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 = "123456789ABCDEFGHI".ToCharArray();
static int mQuestionNo = 1;
static char[,] mQuestionArr; //問題の初期盤面
static int UB_X;
static int UB_Y;
struct JyoutaiDef
{
internal char[,] BanArr;
internal int CurrX;
internal int CurrY;
internal int PieceCnt;
}
//問題を定義
static void QuestionDef()
{
if (mQuestionNo == 1) { UB_X = 9 - 1; UB_Y = 9 - 1; }
if (mQuestionNo == 2) { UB_X = 16 - 1; UB_Y = 9 - 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 PieceNameArr) {
HaitiKouhoListDict[EachPiece] = DeriveHaitiKouhoList(EachPiece);
}
var Stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArr = mQuestionArr;
WillPush.CurrX = WillPush.CurrY = 0;
WillPush.PieceCnt = 0;
Stk.Push(WillPush);
while (Stk.Count > 0) {
JyoutaiDef Popped = Stk.Pop();
//PrintBan(Popped.BanArr);
//クリア判定
if (mQuestionNo == 1 && Popped.PieceCnt == 9
|| mQuestionNo == 2 && Popped.PieceCnt == 16) {
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) 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 == '1') {
if (Popped.CurrX > UB_X / 2) continue;
if (Popped.CurrY > UB_Y / 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] == ' ') {
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.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 + 1;
WillPush.PieceCnt = Popped.PieceCnt + 1;
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 (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 (Popped.BanArr[Popped.CurrX, Popped.CurrY] != ' ') {
WillPush.BanArr = Popped.BanArr;
WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY + 1;
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 == '1') {
wkArr = new bool[4, 3];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
}
//■
//■■■■
//■■■
// ■
if (pPieceName == '2') {
wkArr = new bool[4, 4];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[2, 3] = true;
}
//■
//■■■■
//■■■
//■
if (pPieceName == '3') {
wkArr = new bool[4, 4];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[0, 3] = true;
}
// ■
// ■■■■
//■■■■
if (pPieceName == '4') {
wkArr = new bool[5, 3];
wkArr[1, 0] = true;
wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = wkArr[4, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
}
//■■
// ■■■■
// ■■■
if (pPieceName == '5') {
wkArr = new bool[5, 3];
wkArr[0, 0] = wkArr[1, 0] = true;
wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = wkArr[4, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
}
//■
//■
//■■■■
//■■■
if (pPieceName == '6') {
wkArr = new bool[4, 4];
wkArr[0, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
wkArr[0, 3] = wkArr[1, 3] = wkArr[2, 3] = true;
}
//■
//■■■
//■■■■
// ■
if (pPieceName == '7') {
wkArr = new bool[4, 4];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
wkArr[1, 3] = true;
}
//■
//■■■
//■■■
// ■■
if (pPieceName == '8') {
wkArr = new bool[3, 4];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[1, 3] = wkArr[2, 3] = true;
}
//■
//■■■
//■■■
//■■
if (pPieceName == '9') {
wkArr = new bool[3, 4];
wkArr[0, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[0, 3] = wkArr[1, 3] = true;
}
// ■
// ■■■
//■■■■
// ■
if (pPieceName == 'A') {
wkArr = new bool[4, 4];
wkArr[1, 0] = true;
wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
wkArr[2, 3] = true;
}
//■■
// ■■■
// ■■■
// ■
if (pPieceName == 'B') {
wkArr = new bool[4, 4];
wkArr[0, 0] = wkArr[1, 0] = true;
wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
wkArr[2, 3] = true;
}
//■
//■
//■■■
//■■■
// ■
if (pPieceName == 'C') {
wkArr = new bool[3, 5];
wkArr[0, 0] = true;
wkArr[0, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
wkArr[0, 3] = wkArr[1, 3] = wkArr[2, 3] = true;
wkArr[1, 4] = true;
}
// ■
//■■■■
// ■■■■
if (pPieceName == 'D') {
wkArr = new bool[5, 3];
wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = wkArr[4, 2] = true;
}
// ■
//■■■■
// ■■■
// ■
if (pPieceName == 'E') {
wkArr = new bool[4, 4];
wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
wkArr[3, 3] = true;
}
// ■
//■■■■
// ■■■
// ■
if (pPieceName == 'F') {
wkArr = new bool[4, 4];
wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
wkArr[1, 3] = true;
}
// ■
//■■■■
//■■■■
if (pPieceName == 'G') {
wkArr = new bool[4, 3];
wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
}
//■■
//■■■■
// ■■■
if (pPieceName == 'H') {
wkArr = new bool[4, 3];
wkArr[0, 0] = wkArr[1, 0] = true;
wkArr[0, 1] = wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = true;
wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
}
// ■
// ■
//■■■■
// ■■■
if (pPieceName == 'I') {
wkArr = new bool[4, 4];
wkArr[1, 0] = true;
wkArr[1, 1] = true;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = true;
wkArr[1, 3] = wkArr[2, 3] = wkArr[3, 3] = 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;
}
//空白マスからUnionFindして9の倍数でなかったら枝切り
static bool WillEdakiri(char[,] pBanArr)
{
var SpaceSetList = new List<HashSet<int>>();
for (int X = 0; X <= UB_X; X++) {
for (int Y = 0; Y <= UB_Y; Y++) {
if (pBanArr[X, Y] != ' ') continue;
int CurrHash = GetHash(X, Y);
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);
//9の倍数でなかったら枝切り
if (wkSet.Count % 9 > 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;
}
//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)
{
var Stk = new Stack<JyoutaiDefUnionFind>();
JyoutaiDefUnionFind WillPush;
WillPush.CurrX = pStaX;
WillPush.CurrY = pStaY;
Stk.Push(WillPush);
var VisitedSet = new HashSet<int>();
VisitedSet.Add(GetHash(pStaX, pStaY));
while (Stk.Count > 0) {
JyoutaiDefUnionFind Popped = Stk.Pop();
Action<int, int> PushSyori = (pNewX, pNewY) =>
{
if (pNewX < 0 || UB_X < pNewX) return;
if (pNewY < 0 || UB_Y < pNewY) return;
if (pBanArr[pNewX, pNewY] != ' ') return;
if (VisitedSet.Add(GetHash(pNewX, pNewY)) == false) return;
WillPush.CurrX = pNewX;
WillPush.CurrY = pNewY;
Stk.Push(WillPush);
};
PushSyori(Popped.CurrX, Popped.CurrY - 1);
PushSyori(Popped.CurrX, Popped.CurrY + 1);
PushSyori(Popped.CurrX - 1, Popped.CurrY);
PushSyori(Popped.CurrX + 1, Popped.CurrY);
}
return VisitedSet;
}
static int GetHash(int pX, int pY)
{
return (UB_Y + 1) * pX + pY;
}
//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] == ' ' ? '/' : pBanArr[X, Y]);
}
sb.AppendLine();
}
Console.WriteLine(sb.ToString());
}
}
問題1 この中の９ピースを使い、９×９をつくる(ユニーク解)。 問題2 この中の16ピースを使い、９×16をつくる(ユニーク解)。