C# - Massive, Slow, and inefficient solution
Confession: wrote this solution some time ago when the question was still in the sandbox, but it's not very good: you can do better!
Edit: replaced the boring solving with a less boring, more flexible, and generally better method
You run the program by compiling with csc dominoPrinter.cs and then passing arguments to the executable, for example (the 4-bit prime checker):
dominoPrinter.exe 4 1 0,0,1,1,0,1,0,1,0,0,0,1,0,1,1,1
Explanation:
The "Domino Printer" is a 3-stage program:
Stage 1: The "solver" generates an expression tree of "ifnot" and "or" binary operations with the given inputs, and a "1" from the powerline, there are 2ways this is done, depending on the number of inputs:
If there are fewer than 4 inputs the program brutes a solution of the fewest number of operations
If there are 4 or more inputs the program brutes each 8bit chunk of output and then combines the results to give the desired output. The bruted bits if flexible: the more bruted bits, the smaller the solution, but the longer the run-time.
The "solver" is what takes all the time (or at least it used to), and is also most of the code. I believe there is a well documented, fast, not so memory hungry, and probably optimal solution to this problem, but where would the fun be in looking it up?
The (bruted) expression tree for the 4-bit prime checker is
((2 or 1) ifnot (((0 ifnot 1) or ((1 ifnot 0) or (0 ifnot 2))) ifnot 3))
where the numbers are the indexes of the inputs.
Stage 2: The "organizer" takes the expression tree as input and assembles a "skeleton" layout, which precisely describes a domino layout made from some a set of 4x5 overlapping cells. Below is the skeleton for the bruted 4-bit prime checker (you'll need to change the bruteBase integer variable on line 473 to 4 (or larger) to get this result).
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
This output is effectively made up to two parts, the "evaluator" on the right, which is created from the expression tree from stage 1, and the "switchboard" on the left, which swaps and splits the inputs so that they arrive in the right places for the "evaluator" to handle.
There is considerable scope for compacting the layout at this point, but the program currently does very little such work. The code for this stage is horrible, but pretty simple underneath (see the "orifnot" method). The output is passed to stage 3.
Stage 3: The "printer" takes the output from the "organizer" and prints the corresponding 4x5 overlapping "cells" along with the power line. Below is an animation of the bruted 4-bit prime checker checking whether 5 is prime.
Code the lack of indenting is to avoid going over the SE 30k character limit which it would otherwise:
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();
}
}
}
}
An additional test case:
4 1 0,0,0,1,0,0,1,1,0,0,0,1,1,1,1,1
This checks whether two adjacent (non-wrapping) bits are both 1s (e.g. true for 0110, but false for 0101 and 1001)
All pushed at same time? – l4m2 – 2018-05-01T14:38:10.250
@l4m2 Yes, the inputs in the left-most column are toppled simultaneously. – Martin Ender – 2018-05-01T14:49:21.783