C＃-大量かつ低速で非効率的なソリューション
告白：質問がまだサンドボックスに残っていたときにこのソリューションを書いたが、それはあまり良くない：あなたはもっと良くできる！
編集：退屈な解法を、退屈でなく、より柔軟で、一般的に優れた方法に置き換えました
プログラムをcsc dominoPrinter.cs実行するには、たとえば、実行可能ファイルにコンパイルして引数を渡します（4ビットプライムチェッカー）。
dominoPrinter.exe 4 1 0,0,1,1,0,1,0,1,0,0,0,1,0,1,1,1
説明：
「ドミノプリンター」は3段階のプログラムです。
ステージ1：「ソルバー」は、指定された入力、および電力線からの「1」を使用して、「ifnot」および「or」バイナリ演算の式ツリーを生成します。
「ソルバー」は、常に（または少なくとも以前は）かかっていたものであり、ほとんどのコードでもあります。私は信じています。この問題に十分に文書化、高速ではなく、メモリそう空腹、そしておそらく最適解があるが、どこの楽しみはそれを見にでしょうか？
4ビットプライムチェッカーの（ブルート化された）式ツリーは、
((2 or 1) ifnot (((0 ifnot 1) or ((1 ifnot 0) or (0 ifnot 2))) ifnot 3))
ここで、数字は入力のインデックスです。
ステージ2：「オーガナイザー」は式ツリーを入力として受け取り、「スケルトン」レイアウトを組み立てます。これは、4x5の重複セルのセットから作成されたドミノレイアウトを正確に記述します。以下は、ブルートされた4ビットプライムチェッカーのスケルトンですbruteBase（この結果を得るには、行473の整数変数を4（またはそれ以上）に変更する必要があります）。
18 9
I ___ _ _______ O
v _ X X ____ uu
I X X X u UU/
v X X v ___///
I X X \ u //
v X \ v __//
I_X \ \_u /
\ \ ___/
\_U
この出力は事実上2つの部分で構成されます。右側の「評価者」はステージ1の式ツリーから作成され、左側の「スイッチボード」は入力を交換して分割し、 「評価者」が処理する適切な場所。
この時点でレイアウトを圧縮するためのかなりの範囲がありますが、プログラムは現在そのような作業をほとんど行いません。この段階のコードは恐ろしいですが、その下は非常に単純です（「orifnot」メソッドを参照）。出力はステージ3に渡されます。
ステージ3：「プリンター」は「オーガナイザー」から出力を取得し、対応する4x5の「セル」を電力線とともに印刷します。以下は、5が素数であるかどうかをチェックする、4ビットの素数チェッカーのブルートのアニメーションです。
インデントの欠如のコードは、SE 30kの文字制限を超えないようにすることです。
using System;
using System.Collections.Generic;
namespace dominoPrinter
{
class Program
{
static string bstring(bool[] barr)
{
string str = "";
foreach (bool b in barr)
str += b?1:0;
return str;
}
public static void Main(string[] args)
{
int inputCount;
val[] vals = resolveVals(args[0], args[1], args[2], out inputCount);
System.IO.StringWriter sw = new System.IO.StringWriter();
orifnot(inputCount, vals, sw);
System.IO.StringReader sr = new System.IO.StringReader(sw.ToString());
printDominoes(sr, Console.Out, args.Length > 3 && args[3] == "quite");
}
public abstract class val
{
public int size;
public bool[] rs;
public abstract string strness();
}
public class baseVal : val
{
public bool b;
public int id;
public baseVal(int idN)
{
id = idN;
size = 1;
}
public override string strness()
{
return id.ToString();
}
}
public abstract class biopVal : val
{
public val a, b;
public biopVal(val aN, val bN)
{
a = aN;
b = bN;
size = a.size + b.size;
}
public bool buildCheckApply(nodev ntree)
{
nodev cur = ntree;
rs = new bool[a.rs.Length];
bool notOK = true;
for (int i = 0; i < rs.Length; i++)
{
bool r = rs[i] = go(a.rs[i], b.rs[i]);
if (notOK)
{
if (r)
{
if (cur.a == null)
notOK = false;
else
{
cur = cur.a;
if (cur == nodev.full)
return false;
}
}
else
{
if (cur.b == null)
notOK = false;
else
{
cur = cur.b;
if (cur == nodev.full)
return false;
}
}
}
}
ntree.apply(this, 0);
return true;
}
public abstract bool go(bool a, bool b);
}
public class ifnotVal : biopVal
{
public override bool go(bool a, bool b)
{
return a ? false : b; // b IF NOT a, else FALSE
}
public ifnotVal(val aN, val bN) : base(aN, bN)
{
}
public override string strness()
{
return "(" + b.strness() + " ifnot " + a.strness() + ")";
}
}
public class orval : biopVal
{
public override bool go(bool a, bool b)
{
return a || b; // a OR b
}
public orval(val aN, val bN) : base(aN, bN)
{
}
public override string strness()
{
return "(" + b.strness() + " or " + a.strness() + ")";
}
}
static bool boolCompare(bool[] a, bool b)
{
for (int i = 0; i < a.Length; i++)
{
if (a[i] != b)
{
return false;
}
}
return true;
}
static bool boolFlat(bool[] a)
{
bool p = a[0];
for (int i = 1; i < a.Length; i++)
{
if (a[i] != p)
return false;
}
return true;
}
static bool boolCompare(bool[] a, bool[] b)
{
if (a.Length != b.Length)
return false; // let's do this proeprly
for (int i = 0; i < a.Length; i++)
{
if (a[i] != b[i])
{
return false;
}
}
return true;
}
// solver
// these is something VERY WRONG with the naming in this code
public class nodev
{
public static nodev full = new nodev();
public nodev a, b;
public nodev()
{
a = null;
b = null;
}
public bool contains(bool[] rs)
{
nodev cur = this;
if (cur == full)
return true;
for (int i = 0; i < rs.Length; i++)
{
if (rs[i])
{
if (cur.a == null)
return false;
cur = cur.a;
}
else
{
if (cur.b == null)
return false;
cur = cur.b;
}
if (cur == full)
return true;
}
return true;
}
public bool contains(val v)
{
nodev cur = this;
if (cur == full)
return true;
for (int i = 0; i < v.rs.Length; i++)
{
if (v.rs[i])
{
if (cur.a == null)
return false;
cur = cur.a;
}
else
{
if (cur.b == null)
return false;
cur = cur.b;
}
if (cur == full)
return true;
}
return true;
}
// returns whether it's full or not
public bool apply(val v, int idx)
{
if (v.rs[idx])
{
if (a == null)
{
if (idx == v.rs.Length - 1)
{ // end of the line, fellas
a = full;
if (b == full)
return true;
return false;
}
else
{
a = new nodev();
}
}
if (a.apply(v, idx + 1))
a = full;
if (a == full && b == full)
return true;
}
else
{
if (b == null)
{
if (idx == v.rs.Length - 1)
{ // end of the line, fellas
b = full;
if (a == full)
return true;
return false;
}
else
{
b = new nodev();
}
}
if (b.apply(v, idx + 1))
b = full;
if (a == full && b == full)
return true;
}
return false;
}
}
public static void sortOutIVals(baseVal[] ivals, int rc)
{
for (int i = 0; i < ivals.Length; i++)
{
ivals[i].rs = new bool[rc];
ivals[i].b = false;
}
int eri = 0;
goto next;
again:
for (int i = ivals.Length - 1; i >= 0; i--)
{
if (ivals[i].b == false)
{
ivals[i].b = true;
goto next;
}
ivals[i].b = false;
}
return;
next:
for (int i = ivals.Length - 1; i >= 0; i--)
{
ivals[i].rs[eri] = ivals[i].b;
}
eri++;
goto again;
}
public static val[] resolve(int inputCount, int c, bool[][] erss, out baseVal[] inputs)
{
val[] res = new val[erss.Length];
List<List<val>> bvals = new List<List<val>>();
nodev ntree = new nodev();
List<val> nvals = new List<val>();
baseVal tval = new baseVal(-1);
baseVal fval = new baseVal(-2);
baseVal[] ivals = new baseVal[inputCount];
inputs = new baseVal[inputCount + 2];
for (int i = 0; i < inputCount; i++)
{
ivals[i] = new baseVal(i); // value will change anyway
inputs[i] = ivals[i];
}
inputs[inputCount] = fval;
inputs[inputCount + 1] = tval;
sortOutIVals(ivals, c);
for (int i = 0; i < inputCount; i++)
{
nvals.Add(ivals[i]);
}
tval.rs = new bool[c];
fval.rs = new bool[c];
for (int i = 0; i < c; i++)
{
tval.rs[i] = true;
fval.rs[i] = false;
}
nvals.Add(tval);
nvals.Add(fval); // ifnot and or do nothing with falses
bvals.Add(new List<val>());
foreach (val v in nvals)
{
ntree.apply(v, 0);
if (!boolFlat(v.rs))
bvals[0].Add(v); // I trust these are distinct..
}
Func<biopVal, bool> checkValb = (v) =>
{
if (!v.buildCheckApply(ntree))
{
return false;
}
bvals[v.size-1].Add(v);
return true;
};
Action<biopVal, List<val>> checkVal = (v, li) =>
{
if (checkValb(v))
li.Add(v);
};
int maxSize = 1;
again:
for (int i = 0; i < erss.Length; i++)
{
bool[] ers = erss[i];
if (res[i] == null && ntree.contains(ers))
{
// there is a reason this is separate... I'm sure there is....
foreach (val rv in nvals)
{
if (boolCompare(rv.rs, ers))
{
res[i] = rv;
break;
}
}
}
}
for (int i = 0; i < erss.Length; i++)
{
if (res[i] == null)
goto notoveryet;
}
return res;
notoveryet:
maxSize++;
bvals.Add(new List<val>()); // bvals[maxSize-1] always exists
nvals.Clear();
long cc = 0;
List<val> sbvals = bvals[maxSize - 2];
// NOTs have a habit of working out, get it checked first
for (int i = sbvals.Count - 1; i >= 0; i--)
{ // also known as nvals, but let's ignore that
val arv = sbvals[i];
checkVal(new ifnotVal(arv, tval), nvals);
cc += 1;
}
for (int s = 1; s < maxSize; s++)
{
List<val> abvals = bvals[s - 1];
int t = maxSize - s;
if (t < s)
break;
List<val> bbvals = bvals[t - 1];
for (int i = abvals.Count - 1; i >= 0; i--)
{
val arv = abvals[i];
int jt = t == s ? i : bbvals.Count - 1;
for (int j = jt; j >= 0; j--)
{
val brv = bbvals[j];
checkVal(new ifnotVal(brv, arv), nvals);
checkVal(new ifnotVal(arv, brv), nvals);
checkVal(new orval(brv, arv), nvals); // don't technically need ors, but they are good fun
cc += 3;
}
}
}
int bc = 0;
foreach (List<val> bv in bvals)
bc += bv.Count;
goto again;
}
public static val[] resolveVals(string mStr, string nStr, string erStr, out int inputCount)
{
int ic = int.Parse(mStr);
int oc = int.Parse(nStr);
inputCount = ic;
int bruteBase = 3;
if (inputCount <= bruteBase)
return resolveVals(ic, oc, erStr);
else
return resolveValFours(bruteBase, ic, oc, erStr);
}
public static val joinVals(val low, val high, baseVal inp, baseVal tval, baseVal fval)
{
val lowCut = low == fval ? (val)fval : low == tval ? (val)new ifnotVal(inp, tval) : (val)new ifnotVal(inp, low);
val highCut = high == fval ? (val)fval : high == tval ? (val)inp : (val)new ifnotVal(new ifnotVal(inp, tval), high);
if (highCut == fval)
return lowCut;
if (lowCut == fval)
return highCut;
return new orval(highCut, lowCut);
}
public static val resolveValFour(int n, int m, int inputCount, bool[] ers)
{
// solves fours
int fc = ers.Length / m;
bool[][] fours = new bool[fc][];
for (int i = 0; i < fc; i++)
{
fours[i] = new bool[m];
for (int j = 0; j < m; j++)
{
fours[i][j] = ers[i*m+j];
}
}
baseVal[] inputs;
val[] fres = resolve(n, m, fours, out inputs);
baseVal tval = inputs[inputs.Length - 1];
baseVal fval = inputs[inputs.Length - 2];
for (int i = 0; i < n; i++)
{
inputs[i].id += inputCount - n;
}
// assemble
for (int i = 0, c = 1; c < fc; c *= 2, i++)
{
for (int j = 0; j + c < fc; j += c * 2)
{
fres[j] = joinVals(fres[j], fres[j+c], new baseVal((inputCount - n - 1) - i), tval, fval);
}
}
return fres[0];
}
public static val[] resolveValFours(int n, int inputCount, int outputCount, string erStr)
{
int m = 1;
for (int i = 0; i < n; i++)
m *= 2;
val[] res = new val[outputCount];
string[] data = erStr.Split(',');
for (int i = 0; i < outputCount; i++)
{
bool[] ers = new bool[data.Length];
for (int j = 0; j < data.Length; j++)
ers[j] = data[j][i] == '1';
res[i] = resolveValFour(n, m, inputCount, ers);
}
return res;
}
public static val[] resolveVals(int inputCount, int outputCount, string erStr)
{
val[] res;
string[] data = erStr.Split(',');
bool[][] erss = new bool[outputCount][];
for (int i = 0; i < outputCount; i++)
{
bool[] ers = new bool[data.Length];
for (int j = 0; j < data.Length; j++)
ers[j] = data[j][i] == '1';
erss[i] = ers;
}
baseVal[] inputs; // no need
res = resolve(inputCount, data.Length, erss, out inputs);
return res;
}
// organiser
public class vnode
{
private static vnode[] emptyVC = new vnode[0];
public static vnode oneVN = new vnode('1');
public static vnode noVN = new vnode(' ');
public static vnode flatVN = new vnode('_');
public static vnode moveUpVN = new vnode('/');
public static vnode moveDownVN = new vnode('\\');
public static vnode inputVN = new vnode('I');
public static vnode outputVN = new vnode('O');
public static vnode swapVN = new vnode('X');
public static vnode splitDownVN = new vnode('v');
public int size;
public vnode[] children;
public char c;
public int id = -3;
public vnode(char cN)
{
c = cN;
children = emptyVC;
size = 1;
}
public vnode(val v)
{
biopVal bv = v as biopVal;
if (bv != null)
{
children = new vnode[2];
children[0] = new vnode(bv.a);
children[1] = new vnode(bv.b);
size = children[0].size + children[1].size;
if (bv is orval)
c = 'U';
if (bv is ifnotVal)
c = 'u';
}
else
{
children = emptyVC;
size = 1;
c = 'I';
id = ((baseVal)v).id;
}
}
}
public class nonArray<T>
{
public int w = 0, h = 0;
Dictionary<int, Dictionary<int, T>> map;
public nonArray()
{
map = new Dictionary<int, Dictionary<int, T>>();
}
public T this[int x, int y]
{
get
{
Dictionary<int, T> yd;
if (map.TryGetValue(x, out yd))
{
T v;
if (yd.TryGetValue(y, out v))
{
return v;
}
}
return default(T);
}
set
{
if (x >= w)
w = x + 1;
if (y >= h)
h = y + 1;
Dictionary<int, T> yd;
if (map.TryGetValue(x, out yd))
{
yd[y] = value;
}
else
{
map[x] = new Dictionary<int, T>();
map[x][y] = value;
}
}
}
}
public static int fillOutMap(nonArray<vnode> map, vnode rn, int y, int x)
{
if (rn.children.Length == 0)
{
map[y,x] = rn;
return 1;
}
else
{
map[y+1,x] = rn;
for (int i = 0; i < rn.children.Length; i++)
{
if (i == 0)
{
fillOutMap(map, rn.children[i], y, x + 1);
}
if (i == 1)
{
int ex = x + rn.children[0].size;
for (int j = 1; j < ex - x; j++)
map[y - j + 1,ex - j] = vnode.moveUpVN;
fillOutMap(map, rn.children[i], y, ex);
}
y += rn.children[i].size;
}
}
return rn.size;
}
public static void orifnot(int inputCount, val[] vals, System.IO.TextWriter writer)
{
// step one - build weird tree like thing of death
nonArray<vnode> map = new nonArray<vnode>();
int curY = 0;
foreach (val v in vals)
{
vnode vnt = new vnode(v);
map[curY, 0] = vnode.outputVN;
curY += fillOutMap(map, vnt, curY, 1);
}
// step two - build the thing to get the values to where they need to be
// find Is
List<int> tis = new List<int>();
for (int y = 0; y < map.w; y++)
{
for (int x = map.h - 1; x >= 0; x--)
{
vnode vn = map[y,x];
if (vn != null && vn.c == 'I')
{
tis.Add(vn.id);
if (vn.id > -2)
{
for (;x < map.h; x++)
{
map[y,x] = vnode.flatVN;
}
}
goto next;
}
}
tis.Add(-2);
next:
continue;
}
// I do not like this piece of code, it can be replaced further down for the better if you get round to thinking about it
// add unused Is
for (int z = 0; z < inputCount; z++)
{
if (!tis.Contains(z))
{
int midx = tis.IndexOf(-2);
if (midx != -1)
{
tis[midx] = z;
map[midx,map.h-1] = vnode.noVN;
}
else
{
tis.Add(z);
map[map.w,map.h-1] = vnode.noVN;
}
}
}
int curX = map.h;
MORE:
for (int y = 0; y < map.w; y++)
{
if (y == map.w - 1)
{
if (tis[y] == -2)
map[y,curX] = vnode.noVN;
else
map[y,curX] = vnode.flatVN;
}
else
{
int prev = tis[y];
int cur = tis[y + 1];
if (cur != -2 && (prev == -2 || cur < prev))
{ // swap 'em
map[y,curX] = vnode.noVN;
if (prev == -2)
map[y+1,curX] = vnode.moveDownVN;
else
map[y+1,curX] = vnode.swapVN;
int temp = tis[y];
tis[y] = tis[y + 1];
tis[y + 1] = temp;
y++; // skip
}
else
{
if (/*thatThingThat'sAThing*/ prev == cur && cur != -2)
{
map[y,curX] = vnode.noVN;
map[y+1,curX] = vnode.splitDownVN;
int temp = tis[y];
tis[y+1] = -2;
y++; // skip
}
else
{
if (prev == -2)
map[y,curX] = vnode.noVN;
else
map[y,curX] = vnode.flatVN;
}
}
}
}
// check if sorted
for (int y = 0; y < map.w - 1; y++)
{
int prev = tis[y];
int cur = tis[y + 1];
if (cur != -2 && (prev == -2 || cur < prev))
goto NOTSORTED;
}
goto WHATNOW;
NOTSORTED:
curX++;
goto MORE;
WHATNOW:
tis.Add(-2); // this is to avoid boud checking y+2
// so... it's sorted now, so add the splits
morePlease:
curX++;
for (int y = 0; y < map.w; y++)
{
if (y == map.w - 1)
{
if (tis[y] == -2)
map[y,curX] = vnode.noVN;
else
map[y,curX] = vnode.flatVN;
}
else
{
int prev = tis[y];
int cur = tis[y + 1];
int next = tis[y + 2];
if (cur != -2 && prev == cur && cur != next)
{ // split
map[y,curX] = vnode.noVN;
map[y+1,curX] = vnode.splitDownVN;
tis[y + 1] = -2;
y++; // skip
}
else
{
if (prev == -2)
map[y,curX] = vnode.noVN;
else
map[y,curX] = vnode.flatVN;
}
}
}
// check if collapsed
for (int y = 0; y < map.w - 1; y++)
{
int prev = tis[y];
int cur = tis[y + 1];
if (cur != -2 && prev == cur)
goto morePlease;
}
// ok... now we put in the Is and 1
curX++;
map[0, curX] = vnode.oneVN;
int eyeCount = 0;
int ly = 0;
for (int y = 0; y < map.w; y++)
{
if (tis[y] > -1)
{
map[y, curX] = vnode.inputVN;
eyeCount++;
ly = y;
}
}
// step three - clean up if we can
// push back _ esq things to _
// _/ /
// this /shouldn't/ be necessary if I compact the vals properlu
for (int y = 0; y < map.w - 1; y++)
{
for (int x = 1; x < map.h; x++)
{
if (map[y, x] != null && map[y+1, x] != null && map[y+1, x-1] != null)
{
char uc = map[y+1, x-1].c;
if (map[y, x].c == '_' && map[y+1, x].c == '_'
&& (uc == 'U' || uc == 'u'))
{
map[y, x] = vnode.noVN;
map[y, x-1] = vnode.flatVN;
map[y+1, x] = map[y+1, x-1];
map[y+1, x-1] = vnode.noVN;
}
}
}
}
// step four - write out map
writer.WriteLine(map.h + " " + map.w);
for (int y = 0; y < map.w; y++)
{
for (int x = map.h - 1; x >= 0; x--)
{
vnode vn = map[y,x];
if (vn != null)
writer.Write(vn.c);
else
writer.Write(' ');
}
writer.WriteLine();
}
}
// printer
static string up1 = @" / / / /";
static string input = @" |||||";
static string output = @" | ";
static string flat = @" |/ \ /|\ ";
static string splitDown = @"|// / /\ |\/ / ";
static string splitUp = @" \ |/\ \ \/|\\ ";
static string moveDown = @"|// / / / ";
static string moveUp = @" \ \ \ |\\ ";
static string swap = @"|/ | /\ /\ \/ |\ |";
static string orDown = @"|/ / |/ \ /|\ ";
static string orUp = @"|/ / \ |\ \ |\ ";
static string ifnotDown = @"|/ / - \/ |\ |";
static string ifnotUp = @"|/ | /\ - \ |\ ";
public static void printDominoes(System.IO.TextReader reader, System.IO.TextWriter writer, bool moreverbosemaybe)
{
string line;
string[] data;
line = reader.ReadLine();
data = line.Split(' ');
int w = int.Parse(data[0]);
int h = int.Parse(data[1]);
int ox = 0;
int oy = 0;
int cx = 5;
int cy = 5;
char[,] T = new char[ox + w * cx, oy + h * (cy - 1) + 1];
Action<int, int, string> setBlock = (int x, int y, string str) =>
{
for (int i = 0; i < cx; i++)
{
for (int j = 0; j < cy; j++)
{
char c = str[i + j * cx];
if (c != ' ')
T[ox + x * cx + i, oy + y * (cy - 1) + j] = c;
}
}
};
// read and write
for (int j = 0; j < h; j++)
{
line = reader.ReadLine();
for (int i = 0; i < w; i++)
{
if (line[i] != ' ')
{
switch (line[i])
{
case '1':
setBlock(i, j, up1);
break;
case '_':
setBlock(i, j, flat);
break;
case '^':
setBlock(i, j, splitUp);
break;
case 'v':
setBlock(i, j, splitDown);
break;
case '/':
setBlock(i, j, moveUp);
break;
case '\\':
setBlock(i, j, moveDown);
break;
case 'X':
setBlock(i, j, swap);
break;
case 'U':
setBlock(i, j, orUp);
break;
case 'D':
setBlock(i, j, orDown);
break;
case 'u':
setBlock(i, j, ifnotUp);
break;
case 'd':
setBlock(i, j, ifnotDown);
break;
case 'I':
setBlock(i, j, input);
break;
case 'O':
setBlock(i, j, output);
break;
}
}
}
}
// end
for (int i = 0; i < T.GetLength(0); i++)
{
T[i, 0] = '/';
}
// writeout
w = T.GetLength(0) - cx + 1;
h = T.GetLength(1);
if (moreverbosemaybe)
writer.Write(w + " " + h + " ");
for (int j = 0; j < T.GetLength(1); j++)
{
for (int i = 0; i < T.GetLength(0) - cx + 1; i++)
{
char c = T[i, j];
writer.Write(c == 0 ? ' ' : c);
}
if (!moreverbosemaybe)
writer.WriteLine();
}
}
}
}
追加のテストケース：
4 1 0,0,0,1,0,0,1,1,0,0,0,1,1,1,1,1
これは、2つの隣接する（非ラッピング）ビットが両方とも1であるかどうかをチェックします（たとえば、0110の場合はtrue、0101と1001の場合はfalse）