I managed to solve this problem with a brute force with RNG it takes around 4-5 seconds to find the best solution even though the working grid is a 3x3.
I want to know how do I make it possible to generate the same moves the brute force finds without the brute force.
I'll list 2 examples and the solutions brute force found. I tried to analyze the solutions to figure out why it picked them and I can't figure anything out.
This game works by using cyclic rotation in both directions (left to right) and (right to left)
Left to right cyclic rotation does this
If [a, b, c] then [b, c, a]
Right to left cyclic rotation does this
If [a, b, c] then [c, a, b]
Game Data lets say is this (it can be any permutation of 1 to 9)
For example
Data = 7, 2, 6, 1, 5, 4, 3, 8, 9
I can move the pieces on the table in 8 different ways.
1) Cyclic Rotation (Left To Right) based on Row.
2) Cyclic Rotation (Right to Left) based on Row.
3) Top To Bottom based on Column.
4) Bottom To Top based on Column.
Now 5 to 8 don't require Column or Row since they are set diagonally.
5) Top Left To Bottom Right (Left To Right).
6) Top Left To Bottom Right (Right To Left).
7) Top Right To Bottom Left (Left To Right).
8) Top Right To Bottom Left (Right To Left).
The data is loaded as following
007 | 002 | 006
001 | 005 | 004
003 | 008 | 009
Solution brute forced:
1). [Top-Right] To [Bottom-Left] (Right To Left)
2). Bottom to Top, Column : 0
3). Left To Right, Row : 1
Here is the solution simlutated
1). [Top-Right] To [Bottom-Left] (Right To Left)
007 | 002 | 003
001 | 006 | 004
005 | 008 | 009
2). Bottom to Top, Column : 0
001 | 002 | 003
005 | 006 | 004
007 | 008 | 009
3). Left To Right, Row : 1
001 | 002 | 003
004 | 005 | 006
007 | 008 | 009
Here is example 2 which takes 6 moves to solve
009 | 008 | 007
006 | 005 | 004
003 | 002 | 001
Solve with: (6 moves)
1). [Top-Right] To [Bottom-Left] (Right To Left)
2). Top to Bottom, Column:1
3). Bottom to Top, Column:0
4). [Top-Left] To [Bottom-Right] (Left To Right)
5). Left To Right, Row:1
6). Right to Left, Row:2
So it's a pretty simple puzzle but finding efficient solutions is not a simple task. Can someone guide me in a right direction.
This is how I did it it finds first 6 moves.. then click button again finds 5 moves (if possible) 4, 3 etc..
I want to know how do I make it possible to generate the same moves the brute force finds without the brute force.
I'll list 2 examples and the solutions brute force found. I tried to analyze the solutions to figure out why it picked them and I can't figure anything out.
This game works by using cyclic rotation in both directions (left to right) and (right to left)
Left to right cyclic rotation does this
If [a, b, c] then [b, c, a]
Right to left cyclic rotation does this
If [a, b, c] then [c, a, b]
Game Data lets say is this (it can be any permutation of 1 to 9)
For example
Data = 7, 2, 6, 1, 5, 4, 3, 8, 9
I can move the pieces on the table in 8 different ways.
1) Cyclic Rotation (Left To Right) based on Row.
2) Cyclic Rotation (Right to Left) based on Row.
3) Top To Bottom based on Column.
4) Bottom To Top based on Column.
Now 5 to 8 don't require Column or Row since they are set diagonally.
5) Top Left To Bottom Right (Left To Right).
6) Top Left To Bottom Right (Right To Left).
7) Top Right To Bottom Left (Left To Right).
8) Top Right To Bottom Left (Right To Left).
The data is loaded as following
007 | 002 | 006
001 | 005 | 004
003 | 008 | 009
Solution brute forced:
1). [Top-Right] To [Bottom-Left] (Right To Left)
2). Bottom to Top, Column : 0
3). Left To Right, Row : 1
Here is the solution simlutated
1). [Top-Right] To [Bottom-Left] (Right To Left)
007 | 002 | 003
001 | 006 | 004
005 | 008 | 009
2). Bottom to Top, Column : 0
001 | 002 | 003
005 | 006 | 004
007 | 008 | 009
3). Left To Right, Row : 1
001 | 002 | 003
004 | 005 | 006
007 | 008 | 009
Here is example 2 which takes 6 moves to solve
009 | 008 | 007
006 | 005 | 004
003 | 002 | 001
Solve with: (6 moves)
1). [Top-Right] To [Bottom-Left] (Right To Left)
2). Top to Bottom, Column:1
3). Bottom to Top, Column:0
4). [Top-Left] To [Bottom-Right] (Left To Right)
5). Left To Right, Row:1
6). Right to Left, Row:2
So it's a pretty simple puzzle but finding efficient solutions is not a simple task. Can someone guide me in a right direction.
This is how I did it it finds first 6 moves.. then click button again finds 5 moves (if possible) 4, 3 etc..
Code:
Public Structure Move
Dim moveId As Byte
Dim rowOrColumn As Byte
Public Sub New(ByVal moveId As Byte, ByVal rowOrColumn As Byte)
Me.moveId = moveId
Me.rowOrColumn = rowOrColumn
End Sub
End Structure
Public leastMoves As New List(Of Move)
Public leastMovesTaken As Long = 9999999
Dim rnd As New Random()
Dim answer() As Byte
Public answerSet As Boolean = False
Function SortDataRandomized(ByVal data() As Byte) As List(Of Move)
If data Is Nothing Then
MessageBox.Show("You haven't loaded a box yet")
Return Nothing
End If
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
If answerSet = False Then
ReDim answer(UBound(data))
Buffer.BlockCopy(data, 0, answer, 0, data.Length)
Array.Sort(answer)
answerSet = True
End If
Dim whatToDo As Byte
Dim randomXY As Byte
Dim answersFound As Integer = 0
Dim movesTaken As New List(Of Move)
While answersFound < 100
whatToDo = rnd.Next(0, 8) '0,1,2,3,4,5,6,7
randomXY = rnd.Next(0, 3) '0,1,2
Select Case whatToDo
Case 0
newdata = CyclicRotationLeftToRight(newdata, randomXY)
movesTaken.Add(New Move(0, randomXY))
Case 1
newdata = CyclicRotationRightToLeft(newdata, randomXY)
movesTaken.Add(New Move(1, randomXY))
Case 2
newdata = CyclicRotationTopToBottom(newdata, randomXY)
movesTaken.Add(New Move(2, randomXY))
Case 3
newdata = CyclicRotationBottomToTop(newdata, randomXY)
movesTaken.Add(New Move(3, randomXY))
Case 4
newdata = CyclicRotationTLtoBRLeftToRight(newdata)
movesTaken.Add(New Move(4, 0))
Case 5
newdata = CyclicRotationTLtoBRRightToLeft(newdata)
movesTaken.Add(New Move(5, 0))
Case 6
newdata = CyclicRotationTRtoBLLeftToRight(newdata)
movesTaken.Add(New Move(6, 0))
Case 7
newdata = CyclicRotationTRtoBLRightToLeft(newdata)
movesTaken.Add(New Move(7, 0))
End Select
'Reset any randomized path since its already too long.
If movesTaken.Count > leastMovesTaken Then
movesTaken.Clear()
'resets newdata back to scrambled state
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
End If
For i As Integer = 0 To data.Length - 1
If (newdata(i) <> answer(i)) Then
Exit For
ElseIf (i = newdata.Length - 1) AndAlso newdata(i) = answer(i) Then
answersFound += 1
Form1.lblRandomSortAnswers.Text = "Total Answers: " + answersFound.ToString
If leastMovesTaken > movesTaken.Count Then
leastMoves.Clear()
leastMoves.AddRange(movesTaken)
leastMovesTaken = movesTaken.Count
Form1.lblRandomSortMoves.Text = "Moves Took: " + movesTaken.Count.ToString
If movesTaken.Count <= 6 Then
'Best path found.
Exit While
End If
End If
'Reset any randomized path since its already too long.
movesTaken.Clear()
'resets newdata back to scrambled state.
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Exit For
End If
Next i
Application.DoEvents()
End While
Return leastMoves
End FunctionCode:
Public Function CyclicRotationLeftToRight(ByVal data() As Byte, ByVal YRow As Byte) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim row() As Byte
ReDim row(Side - 1)
For i = 0 To UBound(row)
row(i) = data(i + (YRow * Side))
Next i
row = CyclicRotation(row, False)
For i = 0 To UBound(row)
newdata(i + (YRow * Side)) = row(i)
Next i
Return newdata
End Function
Public Function CyclicRotationRightToLeft(ByVal data() As Byte, ByVal YRow As Byte) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim row() As Byte
ReDim row(Side - 1)
For i = 0 To UBound(row)
row(i) = data(i + (YRow * Side))
Next i
row = CyclicRotation(row, True)
For i = 0 To UBound(row)
newdata(i + (YRow * Side)) = row(i)
Next i
Return newdata
End Function
Public Function CyclicRotationTopToBottom(ByVal data() As Byte, ByVal XColumn As Byte) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim column() As Byte
ReDim column(Side - 1)
For i = 0 To UBound(column)
column(i) = data(XColumn + (i * Side))
Next i
column = CyclicRotation(column, False)
For i = 0 To UBound(column)
newdata(XColumn + (i * Side)) = column(i)
Next i
Return newdata
End Function
Public Function CyclicRotationBottomToTop(ByVal data() As Byte, ByVal XColumn As Byte) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim column() As Byte
ReDim column(Side - 1)
For i = 0 To UBound(column)
column(i) = data(XColumn + (i * Side))
Next i
column = CyclicRotation(column, True)
For i = 0 To UBound(column)
newdata(XColumn + (i * Side)) = column(i)
Next i
Return newdata
End Function
Public Function CyclicRotationTLtoBRLeftToRight(ByVal data As Byte()) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim diagonal() As Byte
ReDim diagonal(Side - 1)
For i = 0 To UBound(diagonal)
diagonal(i) = data(i + (i * Side)) 'X and Y's both increment together to run the diagonal.
Next i
diagonal = CyclicRotation(diagonal, False)
For i = 0 To UBound(diagonal)
newdata(i + (i * Side)) = diagonal(i)
Next i
Return newdata
End Function
Public Function CyclicRotationTLtoBRRightToLeft(ByVal data As Byte()) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim diagonal() As Byte
ReDim diagonal(Side - 1)
For i = 0 To UBound(diagonal)
diagonal(i) = Data(i + (i * Side)) 'X and Y's both increment together to run the diagonal.
Next i
diagonal = CyclicRotation(diagonal, True)
For i = 0 To UBound(diagonal)
newdata(i + (i * Side)) = diagonal(i)
Next i
Return newdata
End Function
Public Function CyclicRotationTRtoBLLeftToRight(ByVal data As Byte()) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim diagonal() As Byte
ReDim diagonal(Side - 1)
Dim y As Long
y = 0
For i = UBound(diagonal) To 0 Step -1
diagonal(i) = data(i + (y * Side)) 'X goes down and Y goes up
y += 1
Next i
diagonal = CyclicRotation(diagonal, False)
y = 0
For i = UBound(diagonal) To 0 Step -1
newdata(i + (y * Side)) = diagonal(i)
y += 1
Next i
Return newdata
End Function
Public Function CyclicRotationTRtoBLRightToLeft(ByVal data As Byte()) As Byte()
Dim Side As Long = Math.Sqrt(UBound(data) + 1)
Dim newdata() As Byte
ReDim newdata(UBound(data))
Buffer.BlockCopy(data, 0, newdata, 0, data.Length)
Dim diagonal() As Byte
ReDim diagonal(Side - 1)
Dim y As Long
y = 0
For i = UBound(diagonal) To 0 Step -1
diagonal(i) = Data(i + (y * Side)) 'X goes down and Y goes up
y += 1
Next i
diagonal = CyclicRotation(diagonal, True)
y = 0
For i = UBound(diagonal) To 0 Step -1
newdata(i + (y * Side)) = diagonal(i)
y += 1
Next i
Return newdata
End Function
Public Function CyclicRotation(ByVal data() As Byte, ByVal leftDirection As Boolean) As Byte()
'Left Direction = true
'--------------------------------------------------------
'Shifted cyclically rotation If [a, b, c] then [b, c, a]
'--------------------------------------------------------
'Left Direction = false
'--------------------------------------------------------
'Shifted cyclically rotation If [a, b, c] then [c, a, b]
'--------------------------------------------------------
Dim newdata() As Byte
ReDim newdata(UBound(data))
If leftDirection = True Then
newdata(UBound(newdata)) = data(0) '1st element will be last.
For i = 0 To UBound(data) - 1
newdata(i) = data(i + 1)
Next i
Else
newdata(0) = data(UBound(data)) 'last element will be first.
For i = 1 To UBound(data)
newdata(i) = data(i - 1)
Next i
End If
Return newdata
End Function