using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
static char[] PieceNameArr = { '1', '2', '3', '4',
'5', '6', '7', '8', '9', 'A'};
static int[] MensekiArr = { 9, 8, 7, 6,
7, 6, 5, 5, 4, 3};
static int[] MaxHabaArr = { 5, 5, 5, 5,
4, 4, 4, 3, 3, 2};
static int PieceNameArrUB = PieceNameArr.GetUpperBound(0);
//ピースごとの配置候補
static Dictionary<char, List<bool[,]>> HaitiKouhoListDict =
new Dictionary<char, List<bool[,]>>();
//組み合わせの状態Def
struct CombinationJyoutaiDef
{
internal int CurrInd; //現在の配列のインデックス
internal Dictionary<int, List<int>> SelectedIndListDict; //選択済インデックスListのDict
}
static void Main()
{
var sw = System.Diagnostics.Stopwatch.StartNew();
//ピースの組み合わせ候補を返す
List<CombinationJyoutaiDef> PieceCombinationList = DerivePieceCombinationList();
Console.WriteLine("ピースの組み合わせは{0}通りです", PieceCombinationList.Count);
Console.WriteLine();
foreach (char AnyPiece in PieceNameArr) {
HaitiKouhoListDict[AnyPiece] = DeriveHaitiKouhoList(AnyPiece);
}
var sb = new System.Text.StringBuilder();
int CombinationCnt = 0;
foreach (CombinationJyoutaiDef EachCombination in PieceCombinationList) {
sb.Length = 0;
sb.AppendFormat("■■■■■組み合わせ{0}■■■■■", ++CombinationCnt);
sb.AppendLine();
for (int I = 1; I <= 4; I++) {
sb.AppendFormat("{0}個目の組み合わせ", I);
foreach (int EachInt in EachCombination.SelectedIndListDict[I]) {
sb.AppendFormat("{0},", PieceNameArr[EachInt]);
}
sb.AppendLine();
}
sb.AppendFormat("幅1のフレームの長方形複数を作成可能か検証中。経過時間={0}", sw.Elapsed);
sb.AppendLine();
Console.WriteLine(sb.ToString());
if (CanCreateHukusuu(EachCombination.SelectedIndListDict)) {
return;
}
}
}
//ピースの組み合わせ候補のListを返す
static List<CombinationJyoutaiDef> DerivePieceCombinationList()
{
var WillReturnList = new List<CombinationJyoutaiDef>();
var stk = new Stack<CombinationJyoutaiDef>();
CombinationJyoutaiDef WillPush;
WillPush.CurrInd = 0;
WillPush.SelectedIndListDict = new Dictionary<int, List<int>>();
for (int P = 1; P <= 4; P++) WillPush.SelectedIndListDict[P] = new List<int>();
stk.Push(WillPush);
while (stk.Count > 0) {
CombinationJyoutaiDef Popped = stk.Pop();
if (IsOKPieceCombination(Popped.SelectedIndListDict)) {
WillReturnList.Add(Popped);
}
if (Popped.CurrInd > PieceNameArrUB) continue;
for (int I = Popped.CurrInd; I <= PieceNameArrUB; I++) {
//使用済ピースは使用不可
bool WillContinue = false;
for (int P = 1; P <= 4; P++) {
if (Popped.SelectedIndListDict[P].Contains(I))
WillContinue = true;
}
if (WillContinue) continue;
//4つの固まりに追加
Action<int> wkAct = (pKeyVal) =>
{
WillPush.CurrInd = I + 1;
WillPush.SelectedIndListDict =
new Dictionary<int, List<int>>(Popped.SelectedIndListDict);
WillPush.SelectedIndListDict[pKeyVal] =
new List<int>(Popped.SelectedIndListDict[pKeyVal]);
WillPush.SelectedIndListDict[pKeyVal].Add(I);
if (IsValidCombination(WillPush))
stk.Push(WillPush);
};
for (int P = 1; P <= 4; P++) wkAct(P);
//ピースを使わない経路
WillPush.CurrInd = I + 1;
WillPush.SelectedIndListDict = Popped.SelectedIndListDict;
stk.Push(WillPush);
}
}
return WillReturnList;
}
//有効な組み合わせかを返す
static bool IsValidCombination(CombinationJyoutaiDef pCombinationJyoutai)
{
//ピース5個以上では、フレームを作成不可
for (int I = 1; I <= 4; I++) {
if (pCombinationJyoutai.SelectedIndListDict[I].Count >= 5) return false;
}
List<int> IndList1 = pCombinationJyoutai.SelectedIndListDict[1];
List<int> IndList2 = pCombinationJyoutai.SelectedIndListDict[2];
List<int> IndList3 = pCombinationJyoutai.SelectedIndListDict[3];
List<int> IndList4 = pCombinationJyoutai.SelectedIndListDict[4];
//1つめの固まりの[0] < 2つめの固まりの[0] < 3つめの固まりの[0] < 4つめの固まりの[0]
if (IndList1.Count > 0 && IndList2.Count > 0)
if (IndList1[0] > IndList2[0]) return false;
if (IndList2.Count > 0 && IndList3.Count > 0)
if (IndList2[0] > IndList3[0]) return false;
if (IndList4 != null && IndList3.Count > 0 && IndList4.Count > 0)
if (IndList3[0] > IndList4[0]) return false;
//固まりごとで[0] < [1] < [2] < [3] < [4] < [n] として対称解の除外
Predicate<List<int>> wkPred = (pIndList) =>
{
for (int I = 1; I <= pIndList.Count - 1; I++) {
if (pIndList[I - 1] > pIndList[I])
return false;
}
return true;
};
if (wkPred(IndList1) == false) return false;
if (wkPred(IndList2) == false) return false;
if (wkPred(IndList3) == false) return false;
if (IndList4 != null && wkPred(IndList4) == false) return false;
return true;
}
//4つの固まりの組み合わせがOKかを判定
static bool IsOKPieceCombination(Dictionary<int, List<int>> pSelectedIndListDict)
{
//長方形を作るので、固まり1つにつき、最低2ピース必要
for (int I = 1; I <= 4; I++) {
if (pSelectedIndListDict[I].Count <= 1)
return false;
}
//幅1のフレームを作成するので、面積合計は2の倍数となる
int[] wkSumArr = new int[4 + 1];
for (int I = 1; I <= 4; I++) {
foreach (int EachInd in pSelectedIndListDict[I]) {
wkSumArr[I] += MensekiArr[EachInd];
}
}
for (int I = 1; I <= 4; I++) {
if (wkSumArr[I] % 2 != 0) return false;
}
return true;
}
//選択済インデックスのカンマ区切りと、幅1のフレームの長方形の配置のDict
static SortedDictionary<string, char[,]> CanCreateFrameDict = new SortedDictionary<string, char[,]>();
//選択済インデックスListのDictを引数として、
//幅1のフレームを複数作成可能かをチェック
static bool CanCreateHukusuu(Dictionary<int, List<int>> pSelectedIndListDict)
{
string[] SelectedIndStrArr = new string[4 + 1];
for (int P = 1; P <= 4; P++) {
SelectedIndStrArr[P] = "";
pSelectedIndListDict[P].ForEach(X => SelectedIndStrArr[P] += X.ToString() + ",");
}
for (int P = 1; P <= 4; P++) {
//幅1のフレームを作成不可な組み合わせが1つでもあったら、NG
if (CanCreateFrameDict.ContainsKey(SelectedIndStrArr[P])) {
if (CanCreateFrameDict[SelectedIndStrArr[P]] == null) return false;
}
}
//選択のピースの少ない組み合わせからチェックできるようにする
int[] wkIndArr = Enumerable.Range(1, 4).OrderBy(X => SelectedIndStrArr[X].Length).ToArray();
foreach (int EachInd in wkIndArr) {
//幅1のフレームが作成可能であることをメモ化してある場合
if (CanCreateFrameDict.ContainsKey(SelectedIndStrArr[EachInd])) continue;
char[,] CanCreateFrame = DeriveCanCreateFrame(pSelectedIndListDict[EachInd]);
if (CanCreateFrame == null) {
CanCreateFrameDict[SelectedIndStrArr[EachInd]] = null;
return false;
}
CanCreateFrameDict[SelectedIndStrArr[EachInd]] = CanCreateFrame;
}
Console.WriteLine("解を発見");
for (int P = 1; P <= 4; P++) {
Console.WriteLine("{0}つ目の配置", P);
PrintAnswer(CanCreateFrameDict[SelectedIndStrArr[P]]);
}
return true;
}
//選択済インデックスListを引数として、
//幅1のフレームの長方形の配置を返す(配置不可ならnullを返す)
static char[,] DeriveCanCreateFrame(List<int> pSelectedIndList)
{
//ピース配列から面積を求める
int MensekiSum = 0;
pSelectedIndList.ForEach(X => MensekiSum += MensekiArr[X]);
//選択したピースの合計面積から、長方形の横幅と縦幅の候補を求める。
//対称解の除外で、 横幅 <= 縦幅 とする。
//フレームを作成するので、幅は最低でも3となる。
for (int X = 3; X <= MensekiSum; X++) {
for (int Y = X; Y <= MensekiSum; Y++) {
if (2 * X + 2 * (Y - 2) > MensekiSum) break;
if (2 * X + 2 * (Y - 2) != MensekiSum) continue;
char[,] ShikitumeTarget = DeriveShikitumeTarget(X, Y);
char[,] wkHaitiArr = DeriveCanHaiti(pSelectedIndList, ShikitumeTarget);
if (wkHaitiArr == null) continue;
return wkHaitiArr;
}
}
return null;
}
//長方形の横幅と縦幅を引数として、敷き詰め対象となる長方形を作成
static char[,] DeriveShikitumeTarget(int pX, int pY)
{
char[,] ShikitumeTarget = new char[pX, pY];
for (int X = 0; X <= ShikitumeTarget.GetUpperBound(0); X++) {
for (int Y = 0; Y <= ShikitumeTarget.GetUpperBound(1); Y++) {
bool IsHashi = false;
if (X == 0 || X == ShikitumeTarget.GetUpperBound(0)) IsHashi = true;
if (Y == 0 || Y == ShikitumeTarget.GetUpperBound(1)) IsHashi = true;
ShikitumeTarget[X, Y] = (IsHashi ? '?' : ' ');
}
}
return ShikitumeTarget;
}
//敷き詰めの状態Def
struct ShikitumeJyoutaiDef
{
internal int Level;
internal char[,] BanArr;
internal int CurrX;
internal int CurrY;
}
//選択済インデックスListと配置を引数として、
//幅1のフレームの長方形が作成可能かをチェック
static char[,] DeriveCanHaiti(List<int> pSelectedIndList, char[,] pBanArr)
{
int UB_X = pBanArr.GetUpperBound(0);
int UB_Y = pBanArr.GetUpperBound(1);
var stk = new Stack<ShikitumeJyoutaiDef>();
ShikitumeJyoutaiDef WillPush;
WillPush.Level = 0;
WillPush.BanArr = pBanArr;
WillPush.CurrX = WillPush.CurrY = 0;
stk.Push(WillPush);
while (stk.Count > 0) {
ShikitumeJyoutaiDef Popped = stk.Pop();
//クリア判定
if (Popped.BanArr.Cast<char>().All(X => X != '?'))
return Popped.BanArr;
//X座標の繰上げ処理(必ずX軸方向の長さは2以上)
if (Popped.CurrX > UB_X - 1) {
Popped.CurrX = 0;
Popped.CurrY++;
}
//最終行の1行前を超えた場合(必ずY軸方向の長さが2以上なので)
if (Popped.CurrY > UB_Y - 1) continue;
//使用済のピース名の配列
char[] UsedPieceArr = Popped.BanArr.Cast<char>().Distinct().ToArray();
foreach (char AnyPiece in PieceNameArr) {
//最初の配置は、0番目を使うこと
if (Popped.Level == 0 && AnyPiece != PieceNameArr[pSelectedIndList[0]])
continue;
//使用済ピースだったらContinue
if (Array.IndexOf(UsedPieceArr, AnyPiece) >= 0) continue;
//使用できないピースだったらContinue
if (pSelectedIndList.Exists(
X => AnyPiece == PieceNameArr[X]) == false) continue;
//ピースの配置候補リスト
List<bool[,]> HaitiKouhoList = new List<bool[,]>();
HaitiKouhoList.AddRange(HaitiKouhoListDict[AnyPiece]);
//現在のマス目が空きマスの場合は、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[,] AnyPieceMap in HaitiKouhoList) {
WillPush.Level = Popped.Level + 1;
WillPush.BanArr = (char[,])Popped.BanArr.Clone();
if (AnyPiece == '4') WillPush.CurrX = Popped.CurrX + 1;
else WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY;
for (int X = 0; X <= AnyPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= AnyPieceMap.GetUpperBound(1); Y++) {
if (AnyPieceMap[X, Y] == false) continue;
WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y] = AnyPiece;
}
}
stk.Push(WillPush);
}
//現在のマス目が空きマスでない場合は、ピースを配置しない経路のPush
if (Popped.BanArr[Popped.CurrX, Popped.CurrY] != '?') {
WillPush.Level = Popped.Level;
WillPush.BanArr = Popped.BanArr;
WillPush.CurrX = Popped.CurrX + 1;
WillPush.CurrY = Popped.CurrY;
stk.Push(WillPush);
}
}
}
return null;
}
//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[5, 5];
wkArr[0, 0] = true; wkArr[1, 0] = wkArr[2, 0] = wkArr[3, 0] = wkArr[4, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = wkArr[4, 1] = false;
wkArr[0, 2] = true; wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = wkArr[4, 2] = false;
wkArr[0, 3] = true; wkArr[1, 3] = wkArr[2, 3] = wkArr[3, 3] = wkArr[4, 3] = false;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = wkArr[3, 4] = wkArr[4, 4] = true;
}
//■
//■
//■
//■
//■■■■
if (pPieceName == '2') {
wkArr = new bool[4, 5];
wkArr[0, 0] = true; wkArr[1, 0] = wkArr[2, 0] = wkArr[3, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = false;
wkArr[0, 2] = true; wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = false;
wkArr[0, 3] = true; wkArr[1, 3] = wkArr[2, 3] = wkArr[3, 3] = false;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = wkArr[3, 4] = true;
}
//■
//■
//■
//■
//■■■
if (pPieceName == '3') {
wkArr = new bool[3, 5];
wkArr[0, 0] = true; wkArr[1, 0] = wkArr[2, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = wkArr[2, 1] = false;
wkArr[0, 2] = true; wkArr[1, 2] = wkArr[2, 2] = false;
wkArr[0, 3] = true; wkArr[1, 3] = wkArr[2, 3] = false;
wkArr[0, 4] = wkArr[1, 4] = wkArr[2, 4] = true;
}
//■
//■
//■
//■
//■■
if (pPieceName == '4') {
wkArr = new bool[2, 5];
wkArr[0, 0] = true; wkArr[1, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = false;
wkArr[0, 2] = true; wkArr[1, 2] = false;
wkArr[0, 3] = true; wkArr[1, 3] = false;
wkArr[0, 4] = wkArr[1, 4] = true;
}
//■
//■
//■
//■■■■
if (pPieceName == '5') {
wkArr = new bool[4, 4];
wkArr[0, 0] = true; wkArr[1, 0] = wkArr[2, 0] = wkArr[3, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = wkArr[2, 1] = wkArr[3, 1] = false;
wkArr[0, 2] = true; wkArr[1, 2] = wkArr[2, 2] = wkArr[3, 2] = false;
wkArr[0, 3] = wkArr[1, 3] = wkArr[2, 3] = wkArr[3, 3] = true;
}
//■
//■
//■
//■■■
if (pPieceName == '6') {
wkArr = new bool[3, 4];
wkArr[0, 0] = true; wkArr[1, 0] = wkArr[2, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = wkArr[2, 1] = false;
wkArr[0, 2] = true; wkArr[1, 2] = wkArr[2, 2] = false;
wkArr[0, 3] = wkArr[1, 3] = wkArr[2, 3] = true;
}
//■
//■
//■
//■■
if (pPieceName == '7') {
wkArr = new bool[2, 4];
wkArr[0, 0] = true; wkArr[1, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = false;
wkArr[0, 2] = true; wkArr[1, 2] = false;
wkArr[0, 3] = wkArr[1, 3] = true;
}
//■
//■
//■■■
if (pPieceName == '8') {
wkArr = new bool[3, 3];
wkArr[0, 0] = true; wkArr[1, 0] = wkArr[2, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = wkArr[2, 0] = false;
wkArr[0, 2] = wkArr[1, 2] = wkArr[2, 2] = true;
}
//■
//■
//■■
if (pPieceName == '9') {
wkArr = new bool[2, 3];
wkArr[0, 0] = true; wkArr[1, 0] = false;
wkArr[0, 1] = true; wkArr[1, 1] = false;
wkArr[0, 2] = wkArr[1, 2] = true;
}
//■
//■■
if (pPieceName == 'A') {
wkArr = new bool[2, 2];
wkArr[0, 0] = true; wkArr[1, 0] = false;
wkArr[0, 1] = wkArr[1, 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)
{
for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
if (pTargetX + X > pBanArr.GetUpperBound(0)) return false;
for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
if (pTargetY + Y > pBanArr.GetUpperBound(1)) return false;
if (pPieceMap[X, Y] && pBanArr[pTargetX + X, pTargetY + Y] != '?')
return false;
}
}
return true;
}
//解を出力
static void PrintAnswer(char[,] pBanArr)
{
var sb = new System.Text.StringBuilder();
for (int Y = 0; Y <= pBanArr.GetUpperBound(1); Y++) {
for (int X = 0; X <= pBanArr.GetUpperBound(0); X++) {
sb.Append(pBanArr[X, Y]);
}
sb.AppendLine();
}
Console.WriteLine(sb.ToString());
}
}
11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。
いずれも、すべてのＬ型ピースを使う問題です。 Q9 幅１の四角形のフレームを４つ、つくる
を４つ
