WillPush.CurrBanInd = 0;
WillPush.CurrX = WillPush.CurrY = 0;
WillPush.UsedPieceSet = new HashSet<char>();
Stk.Push(WillPush);
while (Stk.Count > 0) {
JyoutaiDef Popped = Stk.Pop();
//クリア判定
if (Popped.BanArrList[Popped.CurrBanInd].Cast<char>().All(X => X != ' ')) {
if (++Popped.CurrBanInd > mQuestionArrList.Count - 1) {
Console.WriteLine("解を発見");
Popped.BanArrList.ForEach(X => PrintBan(X));
return;
}
Popped.CurrX = Popped.CurrY = 0;
}
//X座標の繰上げ処理
if (Popped.CurrX > UB_X) {
Popped.CurrX = 0;
Popped.CurrY++;
//特殊枝切り 対称解の除外
if (Popped.CurrY == 1) {
if (Popped.BanArrList[Popped.CurrBanInd][0, 0] >
Popped.BanArrList[Popped.CurrBanInd][UB_X, 0])
continue;
}
}
//最終行を超えた場合
if (Popped.CurrY > UB_Y) continue;
foreach (char EachPiece in PieceNameArr) {
if (Popped.UsedPieceSet.Contains(EachPiece)) continue;
//2問目は、nを使用不可
if (mQuestionNo == 2 && EachPiece == 'n') 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.BanArrList[Popped.CurrBanInd][Popped.CurrX, Popped.CurrY] == ' ')
HaitiKouhoList.RemoveAll(X => X[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.BanArrList[Popped.CurrBanInd]) == false);
WillPush.UsedPieceSet = new HashSet<char>(Popped.UsedPieceSet);
WillPush.UsedPieceSet.Add(EachPiece);
//ピースを配置する経路のPush処理
foreach (bool[,] EachPieceMap in HaitiKouhoList) {
WillPush.CurrBanInd = Popped.CurrBanInd;
WillPush.BanArrList = new List<char[,]>(Popped.BanArrList);
WillPush.BanArrList[WillPush.CurrBanInd] =
(char[,])Popped.BanArrList[Popped.CurrBanInd].Clone();
if (EachPiece == 'F' || EachPiece == 'T' || EachPiece == 'V'
|| EachPiece == 'W' || EachPiece == 'Z' || EachPiece == 'l'
|| EachPiece == 'o' || EachPiece == 'b' || EachPiece == 'd')
WillPush.CurrX = Popped.CurrX;
else WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
for (int X = 0; X <= EachPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= EachPieceMap.GetUpperBound(1); Y++) {
if (EachPieceMap[X, Y] == false) continue;
WillPush.BanArrList[WillPush.CurrBanInd]
[Popped.CurrX + X, Popped.CurrY + Y] = EachPiece;
}
}
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.BanArrList[Popped.CurrBanInd][Popped.CurrX, Popped.CurrY] != ' ') {
WillPush.CurrBanInd = Popped.CurrBanInd;
WillPush.BanArrList = Popped.BanArrList;
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.UsedPieceSet = Popped.UsedPieceSet;
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];
wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = true;
wkArr[1, 2] = true;
}
//■■
//■■
//■
if (pPieceName == 'P') {
wkArr = new bool[2, 3];
wkArr[0, 0] = wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = true;
wkArr[0, 2] = true;
}
//■■■
// ■
// ■
if (pPieceName == 'T') {
wkArr = new bool[3, 3];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[1, 1] = true;
wkArr[1, 2] = true;
}
//■ ■
//■■■
if (pPieceName == 'U') {
wkArr = new bool[3, 2];
wkArr[0, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = true;
}
//■
//■
//■■■
if (pPieceName == 'V') {
wkArr = new bool[3, 3];
wkArr[0, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
}
//■
//■■
// ■■
if (pPieceName == 'W') {
wkArr = new bool[3, 3];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = true;
}
// ■
//■■■
// ■
if (pPieceName == 'X') {
wkArr = new bool[3, 3];
wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = true;
wkArr[1, 2] = true;
}
//■■
// ■
// ■■
if (pPieceName == 'Z') {
wkArr = new bool[3, 3];
wkArr[0, 0] = wkArr[1, 0] = true;
wkArr[1, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = true;
}
//■
//■
//■■
if (pPieceName == 'l') {
wkArr = new bool[2, 3];
wkArr[0, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = true;
}
// ■
//■■
//■
if (pPieceName == 'n') {
wkArr = new bool[2, 3];
wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = true;
wkArr[0, 2] = true;
}
//■■
//■■
if (pPieceName == 'o') {
wkArr = new bool[2, 2];
wkArr[0, 0] = wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = true;
}
//■■■
// ■
if (pPieceName == 't') {
wkArr = new bool[3, 2];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[1, 1] = true;
}
//■
//■
//■
if (pPieceName == 'a') {
wkArr = new bool[1, 3];
wkArr[0, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = true;
}
//■
//■■
if (pPieceName == 'b') {
wkArr = new bool[2, 2];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = true;
}
//■
//■
if (pPieceName == 'd') {
wkArr = new bool[1, 2];
wkArr[0, 0] = true;
wkArr[0, 1] = 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 BaseArrUB_X = pBaseArr.GetUpperBound(0);
int BaseArrUB_Y = pBaseArr.GetUpperBound(1);
for (int I = 1; I <= 8; I++) KaitenArrList.Add(null);
for (int P = 0; P <= 6; P += 2) KaitenArrList[P] = new bool[BaseArrUB_X + 1, BaseArrUB_Y + 1];
for (int P = 1; P <= 7; P += 2) KaitenArrList[P] = new bool[BaseArrUB_Y + 1, BaseArrUB_X + 1];
for (int X = 0; X <= BaseArrUB_X; X++) {
for (int Y = 0; Y <= BaseArrUB_Y; Y++) {
bool SetVal = pBaseArr[X, Y];
KaitenArrList[0][X, Y] = SetVal;
KaitenArrList[1][Y, BaseArrUB_X - X] = SetVal;
KaitenArrList[2][BaseArrUB_X - X, BaseArrUB_Y - Y] = SetVal;
KaitenArrList[3][BaseArrUB_Y - Y, X] = SetVal;
KaitenArrList[4][X, BaseArrUB_Y - Y] = SetVal;
KaitenArrList[5][BaseArrUB_Y - Y, BaseArrUB_X - X] = SetVal;
KaitenArrList[6][BaseArrUB_X - X, Y] = SetVal;
KaitenArrList[7][Y, X] = SetVal;
}
}
//Distinctする
for (int I = KaitenArrList.Count - 1; 0 <= I; I--) {
for (int J = 0; J <= I - 1; J++) {
if (KaitenArrList[I].GetUpperBound(0) !=
KaitenArrList[J].GetUpperBound(0)) continue;
if (KaitenArrList[I].GetUpperBound(1) !=
KaitenArrList[J].GetUpperBound(1)) 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, char[,] pBanArr)
{
if (pTargetX + pPieceMap.GetUpperBound(0) > UB_X) return false;
if (pTargetY + pPieceMap.GetUpperBound(1) > UB_Y) return false;
for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
if (pPieceMap[X, Y] && pBanArr[pTargetX + X, pTargetY + Y] != ' ')
return false;
}
}
return true;
}
//盤面を出力
static void PrintBan(char[,] pBanArr)
{
var sb = new System.Text.StringBuilder();
for (int Y = 0; Y <= UB_Y; Y++) {
for (int X = 0; X <= UB_X; X++) {
sb.Append(pBanArr[X, Y]);
}
sb.AppendLine();
}
Console.WriteLine(sb.ToString());
}
}
15個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。
Q1 ８×８を作る。解数は100万以上
Q2 nを除いたピースで、４×５を３つ作る。
