C # - Solution massive, lente et inefficace
Confession: a écrit cette solution il y a quelque temps alors que la question était encore dans le bac à sable, mais ce n'est pas très bon: vous pouvez faire mieux!
Edit: a remplacé la résolution ennuyeuse par une méthode moins ennuyeuse, plus flexible et généralement meilleure
Vous exécutez le programme en compilant avec csc dominoPrinter.cs, puis en transmettant des arguments à l'exécutable, par exemple (le vérificateur principal 4 bits):
dominoPrinter.exe 4 1 0,0,1,1,0,1,0,1,0,0,0,1,0,1,1,1
Explication:
"Imprimante Domino" est un programme en 3 étapes:
Étape 1 : Le "résolveur" génère un arbre d'expression d'opérations "ifnot" et "ou" avec les entrées indiquées, et un "1" à partir de la ligne à haute tension.
S'il y a moins de 4 entrées, le programme propose une solution du plus petit nombre possible d'opérations.
S'il y a 4 entrées ou plus, le programme brute chaque bloc de sortie de 8 bits, puis combine les résultats pour donner le résultat souhaité. Les bits brutés sont flexibles: plus les bits sont brutes, plus la solution est petite, mais plus le temps d'exécution est long.
Le "résolveur" est ce qui prend tout le temps (ou du moins ce qu’il avait l'habitude de faire), et c'est aussi l'essentiel du code. Je crois qu’il existe une solution bien documentée, rapide, pas très gourmande en mémoire, et probablement optimale à ce problème, mais quel serait le plaisir de le rechercher?
L'arbre d'expression (brute) du vérificateur principal 4 bits est
((2 or 1) ifnot (((0 ifnot 1) or ((1 ifnot 0) or (0 ifnot 2))) ifnot 3))
où les nombres sont les index des entrées.
Etape 2 : "l'organisateur" prend l'arbre d'expression en tant qu'entrée et assemble une présentation "squelette", qui décrit précisément une présentation en domino constituée d'un ensemble de cellules se chevauchant 4x5. Vous trouverez ci-dessous le squelette du vérificateur principal 4 bits bruté (vous devez modifier la bruteBasevariable entière de la ligne 473 en 4 (ou plus) pour obtenir ce résultat).
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
Cette sortie est composée de deux parties, l’évaluateur à droite, créé à partir de l’arbre d’expressions de l’étape 1, et le "tableau" à gauche, qui permute et divise les entrées afin qu’elles arrivent dans la bons endroits pour "l'évaluateur" à gérer.
Il existe une marge considérable pour compacter la mise en page à ce stade, mais le programme effectue actuellement très peu ce travail. Le code pour cette étape est horrible, mais assez simple en dessous (voir la méthode "orifnot"). La sortie est transmise à l'étape 3.
Etape 3 : "L'imprimante" prélève la sortie de "l'organisateur" et imprime les "cellules" 4x5 correspondantes se chevauchant avec la ligne d'alimentation. Vous trouverez ci-dessous une animation du vérificateur d’amorce de 4 bits brute vérifiant si 5 est premier.
Code le manque d'indentation est d'éviter de dépasser la limite de caractères SE 30k qu'il serait autrement :
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();
}
}
}
}
Un cas de test supplémentaire:
4 1 0,0,0,1,0,0,1,1,0,0,0,1,1,1,1,1
Ceci vérifie si deux bits adjacents (non enveloppants) sont des 1 (par exemple, vrai pour 0110, mais faux pour 0101 et 1001)