Pentomino tiling: Difference between revisions
m
→{{header|Wren}}: Minor tidy
(→{{header|C#}}: fix bug) |
m (→{{header|Wren}}: Minor tidy) |
||
| (32 intermediate revisions by 16 users not shown) | |||
Line 1:
{{
A [[wp:Pentomino|pentomino]] is a polyomino that consists of 5 squares. There are 12 pentomino shapes,
Line 39:
<br><br>
=={{header|
{{trans|Nim}}
<syntaxhighlight lang="11l">
F nonrandom(n)
UInt32 :seed = 0
:seed = 1664525 * :seed + 1013904223
R (:seed >> 16) % n
-V
SF = [[1, -1, 1, 0, 1, 1, 2, 1], [0, 1, 1, -1, 1, 0, 2, 0],
[1, 0, 1, 1, 1, 2, 2, 1], [1, 0, 1, 1, 2, -1, 2, 0],
[1, -2, 1, -1, 1, 0, 2, -1], [0, 1, 1, 1, 1, 2, 2, 1],
[1, -1, 1, 0, 1, 1, 2, -1], [1, -1, 1, 0, 2, 0, 2, 1]]
SI = [[0, 1, 0, 2, 0, 3, 0, 4], [1, 0, 2, 0, 3, 0, 4, 0]]
SL = [[1, 0, 1, 1, 1, 2, 1, 3], [1, 0, 2, 0, 3, -1, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 3], [0, 1, 1, 0, 2, 0, 3, 0],
[0, 1, 1, 1, 2, 1, 3, 1], [0, 1, 0, 2, 0, 3, 1, 0],
[1, 0, 2, 0, 3, 0, 3, 1], [1, -3, 1, -2, 1, -1, 1, 0]]
SN = [[0, 1, 1, -2, 1, -1, 1, 0], [1, 0, 1, 1, 2, 1, 3, 1],
[0, 1, 0, 2, 1, -1, 1, 0], [1, 0, 2, 0, 2, 1, 3, 1],
[0, 1, 1, 1, 1, 2, 1, 3], [1, 0, 2, -1, 2, 0, 3, -1],
[0, 1, 0, 2, 1, 2, 1, 3], [1, -1, 1, 0, 2, -1, 3, -1]]
SP = [[0, 1, 1, 0, 1, 1, 2, 1], [0, 1, 0, 2, 1, 0, 1, 1],
[1, 0, 1, 1, 2, 0, 2, 1], [0, 1, 1, -1, 1, 0, 1, 1],
[0, 1, 1, 0, 1, 1, 1, 2], [1, -1, 1, 0, 2, -1, 2, 0],
[0, 1, 0, 2, 1, 1, 1, 2], [0, 1, 1, 0, 1, 1, 2, 0]]
ST = [[0, 1, 0, 2, 1, 1, 2, 1], [1, -2, 1, -1, 1, 0, 2, 0],
[1, 0, 2, -1, 2, 0, 2, 1], [1, 0, 1, 1, 1, 2, 2, 0]]
SU = [[0, 1, 0, 2, 1, 0, 1, 2], [0, 1, 1, 1, 2, 0, 2, 1],
[0, 2, 1, 0, 1, 1, 1, 2], [0, 1, 1, 0, 2, 0, 2, 1]]
SV = [[1, 0, 2, 0, 2, 1, 2, 2], [0, 1, 0, 2, 1, 0, 2, 0],
[1, 0, 2, -2, 2, -1, 2, 0], [0, 1, 0, 2, 1, 2, 2, 2]]
SW = [[1, 0, 1, 1, 2, 1, 2, 2], [1, -1, 1, 0, 2, -2, 2, -1],
[0, 1, 1, 1, 1, 2, 2, 2], [0, 1, 1, -1, 1, 0, 2, -1]]
SX = [[1, -1, 1, 0, 1, 1, 2, 0]]
SY = [[1, -2, 1, -1, 1, 0, 1, 1], [1, -1, 1, 0, 2, 0, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 1], [1, 0, 2, 0, 2, 1, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 2], [1, 0, 1, 1, 2, 0, 3, 0],
[1, -1, 1, 0, 1, 1, 1, 2], [1, 0, 2, -1, 2, 0, 3, 0]]
SZ = [[0, 1, 1, 0, 2, -1, 2, 0], [1, 0, 1, 1, 1, 2, 2, 2],
[0, 1, 1, 1, 2, 1, 2, 2], [1, -2, 1, -1, 1, 0, 2, -2]]
Shapes = [SF, SI, SL, SN, SP, ST, SU, SV, SW, SX, SY, SZ]
Symbols = Array(‘FILNPTUVWXYZ-’)
NRows = 8
NCols = 8
Blank = Shapes.len
T Tiling
[[[Int]]] shapes
[Char] symbols
[[Int]] grid
[Bool] placed
F ()
V indexes = [4, 6, 11, 7, 10, 3, 9, 5, 1, 8, 0, 2]
L(index) indexes
.shapes.append(Shapes[index])
.symbols.append(Symbols[index])
.symbols.append(Symbols.last)
.grid = [[-1] * NCols] * NRows
L 4
L
V randRow = nonrandom(NRows)
V randCol = nonrandom(NCols)
I .grid[randRow][randCol] != Blank
.grid[randRow][randCol] = Blank
L.break
.placed = [0B] * Shapes.len
F tryPlaceOrientation(o, r, c, shapeIndex)
L(i) (0 .< o.len).step(2)
V x = c + o[i + 1]
V y = r + o[i]
I x !C 0 .< NCols | y !C 0 .< NRows | .grid[y][x] != -1
R 0B
.grid[r][c] = shapeIndex
L(i) (0 .< o.len).step(2)
.grid[r + o[i]][c + o[i + 1]] = shapeIndex
R 1B
F removeOrientation(o, r, c)
.grid[r][c] = -1
L(i) (0 .< o.len).step(2)
.grid[r + o[i]][c + o[i + 1]] = -1
F solve(pos, numPlaced)
I numPlaced == .shapes.len
R 1B
V row = pos I/ NCols
V col = pos % NCols
I .grid[row][col] != -1
R .solve(pos + 1, numPlaced)
L(i) 0 .< .shapes.len
I !.placed[i]
L(orientation) .shapes[i]
I !.tryPlaceOrientation(orientation, row, col, i)
L.continue
.placed[i] = 1B
I .solve(pos + 1, numPlaced + 1)
R 1B
.removeOrientation(orientation, row, col)
.placed[i] = 0B
R 0B
F printResult()
L(r) .grid
print(r.map(i -> @.symbols[i]).join(‘ ’))
V tiling = Tiling()
I tiling.solve(0, 0)
tiling.printResult()
E
print(‘No solution’)
</syntaxhighlight>
{{out}}
<pre>
P P U U U V V V
P P U X U L L V
T P X X X L - V
T T T X F L Z Z
T - F F F L Z Y
N N N F W Z Z Y
- - N N W W Y Y
I I I I I W W Y
</pre>
=={{header|BASIC}}==
==={{header|Visual Basic .NET}}===
{{trans|Java}}via{{trans|C#}}
Instead of having a large declaration for each rotation of each pentomino, a small array of encoded positions is supplied '''(seeds)''', and it is expanded into the set of 63 possible orientations. However, the additional expansion routines code does take up about 2/3 of the space that would have been taken by the elaborate Integer array definitions.
<syntaxhighlight lang="vbnet">Module Module1
Dim symbols As Char() = "XYPFTVNLUZWI█".ToCharArray(),
nRows As Integer = 8, nCols As Integer = 8,
target As Integer = 12, blank As Integer = 12,
grid As Integer()() = New Integer(nRows - 1)() {},
placed As Boolean() = New Boolean(target - 1) {},
pens As List(Of List(Of Integer())), rand As Random,
seeds As Integer() = {291, 292, 293, 295, 297, 329, 330, 332, 333, 335, 378, 586}
Sub Main()
Unpack(seeds) : rand = New Random() : ShuffleShapes(2)
For r As Integer = 0 To nRows - 1
grid(r) = Enumerable.Repeat(-1, nCols).ToArray() : Next
For i As Integer = 0 To 3
Dim rRow, rCol As Integer : Do : rRow = rand.Next(nRows) : rCol = rand.Next(nCols)
Loop While grid(rRow)(rCol) = blank : grid(rRow)(rCol) = blank
Next
If Solve(0, 0) Then
PrintResult()
Else
Console.WriteLine("no solution for this configuration:") : PrintResult()
End If
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
Sub ShuffleShapes(count As Integer) ' changes order of the pieces for a more random solution
For i As Integer = 0 To count : For j = 0 To pens.Count - 1
Dim r As Integer : Do : r = rand.Next(pens.Count) : Loop Until r <> j
Dim tmp As List(Of Integer()) = pens(r) : pens(r) = pens(j) : pens(j) = tmp
Dim ch As Char = symbols(r) : symbols(r) = symbols(j) : symbols(j) = ch
Next : Next
End Sub
Sub PrintResult() ' display results
For Each r As Integer() In grid : For Each i As Integer In r
Console.Write("{0} ", If(i < 0, ".", symbols(i)))
Next : Console.WriteLine() : Next
End Sub
' returns first found solution only
Function Solve(ByVal pos As Integer, ByVal numPlaced As Integer) As Boolean
If numPlaced = target Then Return True
Dim row As Integer = pos \ nCols, col As Integer = pos Mod nCols
If grid(row)(col) <> -1 Then Return Solve(pos + 1, numPlaced)
For i As Integer = 0 To pens.Count - 1 : If Not placed(i) Then
For Each orientation As Integer() In pens(i)
If Not TPO(orientation, row, col, i) Then Continue For
placed(i) = True : If Solve(pos + 1, numPlaced + 1) Then Return True
RmvO(orientation, row, col) : placed(i) = False
Next : End If : Next : Return False
End Function
' removes a placed orientation
Sub RmvO(ByVal ori As Integer(), ByVal row As Integer, ByVal col As Integer)
grid(row)(col) = -1 : For i As Integer = 0 To ori.Length - 1 Step 2
grid(row + ori(i))(col + ori(i + 1)) = -1 : Next
End Sub
' checks an orientation, if possible it is placed, else returns false
Function TPO(ByVal ori As Integer(), ByVal row As Integer, ByVal col As Integer,
ByVal sIdx As Integer) As Boolean
For i As Integer = 0 To ori.Length - 1 Step 2
Dim x As Integer = col + ori(i + 1), y As Integer = row + ori(i)
If x < 0 OrElse x >= nCols OrElse y < 0 OrElse y >= nRows OrElse
grid(y)(x) <> -1 Then Return False
Next : grid(row)(col) = sIdx
For i As Integer = 0 To ori.Length - 1 Step 2
grid(row + ori(i))(col + ori(i + 1)) = sIdx
Next : Return True
End Function
'!' the following routines expand the seed values into the 63 orientation arrays.
' source code space savings comparison:
' around 2000 chars for the expansion code, verses about 3000 chars for the integer array defs.
' perhaps not worth the savings?
Sub Unpack(sv As Integer()) ' unpacks a list of seed values into a set of 63 rotated pentominoes
pens = New List(Of List(Of Integer())) : For Each item In sv
Dim Gen As New List(Of Integer()), exi As List(Of Integer) = Expand(item),
fx As Integer() = ToP(exi) : Gen.Add(fx) : For i As Integer = 1 To 7
If i = 4 Then Mir(exi) Else Rot(exi)
fx = ToP(exi) : If Not Gen.Exists(Function(Red) TheSame(Red, fx)) Then Gen.Add(ToP(exi))
Next : pens.Add(Gen) : Next
End Sub
' expands an integer into a set of directions
Function Expand(i As Integer) As List(Of Integer)
Expand = {0}.ToList() : For j As Integer = 0 To 3 : Expand.Insert(1, i And 15) : i >>= 4 : Next
End Function
' converts a set of directions to an array of y, x pairs
Function ToP(p As List(Of Integer)) As Integer()
Dim tmp As List(Of Integer) = {0}.ToList() : For Each item As Integer In p.Skip(1)
tmp.Add(tmp.Item(item >> 2) + {1, 8, -1, -8}(item And 3)) : Next
tmp.Sort() : For i As Integer = tmp.Count - 1 To 0 Step -1 : tmp.Item(i) -= tmp.Item(0) : Next
Dim res As New List(Of Integer) : For Each item In tmp.Skip(1)
Dim adj = If((item And 7) > 4, 8, 0)
res.Add((adj + item) \ 8) : res.Add((item And 7) - adj)
Next : Return res.ToArray()
End Function
' compares integer arrays for equivalency
Function TheSame(a As Integer(), b As Integer()) As Boolean
For i As Integer = 0 To a.Count - 1 : If a(i) <> b(i) Then Return False
Next : Return True
End Function
Sub Rot(ByRef p As List(Of Integer)) ' rotates a set of directions by 90 degrees
For i As Integer = 0 To p.Count - 1 : p(i) = (p(i) And -4) Or ((p(i) + 1) And 3) : Next
End Sub
Sub Mir(ByRef p As List(Of Integer)) ' mirrors a set of directions
For i As Integer = 0 To p.Count - 1 : p(i) = (p(i) And -4) Or (((p(i) Xor 1) + 1) And 3) : Next
End Sub
End Module
</syntaxhighlight>
{{out}}
Solution found result ''(typical output)'':
<pre>Y F F █ L L L L
Y Y F F L P P P
Y T F N N N P P
Y T N N █ V V V
T T T W W Z Z V
U U X █ W W Z V
U X X X █ W Z Z
U U X I I I I I </pre>
Impossible to solve result ''(a somewhat rare occurrence)'':
<pre>no solution for this configuration:
. █ . . . . . .
█ . . █ . . . .
. . . . . . . .
. . . . █ . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . . </pre>
====VB .NET alternative output ''(corner characters)''====
This output may appear better in a command window
[https://tio.run/##rRlLc9u4@e5fgeoQExNKI8nOxvHE7iS20/HUSTySs952eoEoSIJDEVyAlKXNZKbTcw896LCHPfbY4x731@iPpN8H8AWKspN2lRnSBPC938hi1A6k4l@@vJXjNOTEvnp7ZI/A71zMiV7NRzLU5JUmZzOmPEpOSOuHv1y/ufn@3dWHv95etludG4lbr5RiK4/6BhR/0UDeG8DLKOFTrgDyyCfRWYauulrAJExNeeJu9/o@GYUs@ri1XIBNlRhXdj1q@HzH74sVy0yb9HDr0@cSNA5ZwA3waylDzqICNP/OeEJYF5JHRpAroRPv/aR4F0xQ6hPFIoN8AG85L4E152PtsAxUP/Vf9HzSf9HHxwE@nuHjuU8O@i/gcdDFRx8fB/iA3YPnoNNnR999zmw2TEfkLRMgRUHqQxSz4KNnKFJybFmyIlquPFwdztLJJOTDGYu59vol@BupiHJV3yU3khQaLU7mlvAUCnMRpXOu2CjknQGPOUu8di8zPwWXydwFKL/jy8ShJhqoHThU0DMV0Af9Ar7q8WNyLlFG2ARQFLWD@K39jfQI4OwYjhz0V1LG5HYmICKsPABMPYREwawvHu/cKlA5gl1OyFCGC@6BDbuU3Mx45NC8ViJKBlynYVKx3UWouXPsTEYa3LJzq0TCr0TEvVYkCSyliZARmYD6kpnQJJDRRExTxXD5uIWS76AAznA5cdhc6YTPO@eCTSOpExHozjkfpVNQb@dSv0oSFswgYlCCgp0BZ@M/81WGF3GCI1Zc0vWuQKZRNcgp2SfBjEVTrolUYzCjnIAYnMSCB7CGUjEyh0xl7CbnhcCP@o0ldWz27/JFjNzOmdmp@2/hXU1O5fhNiQSVa1zmQ5SIEI69PCV3jViTeVzNGGWmAMyIDyPnuPgrW7sr1u5wDXA04g5meZKGQ1natvgqH@XOXXXHIA5mDl4Ushqd20Z1HApMOBYasumKTFgUrIgyG3rP0So3OW@YAOQUSNo/OhfzOFk5prwAH3NsAAQuI5vnj8sTjsVhX21pBik@KQgB4BwSUetT93PLB1/3BHlJICBbHfjMlSEgcTdpIkPVgn9PyGJ0NannLic2vTOpIq742Du/9QA0R@qqcR@wJqmCQjIRSifg6SnsF@Eso9Dq5U0aBWbF5pDXq@9ZSGJZrSA@sauQdq@LmlYEWFnfqqFenj3JS68J64FhityolLv2g6zqxBiy8Deb1H2ItXB7F1oKu1@la1MnZs4AEyfES7vnULZiIvxTglUj55M@GvBubIOJgNw7mWR1Hoy7nXodp5NK8CgxaXPL/UwQCroFnEmFZG6u33sVFD6qzGjGJxlpdJNERClHmo2oSlZPjAmsELtUgp90t9mqv8F8sYM7k2IqZN@weuGpBIItGZn3wysjW8LggdxjK44@lwsIIZa3XBVGipRiOLR@DNuOAXL/dn0wX3V9j@65/UjhaSfoaMc7nQdodq54NE1mxnmGCY9Jv6G/ARae4mHMFYg4/zK2KKjsSJ1Y63jwETQREccYYoIRowW0TEQkBKq41ZRPOGi2zBSFnousgF73/2vN33Yae0xfjpePZZP/XaWYWJYuZF2lPlm5B6oW2KuF4RJzOnmvsHeCj9OTbObIVlbV7ZXZNp2sXdlSgTH4inrLpjTlhkkWDlsuh@r7HfT0la7nUHMjtEgMTQH6h33Tck1kGMp7LM9KQhGKIGL5MsaRAXdxiCALFqawDMVfmsXvDpysybCz153M12HUkakKONh0DPAwisCTLYAANqnzmCmhoUMtTsOPKVMF@91uF9tCpbO2lltONBJBbD5ZcKUxpYyAVXKwfV5kOjYskTGfVNiKuYJuVJMIsva9VKB3I6Bl7Y@VNiefnxZOYGHDk5odTGkhdHTYtG7ph8GS2QElKQkagn0oI4mci0hy7Q6Tdih7YJ50eh9o0rEo6cVWNP2Jm9pVRVYigWyyFA1dqJnZjKU9RE23s8FkWR9Yb@S1B9iQL6DZeTUee5MlbU6wPfTy53sNdVPA7qGNq7dCWYQmOgcyMV9NnDjEs@KLPFwsQSzt5d7tDaBpQNxDNuf44QMwzeplznOOqbHtMw0FnoLT9KGsbsPEpPXc71wXGAvFDVPazd651usptm6gcmazAXlCoI@FUdqco8WQ0zA8Y9E2MJ3LSHOVeNBAADnA0XuGgIKcnqINatJt1XCYKiHkEt0kE0FRs@jHnZUPyTdm0NbWahUou2kKotTxrr3H5ybarIEyOtzhIO4MP4rY67lWBtTGuvi@BCDj/KAO0qeQUj@Boo58gjcX7aPPdg/VdkC3bi4QwRDyiLfD/3G/7EvBKl2b5E2rUFKnpH1Sfna3yFTGqIb4bswQhrMG0REVG@NUDJNQKdtzSk7JoZG76wIAXaMrD6GeGvwU2v8jaqcju1fF00b8dEc1QojiHughn8MiYfNpmcxtjuc/pgKyLYd5s@ZkWcCzWjM0quXwb2hkWH2qYGgs6AlG@VDxYFfwFSXYNMCQ8l6vBhxaweYY2c/KSHMMjlbkRRcK3VTxSnHZOSs5IsW29ffMGw3YPqTQFRHPrpgxw/r@w9cCmMMfEWEulJJK70yNvwfTdukHwNL7SuaxBSqaHnQve5EBK3GauP4FM33lJoNWLjX2yVim2MFzyJQr04@wIDG1gGh7hC8DHifQM0R8gpeyZWzf1u5EqtFcud/Bqo@XUrd4HwHrTzCA4X1iriV80mrBUDejX5/OLcvtezGGNojpQAiSoNtm9SvIrjJMv5WPa4UuiouOZo04mQtl1h51LoF0ZxiHIvGQd/rt10U5Wuckpkb74bUIaMPS7dK8xbZDRcj04zfPBrTSmjsZETHAQUP/2L7yGyJLUtDy5ug6/emnkHsIYzmi2UVS841xmSbhWA4LUH6zdJ0rhkWwKuEDWRUSCNidmzIB8kIbbY0J9h5z@J6jKNgQg@0xNDMfyC7JXAfIeGOlBbJEm/nCt9sUsqvHckkgw2Z/Zml2hMqs64CVJiqON@N7WcfHmvCNSnxsC9/uGlEA9fcariFbpNffrNeHm/XPm/XfN@tfjzbrf2zW/9ysf9ms/7VZ/3uz/s9m/VvLg3hmNrOxYgTu@iaT1cZdb5QdqJ81/UuJB6uUWT/M1kfFeglzROljvtjkUvhp/@vwy5f/Ag Try it online!]
{{out}}
Solution found result ''(typical output)'':
<pre>┌─────┬─────┬─┬─┐
│ ┌─┐ ├─┐ │ │ │
├─┼─┴─┴─┴─┬─┘ │ │
│ └───┬─┐ │ ┌─┤ │
│ ┌───┼─┼─┴─┘ │ │
├─┘ ┌─┘ └─┐ ┌─┼─┤
│ ┌─┼─┐ ┌─┴─┘ │ │
├─┴─┘ └─┤ ┌───┘ │
└───────┴─┴─────┘</pre>
Impossible to solve result ''(a somewhat rare occurrence)'':
<pre>no solution for this configuration:
┌─┬─┬─┬─┬───────┐
│ └─┘ └─┘ │
│ ┌─┐ │
├─┼─┘ │
├─┘ │
│ │
│ │
│ │
└───────────────┘</pre>
=={{header|C sharp|C#}}==
{{trans|Java}}
<
using System.Linq;
Line 215 ⟶ 532:
static readonly int[][][] shapes = { F, I, L, N, P, T, U, V, W, X, Y, Z };
}
}</
<pre>I N F F - - L L
I N N F F P P L
Line 224 ⟶ 541:
U Y U T Z Z Z V
U U U T Z V V V</pre>
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <algorithm>
#include <cstdint>
#include <iostream>
#include <random>
#include <vector>
const std::vector<std::vector<int32_t>> F = { { 1, -1, 1, 0, 1, 1, 2, 1 }, { 0, 1, 1, -1, 1, 0, 2, 0 },
{ 1, 0, 1, 1, 1, 2, 2, 1 }, { 1, 0, 1, 1, 2, -1, 2, 0 }, { 1, -2, 1, -1, 1, 0, 2, -1 },
{ 0, 1, 1, 1, 1, 2, 2, 1 }, { 1, -1, 1, 0, 1, 1, 2, -1 }, { 1, -1, 1, 0, 2, 0, 2, 1 } };
const std::vector<std::vector<int32_t>> I = { { 0, 1, 0, 2, 0, 3, 0, 4 }, { 1, 0, 2, 0, 3, 0, 4, 0 } };
const std::vector<std::vector<int32_t>> L = { { 1, 0, 1, 1, 1, 2, 1, 3 }, { 1, 0, 2, 0, 3, -1, 3, 0 },
{ 0, 1, 0, 2, 0, 3, 1, 3 }, { 0, 1, 1, 0, 2, 0, 3, 0 }, { 0, 1, 1, 1, 2, 1, 3, 1 },
{ 0, 1, 0, 2, 0, 3, 1, 0 }, { 1, 0, 2, 0, 3, 0, 3, 1 }, { 1, -3, 1, -2, 1, -1, 1, 0 } };
const std::vector<std::vector<int32_t>> N = { { 0, 1, 1, -2, 1, -1, 1, 0 }, { 1, 0, 1, 1, 2, 1, 3, 1 },
{ 0, 1, 0, 2, 1, -1, 1, 0 }, { 1, 0, 2, 0, 2, 1, 3, 1 }, { 0, 1, 1, 1, 1, 2, 1, 3 },
{ 1, 0, 2, -1, 2, 0, 3, -1 }, { 0, 1, 0, 2, 1, 2, 1, 3 }, { 1, -1, 1, 0, 2, -1, 3, -1 } };
const std::vector<std::vector<int32_t>> P = { { 0, 1, 1, 0, 1, 1, 2, 1 }, { 0, 1, 0, 2, 1, 0, 1, 1 },
{ 1, 0, 1, 1, 2, 0, 2, 1 }, { 0, 1, 1, -1, 1, 0, 1, 1 }, { 0, 1, 1, 0, 1, 1, 1, 2 },
{ 1, -1, 1, 0, 2, -1, 2, 0 }, { 0, 1, 0, 2, 1, 1, 1, 2 }, { 0, 1, 1, 0, 1, 1, 2, 0 } };
const std::vector<std::vector<int32_t>> T = { { 0, 1, 0, 2, 1, 1, 2, 1 }, { 1, -2, 1, -1, 1, 0, 2, 0 },
{ 1, 0, 2, -1, 2, 0, 2, 1 }, { 1, 0, 1, 1, 1, 2, 2, 0 } };
const std::vector<std::vector<int32_t>> U = { { 0, 1, 0, 2, 1, 0, 1, 2 }, { 0, 1, 1, 1, 2, 0, 2, 1 },
{ 0, 2, 1, 0, 1, 1, 1, 2 }, { 0, 1, 1, 0, 2, 0, 2, 1 } };
const std::vector<std::vector<int32_t>> V = { { 1, 0, 2, 0, 2, 1, 2, 2 }, { 0, 1, 0, 2, 1, 0, 2, 0 },
{ 1, 0, 2, -2, 2, -1, 2, 0 }, { 0, 1, 0, 2, 1, 2, 2, 2 } };
const std::vector<std::vector<int32_t>> W = { { 1, 0, 1, 1, 2, 1, 2, 2 }, { 1, -1, 1, 0, 2, -2, 2, -1 },
{ 0, 1, 1, 1, 1, 2, 2, 2 }, { 0, 1, 1, -1, 1, 0, 2, -1 } };
const std::vector<std::vector<int32_t>> X = { { 1, -1, 1, 0, 1, 1, 2, 0 } };
const std::vector<std::vector<int32_t>> Y = { { 1, -2, 1, -1, 1, 0, 1, 1 }, { 1, -1, 1, 0, 2, 0, 3, 0 },
{ 0, 1, 0, 2, 0, 3, 1, 1 }, { 1, 0, 2, 0, 2, 1, 3, 0 }, { 0, 1, 0, 2, 0, 3, 1, 2 },
{ 1, 0, 1, 1, 2, 0, 3, 0 }, { 1, -1, 1, 0, 1, 1, 1, 2 }, { 1, 0, 2, -1, 2, 0, 3, 0 } };
const std::vector<std::vector<int32_t>> Z = { { 0, 1, 1, 0, 2, -1, 2, 0 }, { 1, 0, 1, 1, 1, 2, 2, 2 },
{ 0, 1, 1, 1, 2, 1, 2, 2 }, { 1, -2, 1, -1, 1, 0, 2, -2 } };
const int32_t blank_index = 12;
const int32_t nRows = 8;
const int32_t nCols = 8;
std::vector<std::vector<std::vector<int32_t>>> shapes = { F, I, L, N, P, T, U, V, W, X, Y, Z };
std::vector<char> symbols = { 'F', 'I', 'L', 'N', 'P', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '-' };
std::vector<std::vector<int32_t>> grid{nRows, std::vector<int32_t>(nCols, -1)};
std::vector<bool> placed(symbols.size() - 1, false);
std::random_device random;
std::mt19937 generator(random());
std::uniform_real_distribution<double> distribution(0.0F, 1.0F);
void display() {
for ( const std::vector<int32_t>& row : grid ) {
for ( const int32_t& index : row ) {
std::cout << symbols[index] << " ";
}
std::cout << std::endl;
}
}
void shuffle_shapes() {
uint64_t size = shapes.size();
while ( size > 1 ) {
int32_t random = static_cast<int32_t>( distribution(generator) * ( size-- ) );
const std::vector<std::vector<int32_t>> temp = shapes[random];
shapes[random] = shapes[size];
shapes[size] = temp;
const char temp_symbol = symbols[random];
symbols[random] = symbols[size];
symbols[size] = temp_symbol;
}
}
bool place_orientation(const std::vector<int32_t>& orientation,
const int32_t& row, const int32_t& col, const int32_t& shape_index) {
for ( uint64_t i = 0; i < orientation.size(); i += 2 ) {
int32_t x = col + orientation[i + 1];
int32_t y = row + orientation[i];
if ( x < 0 || x >= nCols || y < 0 || y >= nRows || grid[y][x] != -1 ) {
return false;
}
}
grid[row][col] = shape_index;
for ( uint64_t i = 0; i < orientation.size(); i += 2 ) {
grid[row + orientation[i]][col + orientation[i + 1]] = shape_index;
}
return true;
}
void remove_orientation(const std::vector<int32_t>& oorientation, const int32_t& row, const int32_t& col) {
grid[row][col] = -1;
for ( uint64_t i = 0; i < oorientation.size(); i += 2 ) {
grid[row + oorientation[i]][col + oorientation[i + 1]] = -1;
}
}
bool solve(const int32_t& position, const uint64_t& number_placed) {
if ( number_placed == shapes.size() ) {
return true;
}
int32_t row = position / nCols;
int32_t col = position % nCols;
if ( grid[row][col] != -1 ) {
return solve(position + 1, number_placed);
}
for ( uint64_t i = 0; i < shapes.size(); ++i ) {
if ( ! placed[i] ) {
for ( const std::vector<int32_t>& orientation : shapes[i] ) {
if ( ! place_orientation(orientation, row, col, i) ) {
continue;
}
placed[i] = true;
if ( solve(position + 1, number_placed + 1) ) {
return true;
}
remove_orientation(orientation, row, col);
placed[i] = false;
}
}
}
return false;
}
int main() {
shuffle_shapes();
for ( int32_t i = 0; i < 4; ++i ) {
int32_t random_row, random_col;
do {
random_row = static_cast<int32_t>(distribution(generator) * nRows);
random_col = static_cast<int32_t>(distribution(generator) * nCols);
} while ( grid[random_row][random_col] == blank_index );
grid[random_row][random_col] = blank_index;
}
if ( solve(0, 0) ) {
display();
} else {
std::cout << "No solution found" << std::endl;
}
}
</syntaxhighlight>
{{ out }}
<pre>
Y Y Y Y X V V V
U Y U X X X - V
U U U T X W W V
I T T T W W F -
I L Z T W F F F
I L Z Z Z F P P
I L N N Z - P P
I L L N N N - P
</pre>
=={{header|Go}}==
{{trans|Java}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"math/rand"
"time"
)
var F = [][]int{
{1, -1, 1, 0, 1, 1, 2, 1}, {0, 1, 1, -1, 1, 0, 2, 0},
{1, 0, 1, 1, 1, 2, 2, 1}, {1, 0, 1, 1, 2, -1, 2, 0},
{1, -2, 1, -1, 1, 0, 2, -1}, {0, 1, 1, 1, 1, 2, 2, 1},
{1, -1, 1, 0, 1, 1, 2, -1}, {1, -1, 1, 0, 2, 0, 2, 1},
}
var I = [][]int{{0, 1, 0, 2, 0, 3, 0, 4}, {1, 0, 2, 0, 3, 0, 4, 0}}
var L = [][]int{
{1, 0, 1, 1, 1, 2, 1, 3}, {1, 0, 2, 0, 3, -1, 3, 0},
{0, 1, 0, 2, 0, 3, 1, 3}, {0, 1, 1, 0, 2, 0, 3, 0}, {0, 1, 1, 1, 2, 1, 3, 1},
{0, 1, 0, 2, 0, 3, 1, 0}, {1, 0, 2, 0, 3, 0, 3, 1}, {1, -3, 1, -2, 1, -1, 1, 0},
}
var N = [][]int{
{0, 1, 1, -2, 1, -1, 1, 0}, {1, 0, 1, 1, 2, 1, 3, 1},
{0, 1, 0, 2, 1, -1, 1, 0}, {1, 0, 2, 0, 2, 1, 3, 1}, {0, 1, 1, 1, 1, 2, 1, 3},
{1, 0, 2, -1, 2, 0, 3, -1}, {0, 1, 0, 2, 1, 2, 1, 3}, {1, -1, 1, 0, 2, -1, 3, -1},
}
var P = [][]int{
{0, 1, 1, 0, 1, 1, 2, 1}, {0, 1, 0, 2, 1, 0, 1, 1},
{1, 0, 1, 1, 2, 0, 2, 1}, {0, 1, 1, -1, 1, 0, 1, 1}, {0, 1, 1, 0, 1, 1, 1, 2},
{1, -1, 1, 0, 2, -1, 2, 0}, {0, 1, 0, 2, 1, 1, 1, 2}, {0, 1, 1, 0, 1, 1, 2, 0},
}
var T = [][]int{
{0, 1, 0, 2, 1, 1, 2, 1}, {1, -2, 1, -1, 1, 0, 2, 0},
{1, 0, 2, -1, 2, 0, 2, 1}, {1, 0, 1, 1, 1, 2, 2, 0},
}
var U = [][]int{
{0, 1, 0, 2, 1, 0, 1, 2}, {0, 1, 1, 1, 2, 0, 2, 1},
{0, 2, 1, 0, 1, 1, 1, 2}, {0, 1, 1, 0, 2, 0, 2, 1},
}
var V = [][]int{
{1, 0, 2, 0, 2, 1, 2, 2}, {0, 1, 0, 2, 1, 0, 2, 0},
{1, 0, 2, -2, 2, -1, 2, 0}, {0, 1, 0, 2, 1, 2, 2, 2},
}
var W = [][]int{
{1, 0, 1, 1, 2, 1, 2, 2}, {1, -1, 1, 0, 2, -2, 2, -1},
{0, 1, 1, 1, 1, 2, 2, 2}, {0, 1, 1, -1, 1, 0, 2, -1},
}
var X = [][]int{{1, -1, 1, 0, 1, 1, 2, 0}}
var Y = [][]int{
{1, -2, 1, -1, 1, 0, 1, 1}, {1, -1, 1, 0, 2, 0, 3, 0},
{0, 1, 0, 2, 0, 3, 1, 1}, {1, 0, 2, 0, 2, 1, 3, 0}, {0, 1, 0, 2, 0, 3, 1, 2},
{1, 0, 1, 1, 2, 0, 3, 0}, {1, -1, 1, 0, 1, 1, 1, 2}, {1, 0, 2, -1, 2, 0, 3, 0},
}
var Z = [][]int{
{0, 1, 1, 0, 2, -1, 2, 0}, {1, 0, 1, 1, 1, 2, 2, 2},
{0, 1, 1, 1, 2, 1, 2, 2}, {1, -2, 1, -1, 1, 0, 2, -2},
}
var shapes = [][][]int{F, I, L, N, P, T, U, V, W, X, Y, Z}
var symbols = []byte("FILNPTUVWXYZ-")
const (
nRows = 8
nCols = 8
blank = 12
)
var grid [nRows][nCols]int
var placed [12]bool
func tryPlaceOrientation(o []int, r, c, shapeIndex int) bool {
for i := 0; i < len(o); i += 2 {
x := c + o[i+1]
y := r + o[i]
if x < 0 || x >= nCols || y < 0 || y >= nRows || grid[y][x] != -1 {
return false
}
}
grid[r][c] = shapeIndex
for i := 0; i < len(o); i += 2 {
grid[r+o[i]][c+o[i+1]] = shapeIndex
}
return true
}
func removeOrientation(o []int, r, c int) {
grid[r][c] = -1
for i := 0; i < len(o); i += 2 {
grid[r+o[i]][c+o[i+1]] = -1
}
}
func solve(pos, numPlaced int) bool {
if numPlaced == len(shapes) {
return true
}
row := pos / nCols
col := pos % nCols
if grid[row][col] != -1 {
return solve(pos+1, numPlaced)
}
for i := range shapes {
if !placed[i] {
for _, orientation := range shapes[i] {
if !tryPlaceOrientation(orientation, row, col, i) {
continue
}
placed[i] = true
if solve(pos+1, numPlaced+1) {
return true
}
removeOrientation(orientation, row, col)
placed[i] = false
}
}
}
return false
}
func shuffleShapes() {
rand.Shuffle(len(shapes), func(i, j int) {
shapes[i], shapes[j] = shapes[j], shapes[i]
symbols[i], symbols[j] = symbols[j], symbols[i]
})
}
func printResult() {
for _, r := range grid {
for _, i := range r {
fmt.Printf("%c ", symbols[i])
}
fmt.Println()
}
}
func main() {
rand.Seed(time.Now().UnixNano())
shuffleShapes()
for r := 0; r < nRows; r++ {
for i := range grid[r] {
grid[r][i] = -1
}
}
for i := 0; i < 4; i++ {
var randRow, randCol int
for {
randRow = rand.Intn(nRows)
randCol = rand.Intn(nCols)
if grid[randRow][randCol] != blank {
break
}
}
grid[randRow][randCol] = blank
}
if solve(0, 0) {
printResult()
} else {
fmt.Println("No solution")
}
}</syntaxhighlight>
{{out}}
Sample output:
<pre>
Z I I I I I - Y
Z Z Z V - F Y Y
U U Z V - F F Y
U V V V F F X Y
U U P P W X X X
T P P P W W X -
T T T N N W W L
T N N N L L L L
</pre>
=={{header|Java}}==
<
import java.util.*;
Line 379 ⟶ 1,058:
static final int[][][] shapes = {F, I, L, N, P, T, U, V, W, X, Y, Z};
}</
<pre>F I I I I I L L
Line 389 ⟶ 1,068:
U X U W Y T T T
U U U Y Y Y Y T </pre>
=={{header|Julia}}==
{{trans|Zkl}}
<syntaxhighlight lang="julia">using Random
struct GridPoint x::Int; y::Int end
const nrows, ncols, target = 8, 8, 12
const grid = fill('*', nrows, ncols)
const shapeletters = ['F', 'I', 'L', 'N', 'P', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']
const shapevec = [
[(1,-1, 1,0, 1,1, 2,1), (0,1, 1,-1, 1,0, 2,0),
(1,0 , 1,1, 1,2, 2,1), (1,0, 1,1, 2,-1, 2,0), (1,-2, 1,-1, 1,0, 2,-1),
(0,1, 1,1, 1,2, 2,1), (1,-1, 1,0, 1,1, 2,-1), (1,-1, 1,0, 2,0, 2,1)],
[(0,1, 0,2, 0,3, 0,4), (1,0, 2,0, 3,0, 4,0)],
[(1,0, 1,1, 1,2, 1,3), (1,0, 2,0, 3,-1, 3,0),
(0,1, 0,2, 0,3, 1,3), (0,1, 1,0, 2,0, 3,0), (0,1, 1,1, 2,1, 3,1),
(0,1, 0,2, 0,3, 1,0), (1,0, 2,0, 3,0, 3,1), (1,-3, 1,-2, 1,-1, 1,0)],
[(0,1, 1,-2, 1,-1, 1,0), (1,0, 1,1, 2,1, 3,1),
(0,1, 0,2, 1,-1, 1,0), (1,0, 2,0, 2,1, 3,1), (0,1, 1,1, 1,2, 1,3),
(1,0, 2,-1, 2,0, 3,-1), (0,1, 0,2, 1,2, 1,3), (1,-1, 1,0, 2,-1, 3,-1)],
[(0,1, 1,0, 1,1, 2,1), (0,1, 0,2, 1,0, 1,1),
(1,0, 1,1, 2,0, 2,1), (0,1, 1,-1, 1,0, 1,1), (0,1, 1,0, 1,1, 1,2),
(1,-1, 1,0, 2,-1, 2,0), (0,1, 0,2, 1,1, 1,2), (0,1, 1,0, 1,1, 2,0)],
[(0,1, 0,2, 1,1, 2,1), (1,-2, 1,-1, 1,0, 2,0),
(1,0, 2,-1, 2,0, 2,1), (1,0, 1,1, 1,2, 2,0)],
[(0,1, 0,2, 1,0, 1,2), (0,1, 1,1, 2,0, 2,1),
(0,2, 1,0, 1,1, 1,2), (0,1, 1,0, 2,0, 2,1)],
[(1,0, 2,0, 2,1, 2,2), (0,1, 0,2, 1,0, 2,0),
(1,0, 2,-2, 2,-1, 2,0), (0,1, 0,2, 1,2, 2,2)],
[(1,0, 1,1, 2,1, 2,2), (1,-1, 1,0, 2,-2, 2,-1),
(0,1, 1,1, 1,2, 2,2), (0,1, 1,-1, 1,0, 2,-1)],
[(1,-1, 1,0, 1,1, 2,0)],
[(1,-2, 1,-1, 1,0, 1,1), (1,-1, 1,0, 2,0, 3,0),
(0,1, 0,2, 0,3, 1,1), (1,0, 2,0, 2,1, 3,0), (0,1, 0,2, 0,3, 1,2),
(1,0, 1,1, 2,0, 3,0), (1,-1, 1,0, 1,1, 1,2), (1,0, 2,-1, 2,0, 3,0)],
[(0,1, 1,0, 2,-1, 2,0), (1,0, 1,1, 1,2, 2,2),
(0,1, 1,1, 2,1, 2,2), (1,-2, 1,-1, 1,0, 2,-2)]]
const shapes = Dict{Char,Vector{Vector{GridPoint}}}()
const placed = Dict{Char,Bool}()
for (ltr, vec) in zip(shapeletters, shapevec)
shapes[ltr] = [[GridPoint(v[i], v[i + 1]) for i in 1:2:7] for v in vec]
placed[ltr] = false
end
printgrid(m, w, h) = for x in 1:w for y in 1:h print(m[x, y], " ") end; println() end
function tryplaceorientation(o, R, C, shapeindex)
for p in o
r, c = R + p.x, C + p.y
if r < 1 || r > nrows || c < 1 || c > ncols || grid[r, c] != '*'
return false
end
end
grid[R, C] = shapeindex
for p in o
grid[R + p.x, C + p.y] = shapeindex
end
true
end
function removeorientation(o, r, c)
grid[r, c] = '*'
for p in o
grid[r + p.x, c + p.y] = '*'
end
end
function solve(pos, nplaced)
if nplaced == target
return true
end
row, col = divrem(pos, ncols) .+ 1
if grid[row, col] != '*'
return solve(pos + 1, nplaced)
end
for i in keys((shapes))
if !placed[i]
for orientation in shapes[i]
if tryplaceorientation(orientation, row, col, i)
placed[i] = true
if solve(pos + 1, nplaced + 1)
return true
else
removeorientation(orientation, row, col)
placed[i] = false
end
end
end
end
end
false
end
function placepentominoes()
for p in zip(shuffle(collect(1:nrows))[1:4], shuffle(collect(1:ncols))[1:4])
grid[p[1], p[2]] = ' '
end
if solve(0, 0)
printgrid(grid, nrows, ncols)
else
println("No solution found.")
end
end
placepentominoes()
</syntaxhighlight>{{out}}
<pre>
Z Z X P P P V
I Z X X X P P V
I Z Z X L V V V
I T T T L L L L
I N T F F U U
I N T W F F U
N N W W F Y U U
N W W Y Y Y Y
</pre>
=={{header|Kotlin}}==
{{trans|Java}}
<
import java.util.Random
val F = arrayOf(
intArrayOf(1, -1, 1, 0, 1, 1, 2, 1), intArrayOf(0, 1, 1, -1, 1, 0, 2, 0),
Line 410 ⟶ 1,206:
val L = arrayOf(
intArrayOf(1, 0, 1, 1, 1, 2, 1, 3), intArrayOf(1, 0, 2, 0, 3, -1, 3, 0),
intArrayOf(0, 1, 0, 2, 0, 3, 1, 3), intArrayOf(0, 1, 1, 0, 2, 0, 3, 0),
intArrayOf(0, 1, 1, 1, 2, 1, 3, 1), intArrayOf(0, 1, 0, 2, 0, 3, 1, 0),
intArrayOf(1, 0, 2, 0, 3, 0, 3, 1), intArrayOf(1, -3, 1, -2, 1, -1, 1, 0)
)
val N = arrayOf(
Line 433 ⟶ 1,229:
intArrayOf(1, 0, 2, -1, 2, 0, 2, 1), intArrayOf(1, 0, 1, 1, 1, 2, 2, 0)
)
val U = arrayOf(
intArrayOf(0, 1, 0, 2, 1, 0, 1, 2), intArrayOf(0, 1, 1, 1, 2, 0, 2, 1),
Line 453 ⟶ 1,249:
val Y = arrayOf(
intArrayOf(1, -2, 1, -1, 1, 0, 1, 1), intArrayOf(1, -1, 1, 0, 2, 0, 3, 0),
intArrayOf(0, 1, 0, 2, 0, 3, 1, 1), intArrayOf(1, 0, 2, 0, 2, 1, 3, 0),
intArrayOf(0, 1, 0, 2, 0, 3, 1, 2), intArrayOf(1, 0, 1, 1, 2, 0, 3, 0),
intArrayOf(1, -1, 1, 0, 1, 1, 1, 2), intArrayOf(1, 0, 2, -1, 2, 0, 3, 0)
)
val Z = arrayOf(
Line 464 ⟶ 1,260:
val shapes = arrayOf(F, I, L, N, P, T, U, V, W, X, Y, Z)
val rand = Random()
val symbols = "FILNPTUVWXYZ-".toCharArray()
val nRows = 8
val nCols = 8
val blank = 12
val grid = Array(nRows) { IntArray(nCols) }
val placed = BooleanArray(
fun tryPlaceOrientation(o: IntArray, r: Int, c: Int, shapeIndex: Int): Boolean {
Line 492 ⟶ 1,288:
fun solve(pos: Int, numPlaced: Int): Boolean {
if (numPlaced ==
val row = pos / nCols
val col = pos % nCols
Line 509 ⟶ 1,305:
}
return false
}
fun shuffleShapes() {
var n = shapes.size
while (n > 1) {
val r = rand.nextInt(n--)
val tmp = shapes[r]
shapes[r] = shapes[n]
shapes[n] = tmp
val tmpSymbol= symbols[r]
symbols[r] = symbols[n]
symbols[n] = tmpSymbol
}
}
fun printResult() {
for (r in grid) {
for (i in r) print("${symbols[i]} ")
println()
}
Line 522 ⟶ 1,328:
fun main(args: Array<String>) {
for (r in 0 until nRows) grid[r].fill(-1)
for (i in 0..3)
var randRow: Int
var randCol: Int
do {
randRow = rand.nextInt(nRows)
randCol = rand.nextInt(nCols)
}
while (grid[randRow][randCol] == blank)
grid[randRow][randCol] = blank
}
if (solve(0, 0)) printResult()
else println("No solution")
}</
Sample output:
Line 539 ⟶ 1,354:
P P X X X Y Z -
P P P X Y Y Y Y
</pre>
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">import random, sequtils, strutils
const
F = @[[1, -1, 1, 0, 1, 1, 2, 1], [0, 1, 1, -1, 1, 0, 2, 0],
[1, 0, 1, 1, 1, 2, 2, 1], [1, 0, 1, 1, 2, -1, 2, 0],
[1, -2, 1, -1, 1, 0, 2, -1], [0, 1, 1, 1, 1, 2, 2, 1],
[1, -1, 1, 0, 1, 1, 2, -1], [1, -1, 1, 0, 2, 0, 2, 1]]
I = @[[0, 1, 0, 2, 0, 3, 0, 4], [1, 0, 2, 0, 3, 0, 4, 0]]
L = @[[1, 0, 1, 1, 1, 2, 1, 3], [1, 0, 2, 0, 3, -1, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 3], [0, 1, 1, 0, 2, 0, 3, 0],
[0, 1, 1, 1, 2, 1, 3, 1], [0, 1, 0, 2, 0, 3, 1, 0],
[1, 0, 2, 0, 3, 0, 3, 1], [1, -3, 1, -2, 1, -1, 1, 0]]
N = @[[0, 1, 1, -2, 1, -1, 1, 0], [1, 0, 1, 1, 2, 1, 3, 1],
[0, 1, 0, 2, 1, -1, 1, 0], [1, 0, 2, 0, 2, 1, 3, 1],
[0, 1, 1, 1, 1, 2, 1, 3], [1, 0, 2, -1, 2, 0, 3, -1],
[0, 1, 0, 2, 1, 2, 1, 3], [1, -1, 1, 0, 2, -1, 3, -1]]
P = @[[0, 1, 1, 0, 1, 1, 2, 1], [0, 1, 0, 2, 1, 0, 1, 1],
[1, 0, 1, 1, 2, 0, 2, 1], [0, 1, 1, -1, 1, 0, 1, 1],
[0, 1, 1, 0, 1, 1, 1, 2], [1, -1, 1, 0, 2, -1, 2, 0],
[0, 1, 0, 2, 1, 1, 1, 2], [0, 1, 1, 0, 1, 1, 2, 0]]
T = @[[0, 1, 0, 2, 1, 1, 2, 1], [1, -2, 1, -1, 1, 0, 2, 0],
[1, 0, 2, -1, 2, 0, 2, 1], [1, 0, 1, 1, 1, 2, 2, 0]]
U = @[[0, 1, 0, 2, 1, 0, 1, 2], [0, 1, 1, 1, 2, 0, 2, 1],
[0, 2, 1, 0, 1, 1, 1, 2], [0, 1, 1, 0, 2, 0, 2, 1]]
V = @[[1, 0, 2, 0, 2, 1, 2, 2], [0, 1, 0, 2, 1, 0, 2, 0],
[1, 0, 2, -2, 2, -1, 2, 0], [0, 1, 0, 2, 1, 2, 2, 2]]
W = @[[1, 0, 1, 1, 2, 1, 2, 2], [1, -1, 1, 0, 2, -2, 2, -1],
[0, 1, 1, 1, 1, 2, 2, 2], [0, 1, 1, -1, 1, 0, 2, -1]]
X = @[[1, -1, 1, 0, 1, 1, 2, 0]]
Y = @[[1, -2, 1, -1, 1, 0, 1, 1], [1, -1, 1, 0, 2, 0, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 1], [1, 0, 2, 0, 2, 1, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 2], [1, 0, 1, 1, 2, 0, 3, 0],
[1, -1, 1, 0, 1, 1, 1, 2], [1, 0, 2, -1, 2, 0, 3, 0]]
Z = @[[0, 1, 1, 0, 2, -1, 2, 0], [1, 0, 1, 1, 1, 2, 2, 2],
[0, 1, 1, 1, 2, 1, 2, 2], [1, -2, 1, -1, 1, 0, 2, -2]]
Shapes = [F, I, L, N, P, T, U, V, W, X, Y, Z]
Symbols = @"FILNPTUVWXYZ-"
NRows = 8
NCols = 8
Blank = Shapes.len
type Tiling = object
shapes: array[Shapes.len, seq[array[8, int]]] # Shuffled shapes.
symbols: array[Symbols.len, char] # Associated symbols.
grid: array[NRows, array[NCols, int]]
placed: array[Shapes.len, bool]
proc initTiling(): Tiling =
# Build list of shapes and symbols.
var indexes = toSeq(0..11)
indexes.shuffle()
for i, index in indexes:
result.shapes[i] = Shapes[index]
result.symbols[i] = Symbols[index]
result.symbols[^1] = Symbols[^1]
# Fill grid.
for r in result.grid.mitems:
for c in r.mitems:
c = -1
for i in 0..3:
while true:
let randRow = rand(NRows - 1)
let randCol = rand(NCols - 1)
if result.grid[randRow][randCol] != Blank:
result.grid[randRow][randCol] = Blank
break
func tryPlaceOrientation(t: var Tiling; o: openArray[int]; r, c, shapeIndex: int): bool =
for i in countup(0, o.len - 2, 2):
let x = c + o[i + 1]
let y = r + o[i]
if x notin 0..<NCols or y notin 0..<NRows or t.grid[y][x] != - 1: return false
t.grid[r][c] = shapeIndex
for i in countup(0, o.len - 2, 2): t.grid[r + o[i]][c + o[i + 1]] = shapeIndex
result = true
func removeOrientation(t: var Tiling; o: openArray[int]; r, c: int) =
t.grid[r][c] = -1
for i in countup(0, o.len - 2, 2): t.grid[r + o[i]][c + o[i + 1]] = -1
func solve(t: var Tiling; pos, numPlaced: int): bool =
if numPlaced == t.shapes.len: return true
let row = pos div NCols
let col = pos mod NCols
if t.grid[row][col] != -1: return t.solve(pos + 1, numPlaced)
for i in 0..<t.shapes.len:
if not t.placed[i]:
for orientation in t.shapes[i]:
if not t.tryPlaceOrientation(orientation, row, col, i): continue
t.placed[i] = true
if t.solve(pos + 1, numPlaced + 1): return true
t.removeOrientation(orientation, row, col)
t.placed[i] = false
proc printResult(t: Tiling) =
for r in t.grid:
echo r.mapIt(t.symbols[it]).join(" ")
when isMainModule:
randomize()
var tiling = initTiling()
if tiling.solve(0, 0): tiling.printResult
else: echo "No solution"</syntaxhighlight>
{{out}}
<pre>T T T F - P P P
Y T F F F X P P
Y T F W X X X -
Y Y W W U X U I
Y W W Z U U U I
- Z Z Z N N V I
L Z N N N - V I
L L L L V V V I</pre>
=={{header|Perl}}==
Generates one tiling at random. To generate more during one run, change the "exit" to "return".
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'bitwise';
my $size = shift // 8;
sub rotate
{
local $_ = shift;
my $ans = '';
$ans .= "\n" while s/.$/$ans .= $&; ''/gem;
$ans;
}
sub topattern
{
local $_ = shift;
s/.+/ $& . ' ' x ($size - length $&)/ge;
s/^\s+|\s+\z//g;
[ tr/ \nA-Z/.. /r, lc tr/ \n/\0/r, substr $_, 0, 1 ]; # pattern, xor-update
}
my %all;
@all{ " FF\nFF \n F \n", "IIIII\n", "LLLL\nL \n", "NNN \n NN\n",
"PPP\nPP \n", "TTT\n T \n T \n", "UUU\nU U\n", "VVV\nV \nV \n",
"WW \n WW\n W\n", " X \nXXX\n X \n", "YYYY\n Y \n", "ZZ \n Z \n ZZ\n",
} = ();
@all{map rotate($_), keys %all} = () for 1 .. 3; # all four rotations
@all{map s/.+/reverse $&/ger, keys %all} = (); # mirror
my @all = map topattern($_), keys %all;
my $grid = ( ' ' x $size . "\n" ) x $size;
my %used;
find( $grid );
# looks for the first open space
sub find
{
my $grid = shift;
%used >= 12 and exit not print $grid;
for ( grep ! $used{ $_->[2] }, @all )
{
my ($pattern, $pentomino, $letter) = @$_;
local $used{$letter} = 1;
$grid =~ /^[^ ]*\K$pattern/s and find( $grid ^. "\0" x $-[0] . $pentomino );
}
}</syntaxhighlight>
{{out}}
<pre>
FNNNTTTP
FFFNNTPP
IFUUZTPP
ILLUZZZY
ILUUWWZY
ILVWWXYY
ILVWXXXY
VVVX
</pre>
=={{header|Phix}}==
Apart from the shape table creation, the solving part is a translation of Go.<br>
I also added a fast unsolveable() check routine, not that it desperately needed it.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">pentominoes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"""
......I................................................................
......I.....L......N.........................................Y.........
.FF...I.....L.....NN....PP....TTT...........V.....W....X....YY.....ZZ..
FF....I.....L.....N.....PP.....T....U.U.....V....WW...XXX....Y.....Z...
.F....I.....LL....N.....P......T....UUU...VVV...WW.....X.....Y....ZZ..."""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'\n'</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- </span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_shapes</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">offset</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pentominoes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">by</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">--
-- scan left/right, and up/down, both ways, to give 8 orientations
-- (computes the equivalent of those hard-coded tables in
-- other examples, albeit in a slightly different order.)
--</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">shapes</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">letter</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">orientation</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">7</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">shape</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">found</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">fr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fc</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">rr</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orientation</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#01</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">6</span><span style="color: #0000FF;">-</span><span style="color: #000000;">r</span><span style="color: #0000FF;">:</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">cc</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orientation</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#02</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">6</span><span style="color: #0000FF;">-</span><span style="color: #000000;">c</span><span style="color: #0000FF;">:</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orientation</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#04</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cc</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">cc</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pentominoes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">offset</span><span style="color: #0000FF;">+</span><span style="color: #000000;">cc</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">'.'</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">found</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">found</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fc</span><span style="color: #0000FF;">,</span><span style="color: #000000;">letter</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">shape</span> <span style="color: #0000FF;">&=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">fr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">fc</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shape</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">shapes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shape</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">letter</span><span style="color: #0000FF;">&</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">shapes</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_shapes</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">nRows</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">nCols</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">8</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">grid</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nCols</span><span style="color: #0000FF;">),</span><span style="color: #000000;">nRows</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">placed</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">re_place</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">can_place</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">></span><span style="color: #000000;">nCols</span>
<span style="color: #008080;">or</span> <span style="color: #000000;">y</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">></span><span style="color: #000000;">nRows</span>
<span style="color: #008080;">or</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">][</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">re_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">pos</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">numPlaced</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">numPlaced</span> <span style="color: #0000FF;">==</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">/</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">col</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">numPlaced</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">placed</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">can_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">placed</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">numPlaced</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">re_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">placed</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">unsolveable</span><span style="color: #0000FF;">()</span>
<span style="color: #000080;font-style:italic;">--
-- The only unsolvable grids seen have
-- -.- or -..- or -... at edge/corner,
-- - -- --- -
-- or somewhere in the middle a -.-
-- -
--
-- Simply place all shapes at all positions/orientations,
-- all the while checking for any untouchable cells.
--</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">griddled</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">can_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">' '</span>
<span style="color: #000000;">griddled</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">' '</span>
<span style="color: #000000;">griddled</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">griddled</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">'-'</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">true</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">add_four_randomly</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><</span><span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rand</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rand</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">add_four_randomly</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">unsolveable</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"No solution\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
FFPPPVVV
YFFPPX-V
YFUUXXXV
YYU-ZX-I
YTUUZZZI
-TTTWWZI
LTNNNWWI
LLLLNNWI
</pre>
=={{header|Picat}}==
<syntaxhighlight lang="picat">
import sat, util.
rotate(Q) = Res => % rotate right by 90 degrees
NZ = len(Q[1]), NS = len(Q), Res = new_array(NZ,NS),
foreach(Z in 1..NZ, S in 1..NS) Res[Z,S] = Q[S,NZ+1-Z] end.
matprint(Q) =>
NZ = len(Q), NS = len(Q[1]),
foreach(Z in 1..NZ, S in 1..NS)
printf("%d|", Q[Z,S]),
if S=NS then nl end
end, nl.
generate(Res) =>
P0 = [{{1,1,1,1}, % L
{1,0,0,0}},
{{0,1,1,1}, % N
{1,1,0,0}},
{{1,1,1,1}, % Y
{0,1,0,0}},
{{1,1,0}, % F
{0,1,1},
{0,1,0}},
{{1,1,1}, % T
{0,1,0},
{0,1,0}},
{{0,0,1}, % W
{0,1,1},
{1,1,0}},
{{1,1,1}, % P
{1,1,0}},
{{0,0,1}, % V
{0,0,1},
{1,1,1}},
{{1,0,1}, % U
{1,1,1}},
{{1,0,0}, % Z
{1,1,1},
{0,0,1}},
{{1,1,1,1,1}}, % I
{{0,1,0}, % X
{1,1,1},
{0,1,0}}],
Np = len(P0), P = [],
foreach(I in 1..Np)
VarI = [P0[I]],
foreach(_ in 1..3) VarI := [rotate(head(VarI))|VarI] end,
P := [VarI|P]
end,
Res = P.
main =>
N = 8, M = new_array(N+4,N+4),
foreach(R in N+1..N+4, C in 1..N) M[R,C] #= 0 end,
foreach(R in 1..N, C in N+1..N+4) M[R,C] #= 0 end,
generate(P), % P[1] = X-Pentomino, then P[2] = I, P[3] = Z, and so on U, V, P, X, W, T, F, Y, N, L
Np = len(P), M :: 0..Np,
foreach(I in 1..Np) count(I, vars(M), 5) end, % 12 pentomino
Idx = new_list(Np), % X has 1 rotation variant, I and Z each 2, the rest 4:
Idx[1] #= 1, [Idx[2],Idx[3]] :: 1..2, Idx :: 1..4,
DZ = new_list(Np), DZ :: 0..N-1, % translation of I.th pentomino
DS = new_list(Np), DS :: 0..N-1,
foreach(I in 1..Np, J in 1..4) % Constraint only if Idx[I] #= J!
NZ = len(P[I,J]), NS = len(P[I,J,1]),
foreach(DZI in 0..N-1, DSI in 0..N-1, Z in 1..NZ, S in 1..NS, P[I,J,Z,S]=1)
(Idx[I] #= J #/\ DZ[I] #= DZI #/\ DS[I] #= DSI) #=> M[DZI+Z,DSI+S] #= I
end
end,
solve(vars(M) ++ DZ ++ DS ++ Idx),
Chr = " XIZUVPWTFYNL",
foreach(Z in 1..N)
foreach(S in 1..N)
printf("%c|", Chr[1 + M[Z,S]])
end, nl
end.
</syntaxhighlight>
Output:
<pre>Y|Y|Y|Y|P|P|Z|Z|
L|Y|X|P|P|P|Z|I|
L|X|X|X|F|Z|Z|I|
L| |X|F|F|U|U|I|
L|L|T|W|F|F|U|I|
V| |T|W|W|U|U|I|
V|T|T|T|W|W|N|N|
V|V|V| |N|N|N| |</pre>
=={{header|Racket}}==
{{trans|Java}}
(although purely functional, so no need to undo the tiling attempts)
<syntaxhighlight lang="racket">#lang racket
(require racket/hash)
(module+ main (Pentomino-tiling))
(define n-rows 8)
(define n-cols 8)
(define blank '-)
(define (build-grid)
(for/fold ((grid (for*/hash ((r n-rows) (c n-cols)) (values (cons r c) #f)))) ((_ 4))
(hash-set grid (cons (random n-rows) (random n-cols)) blank)))
(define (make-shapes-map)
(hash 'F (F) 'I (I) 'L (L) 'N (N) 'P (P) 'T (T) 'U (U) 'V (V) 'W (W) 'X (X) 'Y (Y) 'Z (Z)))
(define (print-grid grid)
(for ((r n-rows) #:when (when (positive? r) (newline)) (c n-cols))
(write (hash-ref grid (cons r c))))
(newline))
(define (Pentomino-tiling (grid (build-grid)))
(define solution (solve 0 grid (make-shapes-map)))
(if solution (print-grid solution) (displayln "no solution")))
(define (solve p grid shapes (failed-shapes (hash)))
(define-values (r c) (quotient/remainder p n-cols))
(cond [(not grid) #f]
[(hash-empty? shapes) (and (hash-empty? failed-shapes) grid)]
[(hash-ref grid (cons r c) #f) (solve (add1 p) grid shapes failed-shapes)]
[else
(define s (car (hash-keys shapes)))
(define os (hash-ref shapes s))
(define shapes-s (hash-remove shapes s))
(define (try-place-orientation o)
(and (for/and ((dy.dx o))
(let ((y (+ r (car dy.dx))) (x (+ c (cdr dy.dx))))
(and (>= x 0) (>= y 0) (< x n-cols) (< y n-rows) (not (hash-ref grid (cons y x))))))
(for/fold ((grid (hash-set grid (cons r c) s))) ((dy.dx o))
(hash-set grid (cons (+ r (car dy.dx)) (+ c (cdr dy.dx))) s))))
(or (for*/first
((o os)
(solution (in-value (solve (add1 p)
(try-place-orientation o)
(hash-union shapes-s failed-shapes))))
#:when solution)
solution)
(solve p grid shapes-s (hash-set failed-shapes s os)))]))
(define (F) '(((1 . -1) (1 . 0) (1 . 1) (2 . 1))
((0 . 1) (1 . -1) (1 . 0) (2 . 0))
((1 . 0) (1 . 1) (1 . 2) (2 . 1))
((1 . 0) (1 . 1) (2 . -1) (2 . 0))
((1 . -2) (1 . -1) (1 . 0) (2 . -1))
((0 . 1) (1 . 1) (1 . 2) (2 . 1))
((1 . -1) (1 . 0) (1 . 1) (2 . -1))
((1 . -1) (1 . 0) (2 . 0) (2 . 1))))
(define (I) '(((0 . 1) (0 . 2) (0 . 3) (0 . 4))
((1 . 0) (2 . 0) (3 . 0) (4 . 0))))
(define (L) '(((1 . 0) (1 . 1) (1 . 2) (1 . 3))
((1 . 0) (2 . 0) (3 . -1) (3 . 0))
((0 . 1) (0 . 2) (0 . 3) (1 . 3))
((0 . 1) (1 . 0) (2 . 0) (3 . 0))
((0 . 1) (1 . 1) (2 . 1) (3 . 1))
((0 . 1) (0 . 2) (0 . 3) (1 . 0))
((1 . 0) (2 . 0) (3 . 0) (3 . 1))
((1 . -3) (1 . -2) (1 . -1) (1 . 0))))
(define (N) '(((0 . 1) (1 . -2) (1 . -1) (1 . 0))
((1 . 0) (1 . 1) (2 . 1) (3 . 1))
((0 . 1) (0 . 2) (1 . -1) (1 . 0))
((1 . 0) (2 . 0) (2 . 1) (3 . 1))
((0 . 1) (1 . 1) (1 . 2) (1 . 3))
((1 . 0) (2 . -1) (2 . 0) (3 . -1))
((0 . 1) (0 . 2) (1 . 2) (1 . 3))
((1 . -1) (1 . 0) (2 . -1) (3 . -1))))
(define (P) '(((0 . 1) (1 . 0) (1 . 1) (2 . 1))
((0 . 1) (0 . 2) (1 . 0) (1 . 1))
((1 . 0) (1 . 1) (2 . 0) (2 . 1))
((0 . 1) (1 . -1) (1 . 0) (1 . 1))
((0 . 1) (1 . 0) (1 . 1) (1 . 2))
((1 . -1) (1 . 0) (2 . -1) (2 . 0))
((0 . 1) (0 . 2) (1 . 1) (1 . 2))
((0 . 1) (1 . 0) (1 . 1) (2 . 0))))
(define (T) '(((0 . 1) (0 . 2) (1 . 1) (2 . 1))
((1 . -2) (1 . -1) (1 . 0) (2 . 0))
((1 . 0) (2 . -1) (2 . 0) (2 . 1))
((1 . 0) (1 . 1) (1 . 2) (2 . 0))))
(define (U) '(((0 . 1) (0 . 2) (1 . 0) (1 . 2))
((0 . 1) (1 . 1) (2 . 0) (2 . 1))
((0 . 2) (1 . 0) (1 . 1) (1 . 2))
((0 . 1) (1 . 0) (2 . 0) (2 . 1))))
(define (V) '(((1 . 0) (2 . 0) (2 . 1) (2 . 2))
((0 . 1) (0 . 2) (1 . 0) (2 . 0))
((1 . 0) (2 . -2) (2 . -1) (2 . 0))
((0 . 1) (0 . 2) (1 . 2) (2 . 2))))
(define (W) '(((1 . 0) (1 . 1) (2 . 1) (2 . 2))
((1 . -1) (1 . 0) (2 . -2) (2 . -1))
((0 . 1) (1 . 1) (1 . 2) (2 . 2))
((0 . 1) (1 . -1) (1 . 0) (2 . -1))))
(define (X) '(((1 . -1) (1 . 0) (1 . 1) (2 . 0))))
(define (Y) '(((1 . -2) (1 . -1) (1 . 0) (1 . 1))
((1 . -1) (1 . 0) (2 . 0) (3 . 0))
((0 . 1) (0 . 2) (0 . 3) (1 . 1))
((1 . 0) (2 . 0) (2 . 1) (3 . 0))
((0 . 1) (0 . 2) (0 . 3) (1 . 2))
((1 . 0) (1 . 1) (2 . 0) (3 . 0))
((1 . -1) (1 . 0) (1 . 1) (1 . 2))
((1 . 0) (2 . -1) (2 . 0) (3 . 0))))
(define (Z) '(((0 . 1) (1 . 0) (2 . -1) (2 . 0))
((1 . 0) (1 . 1) (1 . 2) (2 . 2))
((0 . 1) (1 . 1) (2 . 1) (2 . 2))
((1 . -2) (1 . -1) (1 . 0) (2 . -2))))
</syntaxhighlight>
{{out}}
<pre>-UUUPPPI
NUXUPPTI
NXXXTTTI
NNXVVVTI
-NZ-WVFI
ZZZWWVFF
ZYWWLFF-
YYYYLLLL</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">from itertools import product
minos = (((197123, 7, 6), (1797, 6, 7), (1287, 6, 7), (196867, 7, 6)),
((263937, 6, 6), (197126, 6, 6), (393731, 6, 6), (67332, 6, 6)),
((16843011, 7, 5), (2063, 5, 7), (3841, 5, 7), (271, 5, 7), (3848, 5, 7), (50463234, 7, 5), (50397441, 7, 5), (33686019, 7, 5)),
((131843, 7, 6), (1798, 6, 7), (775, 6, 7), (1795, 6, 7), (1543, 6, 7), (197377, 7, 6), (197378, 7, 6), (66307, 7, 6)),
((132865, 6, 6), (131846, 6, 6), (198146, 6, 6), (132611, 6, 6), (393986, 6, 6), (263938, 6, 6), (67330, 6, 6), (132868, 6, 6)),
((1039, 5, 7), (33751554, 7, 5), (16843521, 7, 5), (16974081, 7, 5), (33686274, 7, 5), (3842, 5, 7), (3844, 5, 7), (527, 5, 7)),
((1804, 5, 7), (33751297, 7, 5), (33686273, 7, 5), (16974338, 7, 5), (16843522, 7, 5), (782, 5, 7), (3079, 5, 7), (3587, 5, 7)),
((263683, 6, 6), (198148, 6, 6), (66310, 6, 6), (393985, 6, 6)),
((67329, 6, 6), (131591, 6, 6), (459266, 6, 6), (263940, 6, 6)),
((459780, 6, 6), (459009, 6, 6), (263175, 6, 6), (65799, 6, 6)),
((4311810305, 8, 4), (31, 4, 8)),
((132866, 6, 6),))
boxchar_double_width = ' ╶╺╵└┕╹┖┗╴─╼┘┴┶┚┸┺╸╾━┙┵┷┛┹┻╷┌┍│├┝╿┞┡┐┬┮┤┼┾┦╀╄┑┭┯┥┽┿┩╃╇╻┎┏╽┟┢┃┠┣┒┰┲┧╁╆┨╂╊┓┱┳┪╅╈┫╉╋'
boxchar_single_width = [c + ' ─━'[i%3] for i, c in enumerate(boxchar_double_width)]
# choose drawing alphabet based on terminal font
patterns = boxchar_single_width
tiles = []
for row in reversed(minos):
tiles.append([])
for n, x, y in row:
for shift in (b*8 + a for a, b in product(range(x), range(y))):
tiles[-1].append(n << shift)
def img(seq):
b = [[0]*10 for _ in range(10)]
for i, s in enumerate(seq):
for j, k in product(range(8), range(8)):
if s & (1<<(j*8 + k)):
b[j + 1][k + 1] = i + 1
idices = [[0]*9 for _ in range(9)]
for i, j in product(range(9), range(9)):
n = (b[i+1][j+1], b[i][j+1], b[i][j], b[i+1][j], b[i+1][j+1])
idices[i][j] = sum((a != b)*(1 + (not a or not b))*3**i for i, (a,b) in enumerate(zip(n, n[1:])))
return '\n'.join(''.join(patterns[i] for i in row) for row in idices)
def tile(board=0, seq=tuple(), tiles=tiles):
if not tiles:
yield img(seq)
return
for c in tiles[0]:
b = board | c
tnext = [] # not using list comprehension ...
for t in tiles[1:]:
tnext.append(tuple(n for n in t if not n&b))
if not tnext[-1]: break # because early break is faster
else:
yield from tile(b, seq + (c,), tnext)
for x in tile():
print(x)</syntaxhighlight>
{{out}}
<pre> ┏━┯━━━┯━━━━━━━┓
┏━┛ └─┐ └─┬─┐ ┌─┨
┠─┐ ┌─╆━┓ │ └─┘ ┃
┃ ├─┤ ┗━┹─╆━┱───┨
┃ │ └───┐ ┡━┹─┐ ┃
┃ │ ┌─┬─┴─┘ ┌─┤ ┃
┃ ┢━┪ ├───┬─┘ │ ┃
┠─┺━┛ │ └─┐ └─┨
┗━━━━━┷━━━━━┷━━━┛
┏━┯━━━┓ ┏━┯━━━┓
┏━┛ └─┐ ┗━┩ └─┐ ┃
┠─┐ ┌─╆━┓ │ ┌─┘ ┃
┃ ├─┤ ┗━┹─┤ ├───┨
┃ │ └───┐ ├─┴─┐ ┃
┃ │ ┌─┬─┴─┘ ┌─┤ ┃
┃ ┢━┪ ├───┬─┘ │ ┃
┠─┺━┛ │ └─┐ └─┨
┗━━━━━┷━━━━━┷━━━┛
(goes on and on)
</pre>
=={{header|Raku}}==
{{trans|Java}}
<syntaxhighlight lang="raku" line># 20201028 Raku programming solution
my \F = [ <1 -1 1 0 1 1 2 1>, <0 1 1 -1 1 0 2 0>, <1 0 1 1 1 2 2 1>,
<1 0 1 1 2 -1 2 0>, <1 -2 1 -1 1 0 2 -1>, <0 1 1 1 1 2 2 1>,
<1 -1 1 0 1 1 2 -1>, <1 -1 1 0 2 0 2 1> ];
my \I = [ <0 1 0 2 0 3 0 4>, <1 0 2 0 3 0 4 0> ];
my \L = [ <1 0 1 1 1 2 1 3>, <1 0 2 0 3 0 3 1>, <0 1 0 2 0 3 1 3>,
<0 1 1 0 2 0 3 0>, <0 1 1 1 2 1 3 1>, <0 1 0 2 0 3 1 0>,
<1 0 2 0 3 -1 3 0>, <1 -3 1 -2 1 -1 1 0> ];
my \N = [ <0 1 1 -2 1 -1 1 0>, <1 0 1 1 2 1 3 1>, <0 1 0 2 1 -1 1 0>,
<1 0 2 0 2 1 3 1>, <0 1 1 1 1 2 1 3>, <1 0 2 -1 2 0 3 -1>,
<0 1 0 2 1 2 1 3>, <1 -1 1 0 2 -1 3 -1> ];
my \P = [ <0 1 1 0 1 1 2 1>, <0 1 0 2 1 0 1 1>, <1 0 1 1 2 0 2 1>,
<0 1 1 -1 1 0 1 1>, <0 1 1 0 1 1 1 2>, <1 -1 1 0 2 -1 2 0>,
<0 1 0 2 1 1 1 2>, <0 1 1 0 1 1 2 0> ];
my \T = [ <0 1 0 2 1 1 2 1>, <1 -2 1 -1 1 0 2 0>,
<1 0 2 -1 2 0 2 1>, <1 0 1 1 1 2 2 0> ];
my \U = [ <0 1 0 2 1 0 1 2>, <0 1 1 1 2 0 2 1>,
<0 2 1 0 1 1 1 2>, <0 1 1 0 2 0 2 1> ];
my \V = [ <1 0 2 0 2 1 2 2>, <0 1 0 2 1 0 2 0>,
<1 0 2 -2 2 -1 2 0>, <0 1 0 2 1 2 2 2> ];
my \W = [ <1 0 1 1 2 1 2 2>, <1 -1 1 0 2 -2 2 -1>,
<0 1 1 1 1 2 2 2>, <0 1 1 -1 1 0 2 -1> ];
my \X = [ <1 -1 1 0 1 1 2 0> , ]; # self-ref: reddit.com/r/rakulang/comments/jpys5p/gbi71jt/
my \Y = [ <1 -2 1 -1 1 0 1 1>, <1 -1 1 0 2 0 3 0>, <0 1 0 2 0 3 1 1>,
<1 0 2 0 2 1 3 0>, <0 1 0 2 0 3 1 2>, <1 0 1 1 2 0 3 0>,
<1 -1 1 0 1 1 1 2>, <1 0 2 -1 2 0 3 0> ];
my \Z = [ <0 1 1 0 2 -1 2 0>, <1 0 1 1 1 2 2 2>,
<0 1 1 1 2 1 2 2>, <1 -2 1 -1 1 0 2 -2> ];
our @shapes = F, I, L, N, P, T, U, V, W, X, Y, Z ;
my @symbols = "FILNPTUVWXYZ-".comb;
my %symbols = @symbols.pairs;
my $nRows = my $nCols = 8; my $blank = 12;
my @grid = [ [-1 xx $nCols ] xx $nRows ];
my @placed;
sub shuffleShapes {
my @rand = (0 ..^+@shapes).pick(*);
for (0 ..^+@shapes) -> \i {
(@shapes[i], @shapes[@rand[i]]) = (@shapes[@rand[i]], @shapes[i]);
(@symbols[i], @symbols[@rand[i]]) = (@symbols[@rand[i]], @symbols[i])
}
}
sub solve($pos,$numPlaced) {
return True if $numPlaced == +@shapes;
my \row = $pos div $nCols;
my \col = $pos mod $nCols;
return solve($pos + 1, $numPlaced) if @grid[row;col] != -1;
for ^+@shapes -> \i {
if !@placed[i] {
for @shapes[i] -> @orientation {
for @orientation -> @o {
next if !tryPlaceOrientation(@o, row, col, i);
@placed[i] = True;
return True if solve($pos + 1, $numPlaced + 1);
removeOrientation(@o, row, col);
@placed[i] = False;
}
}
}
}
return False
}
sub tryPlaceOrientation (@o, $r, $c, $shapeIndex) {
loop (my $i = 0; $i < +@o; $i += 2) {
my \x = $c + @o[$i + 1];
my \y = $r + @o[$i];
return False if
(x < 0 or x ≥ $nCols or y < 0 or y ≥ $nRows or @grid[y;x] != -1)
}
@grid[$r;$c] = $shapeIndex;
loop ($i = 0; $i < +@o; $i += 2) {
@grid[ $r + @o[$i] ; $c + @o[$i + 1] ] = $shapeIndex;
}
return True
}
sub removeOrientation(@o, $r, $c) {
@grid[$r;$c] = -1;
loop (my $i = 0; $i < +@o; $i += 2) {
@grid[ $r + @o[$i] ; $c + @o[$i + 1] ] = -1;
}
}
sub PrintResult {
my $output;
for @grid[*] -> @line {
$output ~= "%symbols{$_} " for @line;
$output ~= "\n"
}
if my \Embedded_Marketing_Mode = True {
$output .= subst('-', $_.chr) for < 0x24c7 0x24b6 0x24c0 0x24ca >
}
say $output
}
#shuffleShapes(); # xkcd.com/221
for ^4 {
loop {
if @grid[my \R = (^$nRows).roll;my \C = (^$nCols).roll] != $blank
{ @grid[R;C] = $blank and last }
}
}
PrintResult() if solve 0,0</syntaxhighlight>
{{out}}
<pre>F F Ⓡ I I I I I
Ⓐ F F N L L L L
P F N N X U U L
P P N X X X U Ⓚ
P P N W X U U T
V Z Ⓤ W W T T T
V Z Z Z W W Y T
V V V Z Y Y Y Y</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|Wren-iterate}}
<syntaxhighlight lang="wren">import "random" for Random
import "./iterate" for Stepped
var F = [
[1, -1, 1, 0, 1, 1, 2, 1], [0, 1, 1, -1, 1, 0, 2, 0],
[1, 0, 1, 1, 1, 2, 2, 1], [1, 0, 1, 1, 2, -1, 2, 0],
[1, -2, 1, -1, 1, 0, 2, -1], [0, 1, 1, 1, 1, 2, 2, 1],
[1, -1, 1, 0, 1, 1, 2, -1], [1, -1, 1, 0, 2, 0, 2, 1]
]
var I = [
[0, 1, 0, 2, 0, 3, 0, 4], [1, 0, 2, 0, 3, 0, 4, 0]
]
var L = [
[1, 0, 1, 1, 1, 2, 1, 3], [1, 0, 2, 0, 3, -1, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 3], [0, 1, 1, 0, 2, 0, 3, 0],
[0, 1, 1, 1, 2, 1, 3, 1], [0, 1, 0, 2, 0, 3, 1, 0],
[1, 0, 2, 0, 3, 0, 3, 1], [1, -3, 1, -2, 1, -1, 1, 0]
]
var N = [
[0, 1, 1, -2, 1, -1, 1, 0], [1, 0, 1, 1, 2, 1, 3, 1],
[0, 1, 0, 2, 1, -1, 1, 0], [1, 0, 2, 0, 2, 1, 3, 1],
[0, 1, 1, 1, 1, 2, 1, 3], [1, 0, 2, -1, 2, 0, 3, -1],
[0, 1, 0, 2, 1, 2, 1, 3], [1, -1, 1, 0, 2, -1, 3, -1]
]
var P = [
[0, 1, 1, 0, 1, 1, 2, 1], [0, 1, 0, 2, 1, 0, 1, 1],
[1, 0, 1, 1, 2, 0, 2, 1], [0, 1, 1, -1, 1, 0, 1, 1],
[0, 1, 1, 0, 1, 1, 1, 2], [1, -1, 1, 0, 2, -1, 2, 0],
[0, 1, 0, 2, 1, 1, 1, 2], [0, 1, 1, 0, 1, 1, 2, 0]
]
var T = [
[0, 1, 0, 2, 1, 1, 2, 1], [1, -2, 1, -1, 1, 0, 2, 0],
[1, 0, 2, -1, 2, 0, 2, 1], [1, 0, 1, 1, 1, 2, 2, 0]
]
var U = [
[0, 1, 0, 2, 1, 0, 1, 2], [0, 1, 1, 1, 2, 0, 2, 1],
[0, 2, 1, 0, 1, 1, 1, 2], [0, 1, 1, 0, 2, 0, 2, 1]
]
var V = [
[1, 0, 2, 0, 2, 1, 2, 2], [0, 1, 0, 2, 1, 0, 2, 0],
[1, 0, 2, -2, 2, -1, 2, 0], [0, 1, 0, 2, 1, 2, 2, 2]
]
var W = [
[1, 0, 1, 1, 2, 1, 2, 2], [1, -1, 1, 0, 2, -2, 2, -1],
[0, 1, 1, 1, 1, 2, 2, 2], [0, 1, 1, -1, 1, 0, 2, -1]
]
var X = [[1, -1, 1, 0, 1, 1, 2, 0]]
var Y = [
[1, -2, 1, -1, 1, 0, 1, 1], [1, -1, 1, 0, 2, 0, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 1], [1, 0, 2, 0, 2, 1, 3, 0],
[0, 1, 0, 2, 0, 3, 1, 2], [1, 0, 1, 1, 2, 0, 3, 0],
[1, -1, 1, 0, 1, 1, 1, 2], [1, 0, 2, -1, 2, 0, 3, 0]
]
var Z = [
[0, 1, 1, 0, 2, -1, 2, 0], [1, 0, 1, 1, 1, 2, 2, 2],
[0, 1, 1, 1, 2, 1, 2, 2], [1, -2, 1, -1, 1, 0, 2, -2]
]
var shapes = [F, I, L, N, P, T, U, V, W, X, Y, Z]
var rand = Random.new()
var symbols = "FILNPTUVWXYZ-".toList
var nRows = 8
var nCols = 8
var blank = 12
var grid = List.filled(nRows, null)
for (i in 0...nRows) grid[i] = List.filled(nCols, 0)
var placed = List.filled(symbols.count - 1, false)
var tryPlaceOrientation = Fn.new { |o, r, c, shapeIndex|
for (i in Stepped.new(0...o.count, 2)) {
var x = c + o[i + 1]
var y = r + o[i]
if (x < 0 || x >= nCols || y < 0 || y >= nRows || grid[y][x] != - 1) return false
}
grid[r][c] = shapeIndex
for (i in Stepped.new(0...o.count, 2)) grid[r + o[i]][c + o[i + 1]] = shapeIndex
return true
}
var removeOrientation = Fn.new { |o, r, c|
grid[r][c] = -1
for (i in Stepped.new(0...o.count, 2)) grid[r + o[i]][c + o[i + 1]] = -1
}
var solve // recursive
solve = Fn.new { |pos, numPlaced|
if (numPlaced == shapes.count) return true
var row = (pos / nCols).floor
var col = pos % nCols
if (grid[row][col] != -1) return solve.call(pos + 1, numPlaced)
for (i in 0...shapes.count) {
if (!placed[i]) {
for (orientation in shapes[i]) {
if (!tryPlaceOrientation.call(orientation, row, col, i)) continue
placed[i] = true
if (solve.call(pos + 1, numPlaced + 1)) return true
removeOrientation.call(orientation, row, col)
placed[i] = false
}
}
}
return false
}
var shuffleShapes = Fn.new {
var n = shapes.count
while (n > 1) {
var r = rand.int(n)
n = n - 1
shapes.swap(r, n)
symbols.swap(r, n)
}
}
var printResult = Fn.new {
for (r in grid) {
for (i in r) System.write("%(symbols[i]) ")
System.print()
}
}
shuffleShapes.call()
for (r in 0...nRows) {
for (c in 0...grid[r].count) grid[r][c] = -1
}
for (i in 0..3) {
var randRow
var randCol
while (true) {
randRow = rand.int(nRows)
randCol = rand.int(nCols)
if (grid[randRow][randCol] != blank) break
}
grid[randRow][randCol] = blank
}
if (solve.call(0, 0)) printResult.call() else System.print("No solution")</syntaxhighlight>
{{out}}
Sample run:
<pre>
L L L L V U U U
Y Z Z L V U - U
Y Y Z - V V V T
Y W Z Z X T T T
Y W W X X X F T
P P W W X F F F
P P N N N F - -
P N N I I I I I
</pre>
=={{header|zkl}}==
{{trans|Java}}
<
{ foreach row in (grid){ row.apply(symbols.get).concat(" ").println() } }
fcn tryPlaceOrientation(o, R,C, shapeIndex){
Line 572 ⟶ 2,383:
}
False
}</
<
_F=T(T(1,-1, 1,0, 1,1, 2,1), T(0,1, 1,-1, 1,0, 2,0),
T(1,0 , 1,1, 1,2, 2,1), T(1,0, 1,1, 2,-1, 2,0), T(1,-2, 1,-1, 1,0, 2,-1),
Line 609 ⟶ 2,420:
symbols="FILNPTUVWXYZ-".split(""),
shapes=T(_F,_I,_L,_N,_P,_T,_U,_V,_W,_X,_Y,_Z) // ((a,b, c,d))-->(((a,b),(c,d)))
.pump(List,List("pump",List,List("pump",List,Void.Read,T.create)));</
<
{ grid[r][c]=blank } // make sure 4 unique random spots
if(solve(0,0)) printResult();
else println("No solution");</
{{out}}
<pre>
| |||