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[,]>>();
//ピースごとの必要面積のDict
static Dictionary<char, int> MensekiDict = new Dictionary<char, int>();
static char[] PieceArr = "0123456789".ToCharArray();
static int mQuestionNo = 1;
static char[,] mQuestionArr; //問題の初期盤面
static int mNeedMenseki;
static int UB_X;
static int UB_Y;
struct JyoutaiDef
{
internal char[,] BanArr;
internal int CurrX;
internal int CurrY;
internal List<char> UsedPieceList;
}
//問題を定義
static void QuestionDef()
{
if (mQuestionNo == 1) { UB_X = 11 - 1; UB_Y = 11 - 1; }
if (mQuestionNo == 2) { UB_X = 25 - 1; UB_Y = 5 - 1; }
if (mQuestionNo == 3) { UB_X = 21 - 1; UB_Y = 6 - 1; }
if (mQuestionNo == 4) { UB_X = 18 - 1; UB_Y = 7 - 1; }
if (mQuestionNo == 5) { UB_X = 14 - 1; UB_Y = 9 - 1; }
if (mQuestionNo == 6) { UB_X = 15 - 1; UB_Y = 8 - 1; }
if (mQuestionNo == 7) { UB_X = 11 - 1; UB_Y = 11 - 1; }
mQuestionArr = new char[UB_X + 1, UB_Y + 1];
for (int X = 0; X <= UB_X; X++)
for (int Y = 0; Y <= UB_Y; Y++)
mQuestionArr[X, Y] = ' ';
}
static void Main()
{
var sw = System.Diagnostics.Stopwatch.StartNew();
//問題を定義
QuestionDef();
foreach (char EachPiece in PieceArr) {
HaitiKouhoListDict[EachPiece] = DeriveHaitiKouhoList(EachPiece);
MensekiDict[EachPiece] = HaitiKouhoListDict[EachPiece][0].Cast<bool>().Count(A => A);
mNeedMenseki += MensekiDict[EachPiece];
}
if (mQuestionNo == 7) mNeedMenseki += 5; //ピース1の分
//回転解の除外
//if (mQuestionNo == 1)
// HaitiKouhoListDict['3'].RemoveRange(1, HaitiKouhoListDict['3'].Count - 1);
if (mQuestionNo == 6)
HaitiKouhoListDict['3'].RemoveRange(2, HaitiKouhoListDict['3'].Count - 2);
if (mQuestionNo == 7)
HaitiKouhoListDict['3'].RemoveRange(1, HaitiKouhoListDict['3'].Count - 1);
var sb = new System.Text.StringBuilder();
foreach (var EachPair in HaitiKouhoListDict.OrderBy(A => A.Key)) {
sb.AppendFormat("{0}の回転は", EachPair.Key);
sb.AppendLine();
foreach (bool[,] EachHaiti in EachPair.Value) {
for (int Y = 0; Y <= EachHaiti.GetUpperBound(1); Y++) {
for (int X = 0; X <= EachHaiti.GetUpperBound(0); X++) {
sb.Append(EachHaiti[X, Y] ? '■' : ' ');
}
sb.AppendLine();
}
sb.AppendLine();
}
}
//Console.WriteLine(sb.ToString());
//return;
var Stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArr = mQuestionArr;
WillPush.CurrX = WillPush.CurrY = 0;
WillPush.UsedPieceList = new List<char>();
Stk.Push(WillPush);
int PopID = 0;
while (Stk.Count > 0) {
JyoutaiDef Popped = Stk.Pop();
//if (PopID < 5000) {
// PrintBan(Popped.BanArr);
//}
if (++PopID % 500000 == 0) {
Console.WriteLine("PopID={0}", PopID);
PrintBan(Popped.BanArr);
}
//クリア判定
if (Popped.UsedPieceList.Count == (mQuestionNo == 7 ? 11 : 10)) {
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_X) {
Popped.CurrX = 0;
Popped.CurrY++;
//右側が全て空白なら枝切り
bool WillContinue = true;
for (int Y = 0; Y <= Popped.CurrY - 1; Y++) {
if (Popped.BanArr[UB_X, Y] != ' ')
WillContinue = false;
}
if (WillContinue) continue;
//残り面積で枝切り
int RestMenseki = 0;
for (int X = 0; X <= UB_X; X++) {
for (int Y = Popped.CurrY; Y <= UB_Y; Y++) {
if (Popped.BanArr[X, Y] == ' ') RestMenseki++;
}
}
foreach (char EachPiece in PieceArr) {
if (Popped.UsedPieceList.Contains(EachPiece)) continue;
RestMenseki -= MensekiDict[EachPiece];
}
if (RestMenseki < 0) continue;
if (Popped.CurrY >= UB_Y - 1) {
if (Popped.UsedPieceList.Contains('0') == false) continue;
if (Popped.UsedPieceList.Contains('2') == false) continue;
if (Popped.UsedPieceList.Contains('3') == false) continue;
if (Popped.UsedPieceList.Contains('4') == false) continue;
if (Popped.UsedPieceList.Contains('5') == false) continue;
if (Popped.UsedPieceList.Contains('6') == false) continue;
if (Popped.UsedPieceList.Contains('7') == false) continue;
if (Popped.UsedPieceList.Contains('8') == false) continue;
if (Popped.UsedPieceList.Contains('9') == false) continue;
}
//最終行を超えた場合
if (Popped.CurrY > UB_Y) continue;
}
foreach (char EachPiece in PieceArr) {
if (mQuestionNo == 7 && EachPiece == 1) {
if (Popped.UsedPieceList.Count(A => A == 1) == 2) {
continue;
}
}
else if (Popped.UsedPieceList.Contains(EachPiece))
continue;
//0と8は、0を先に使う
if (EachPiece == '8' && Popped.UsedPieceList.Contains('0') == false)
continue;
//2と5は、2を先に使う
if (mQuestionNo == 6 || mQuestionNo == 7)
if (EachPiece == '5' && Popped.UsedPieceList.Contains('2') == false)
continue;
//6と9は、6を先に使う
if (EachPiece == '9' && Popped.UsedPieceList.Contains('6') == false)
continue;
//ピースの配置候補リスト
List<bool[,]> HaitiKouhoList = new List<bool[,]>();
HaitiKouhoList.AddRange(HaitiKouhoListDict[EachPiece]);
//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.BanArr) == false);
//ピースを配置する経路のPush処理
foreach (bool[,] EachPieceMap in HaitiKouhoList) {
//2問目の特殊枝切り
if (mQuestionNo == 2) {
//縦に置く場合は、018の順序とする
if (EachPiece == '0' && EachPieceMap.GetLength(1) == 5) {
if (Popped.CurrX != UB_X - 2
&& Popped.CurrX != UB_X - 3
&& Popped.CurrX != UB_X - 6) continue;
}
if (EachPiece == '1' && EachPieceMap.GetLength(1) == 5) {
if (Popped.CurrX != UB_X - 3
&& Popped.CurrX != UB_X) continue;
}
if (EachPiece == '8' && EachPieceMap.GetLength(1) == 5) {
if (Popped.CurrX != UB_X - 2) continue;
}
}
WillPush.BanArr = (char[,])Popped.BanArr.Clone();
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
WillPush.UsedPieceList = new List<char>(Popped.UsedPieceList);
WillPush.UsedPieceList.Add(EachPiece);
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.BanArr[Popped.CurrX + X, Popped.CurrY + Y] = EachPiece;
}
}
if (EachPiece == '7') WillPush.CurrX = Popped.CurrX + 1;
else WillPush.CurrX = Popped.CurrX + EachPieceMap.GetLength(0);
//1個目のピースを配置後の枝切り
if (Popped.CurrX == 0 && Popped.CurrY == 0 && WillEdakiri(WillPush.BanArr))
continue;
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.UsedPieceList = Popped.UsedPieceList;
Stk.Push(WillPush);
}
}
//1個目のピースを配置後の枝切り
static bool WillEdakiri(char[,] pBanArr)
{
if (pBanArr[3, 0] == '7' && pBanArr[4, 0] == '7'
&& pBanArr[4, 1] == '7' && pBanArr[4, 2] == '7'
&& pBanArr[3, 2] == '7' && pBanArr[2, 2] == '7'
&& pBanArr[1, 2] == '7' && pBanArr[0, 2] == '7') return true;
//2問目の特殊枝切り
if (mQuestionNo == 2) {
if (pBanArr[0, 0] == '7' && pBanArr[2, 0] == '7'
&& pBanArr[2, 4] == '7' && pBanArr[0, 1] == '7') return true;
}
if (pBanArr[0, 0] == '6' && pBanArr[4, 1] == '6' && pBanArr[4, 2] == '6') return true;
if (pBanArr[0, 0] == '6' && pBanArr[2, 4] == '6' && pBanArr[2, 1] == '6') return true;
if (pBanArr[4, 0] == '4' && pBanArr[4, 2] == '4' && pBanArr[0, 2] == '4') return true;
//2問目の特殊枝切り
if (mQuestionNo == 2) {
if (pBanArr[0, 0] == '4' && pBanArr[2, 0] == '4' && pBanArr[2, 4] == '4') return true;
}
if (pBanArr[0, 0] == '3' && pBanArr[2, 0] == '3'
&& pBanArr[2, 4] == '3' && pBanArr[2, 1] == '3') return true;
return false;
}
//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 pPiece)
{
bool[,] wkArr = null;
//■■■
//■ ■
//■ ■
//■ ■
//■■■
if (pPiece == '0') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[2, 2] = true;
wkArr[0, 3] = wkArr[2, 3] = true;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = true;
}
//■
//■
//■
//■
//■
if (pPiece == '1') {
wkArr = new bool[1, 5];
wkArr[0, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = true;
wkArr[0, 3] = true;
wkArr[0, 4] = true;
}
//■■■
// ■
//■■■
//■
//■■■
if (pPiece == '2') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[0, 3] = true;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = true;
}
//■■■
// ■
//■■■
// ■
//■■■
if (pPiece == '3') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[2, 3] = true;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = true;
}
//■ ■
//■ ■
//■■■
// ■
// ■
if (pPiece == '4') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[2, 3] = true;
wkArr[2, 4] = true;
}
//■■■
//■
//■■■
// ■
//■■■
if (pPiece == '5') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[2, 3] = true;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = true;
}
//■■■
//■
//■■■
//■ ■
//■■■
if (pPiece == '6') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[0, 3] = wkArr[2, 3] = true;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = true;
}
//■■■
//■ ■
// ■
// ■
// ■
if (pPiece == '7') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = wkArr[2, 1] = true;
wkArr[2, 2] = true;
wkArr[2, 3] = true;
wkArr[2, 4] = true;
}
//■■■
//■ ■
//■■■
//■ ■
//■■■
if (pPiece == '8') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[0, 3] = wkArr[2, 3] = true;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = true;
}
//■■■
//■ ■
//■■■
// ■
//■■■
if (pPiece == '9') {
wkArr = new bool[3, 5];
wkArr[0, 0] = wkArr[1, 0] = wkArr[2, 0] = true;
wkArr[0, 1] = wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[2, 3] = true;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = 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;
}
}
//問6と問7以外はピースの裏返し不可
if (mQuestionNo != 6 && mQuestionNo != 7) {
KaitenArrList.RemoveRange(4, 4);
}
//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;
}
}
//上が全て空白なら敷き詰め不可
if (pTargetY > 0) {
bool IsAllSpace = true;
for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
if (pPieceMap[X, 0] && pBanArr[pTargetX + X, pTargetY - 1] != ' ')
IsAllSpace = false;
}
if (IsAllSpace) return false;
}
//左が全て空白なら敷き詰め不可
if (pTargetX > 0) {
bool IsAllSpace = true;
for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
if (pPieceMap[0, Y] && pBanArr[pTargetX - 1, pTargetY + Y] != ' ')
IsAllSpace = false;
}
if (IsAllSpace) 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++) {
char CurrChar = pBanArr[X, Y];
sb.Append(CurrChar == ' ' ? '/' : CurrChar);
}
sb.AppendLine();
}
Console.WriteLine(sb.ToString());
}
}
問１．11×11に入れる (ピースの裏返しは禁止)
問２．5×25に入れる (ピースの裏返しは禁止)
問３．6×21に入れる (ピースの裏返しは禁止)
問４．7×18に入れる (ピースの裏返しは禁止)
問５．9×14に入れる (ピースの裏返しは禁止)
問６．8×15に入れる (ピースの裏返しは可)
問７．すき間にもう1つ「1」が入るように11×11に入れる (ピースの裏返しは可)
