Question

I have a program that scans an image and converts gems to specific numbers. Look at the picture below:

So i have a table with numbers. Number 1 is for yellow gem, 2 for blue, etc…

Like:

    A  B  C  D  E
1 | 1  2  3  4  5
2 | 3  5  2  4  1
3 | 1  4  4  1  2
4 | 3  3  2  1  5
5 | 5  1  5  2  5

I want to calculate a step, to get 3 equal numbers (gems) horizontally or vertically. For example, in this table if i swap E2 with D2, D2 will be 1, and D2,D3,D4 creates a valid step, because it’s all 1. I’m using VB.NET 2010.

My table is 8×8 size, it’s just an example above.

At now i’m just have the values in multiple variables (A1=1, A2=3, so on..)

I hope you understand my question, any help would be appreciated.

Answer 1

Here you go:

Module Module1

    Sub Main()
        Dim input = {{1, 3, 2, 4, 1, 1, 2, 1},
                     {1, 2, 5, 3, 2, 1, 3, 4},
                     {2, 1, 5, 4, 3, 2, 5, 4},
                     {3, 5, 1, 5, 2, 4, 1, 2},
                     {4, 2, 5, 1, 5, 2, 4, 2},
                     {2, 3, 2, 2, 5, 1, 3, 1},
                     {2, 1, 5, 4, 3, 2, 5, 4},
                     {3, 5, 1, 3, 2, 4, 1, 2}}

        Console.WriteLine("INPUT:")
        Console.Write("   |")
        For i = 1 To input.GetLength(1)
            Console.Write("{0,3}", GetColumnName(i))
        Next
        Console.Write(vbCrLf)
        Console.Write("---+")
        For i = 1 To input.GetLength(1)
            Console.Write("---")
        Next
        Console.Write(vbCrLf)

        For y = 0 To input.GetUpperBound(0)
            Console.Write("{0,3}|", y + 1)
            For x = 0 To input.GetUpperBound(1)
                Console.Write("{0,3}", input(y, x))
            Next
            Console.Write(vbCrLf)
        Next

        Console.WriteLine("{0}{0}SOLUTION:", vbCrLf)
        For Each match In Solve(input)
            Console.WriteLine("Move {0} {1} for a match of {2}", match.Item1, match.Item2, match.Item3)
        Next
        Console.ReadLine()
    End Sub

    Function Solve(ByVal input As Integer(,)) As IEnumerable(Of Tuple(Of String, Char, Integer))
        Dim matches As New List(Of Tuple(Of String, Char, Integer))
        Dim result As Tuple(Of Boolean, Tuple(Of String, Char, Integer))
        Dim test As Integer(,)

        Dim maxX = input.GetUpperBound(0) - 1
        Dim maxY = input.GetUpperBound(1) - 1

        For x = 0 To maxX
            For y = 0 To maxY
                ReDim test(If(maxX - x > 4, 3, maxX - x), If(maxY - y > 4, 3, maxY - y))
                For x1 = x To x + test.GetLength(0) - 1
                    For y1 = y To y + test.GetLength(1) - 1
                        test(x1 - x, y1 - y) = input(y1, x1)
                    Next
                Next

                'check if the result is a match
                For Each result In {IsMatchOnThird(test), IsMatchOnSecond(test), IsMatchOnFirst(test)}  '<-- Updated Line
                    If result.Item1 = True Then
                        Dim matchPoint = Tuple.Create(CInt(result.Item2.Item1.Split(","c)(0)),
                                                      CInt(result.Item2.Item1.Split(","c)(1)))

                        matches.Add(Tuple.Create(GetColumnName(matchPoint.Item1 + x + 1) & CStr(matchPoint.Item2 + y + 1),
                                                 result.Item2.Item2, result.Item2.Item3))
                    End If
                Next
            Next
        Next

        Return RemoveDuplicates(matches)
    End Function

   Public Function GetColumnName(ByVal colIndex As Integer) As String
        Dim result As New List(Of String)

        Do While colIndex > 0
            result.Insert(0, Chr(65 + CInt((colIndex - 1) Mod 26)))
            colIndex = (colIndex - 1) \ 26
        Loop

        Return String.Join("", result.ToArray)
    End Function

    Function RemoveDuplicates(ByVal list As IEnumerable(Of Tuple(Of String, Char, Integer))) As IEnumerable(Of Tuple(Of String, Char, Integer))

        'remove those where gems and swap direction are the same
        Dim l = (From i In list Order By i.Item3 Descending, i.Item1, i.Item2).ToList
        For i = l.Count - 1 To 1 Step -1
            If (l(i).Item1 = l(i - 1).Item1) AndAlso (l(i).Item2 = l(i - 1).Item2) Then
                l.RemoveAt(i)
            End If
        Next

        l = (From i In list Order By i.Item1, i.Item3 Descending).ToList
        For i = l.Count - 1 To 1 Step -1
            If (l(i).Item1 = l(i - 1).Item1) AndAlso (l(i).Item2 = l(i - 1).Item2) Then
                l.RemoveAt(i)
            End If
        Next

        Return From i In l Order By i.Item3 Descending, i.Item1
    End Function

    Function IsMatchOnThird(ByVal input As Integer(,)) As Tuple(Of Boolean, Tuple(Of String, Char, Integer))
        Dim size = Math.Min(input.GetLength(0), 4).ToString & "C," & Math.Min(input.GetLength(1), 4).ToString & "R"
        Dim i = input
        Dim isValid = Function(test As Integer()) test.All(Function(v) v = test(0))


        Select Case size
            Case "4C,4R"
                If isValid({i(0, 0), i(0, 1), i(1, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("1,2", "L"c, If(isValid({i(0, 0), i(0, 3)}), 4, 3)))
                ElseIf isValid({i(1, 0), i(1, 1), i(0, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("0,2", "R"c, If(isValid({i(1, 0), i(1, 3)}), 4, 3)))
                ElseIf isValid({i(0, 0), i(1, 0), i(2, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,1", "U"c, If(isValid({i(0, 1), i(3, 0)}), 4, 3)))
                ElseIf isValid({i(0, 1), i(1, 1), i(2, 0)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,0", "D"c, If(isValid({i(0, 1), i(3, 1)}), 4, 3)))
                End If
            Case "4C,3R"
                If isValid({i(0, 0), i(0, 1), i(1, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("1,2", "L"c, 3))
                ElseIf isValid({i(1, 0), i(1, 1), i(0, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("0,2", "R"c, 3))
                ElseIf isValid({i(0, 0), i(1, 0), i(2, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,1", "U"c, If(isValid({i(0, 1), i(3, 0)}), 4, 3)))
                ElseIf isValid({i(0, 1), i(1, 1), i(2, 0)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,0", "D"c, If(isValid({i(0, 1), i(3, 1)}), 4, 3)))
                End If
            Case "4C,2R"
                If isValid({i(0, 0), i(1, 0), i(2, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,1", "U"c, If(isValid({i(0, 1), i(3, 0)}), 4, 3)))
                ElseIf isValid({i(0, 1), i(1, 1), i(2, 0)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,0", "D"c, If(isValid({i(0, 1), i(3, 1)}), 4, 3)))
                End If
            Case "3C,4R"
                If isValid({i(0, 0), i(0, 1), i(1, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("1,2", "L"c, If(isValid({i(0, 0), i(0, 3)}), 4, 3)))
                ElseIf isValid({i(1, 0), i(1, 1), i(0, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("0,2", "R"c, If(isValid({i(1, 0), i(1, 3)}), 4, 3)))
                ElseIf isValid({i(0, 0), i(1, 0), i(2, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,1", "U"c, 3))
                ElseIf isValid({i(0, 1), i(1, 1), i(2, 0)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,0", "D"c, 3))
                End If
            Case "3C,3R"
                If isValid({i(0, 0), i(0, 1), i(1, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("1,2", "L"c, 3))
                ElseIf isValid({i(1, 0), i(1, 1), i(0, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("0,2", "R"c, 3))
                ElseIf isValid({i(0, 0), i(1, 0), i(2, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,1", "U"c, 3))
                ElseIf isValid({i(0, 1), i(1, 1), i(2, 0)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,0", "D"c, 3))
                End If
            Case "3C,2R"
                If isValid({i(0, 0), i(1, 0), i(2, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,1", "U"c, 3))
                ElseIf isValid({i(0, 1), i(1, 1), i(2, 0)}) Then
                    Return Tuple.Create(True, Tuple.Create("2,0", "D"c, 3))
                End If
            Case "2C,4R"
                If isValid({i(0, 0), i(0, 1), i(1, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("1,1", "L"c, If(isValid({i(0, 1), i(0, 3)}), 4, 3)))
                ElseIf isValid({i(1, 0), i(1, 1), i(0, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("0,2", "R"c, If(isValid({i(1, 0), i(1, 3)}), 4, 3)))
                End If
            Case "2C,3R"
                If isValid({i(0, 0), i(0, 1), i(1, 1)}) Then
                    Return Tuple.Create(True, Tuple.Create("1,1", "L"c, 3))
                ElseIf isValid({i(1, 0), i(1, 1), i(0, 2)}) Then
                    Return Tuple.Create(True, Tuple.Create("0,2", "R"c, 3))
                End If
        End Select

        Return Tuple.Create(False, Tuple.Create("None", "."c, 0))
    End Function

    Function IsMatchOnSecond(ByVal input As Integer(,)) As Tuple(Of Boolean, Tuple(Of String, Char, Integer))
        Dim i = input
        Dim isValid = Function(test As Integer()) test.All(Function(v) v = test(0))
        Dim xLength = input.GetLength(0)
        Dim yLength = input.GetLength(1)

        If xLength >= 3 AndAlso yLength >= 3 Then
            If isValid({i(0, 0), i(1, 1), i(0, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("1,1", "L"c, 3))
            ElseIf isValid({i(1, 0), i(2, 1), i(1, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("2,1", "L"c, 3))
            ElseIf isValid({i(1, 0), i(0, 1), i(1, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("0,1", "R"c, 3))
            ElseIf isValid({i(2, 0), i(1, 1), i(2, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("1,1", "R"c, 3))
            ElseIf isValid({i(0, 0), i(1, 1), i(2, 0)}) Then
                Return Tuple.Create(True, Tuple.Create("1,1", "U"c, 3))
            ElseIf isValid({i(0, 1), i(1, 2), i(2, 1)}) Then
                Return Tuple.Create(True, Tuple.Create("1,2", "U"c, 3))
            ElseIf isValid({i(0, 2), i(1, 1), i(2, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("1,1", "D"c, 3))
            ElseIf isValid({i(0, 1), i(1, 0), i(2, 1)}) Then
                Return Tuple.Create(True, Tuple.Create("1,0", "D"c, 3))
            End If
        End If

        Return Tuple.Create(False, Tuple.Create("None", "."c, 0))
    End Function

    Private Function IsMatchOnFirst(ByVal input As Integer(,)) As Tuple(Of Boolean, Tuple(Of String, Char, Integer)) '<-- New method
        Dim i = input
        Dim isValid = Function(test As Integer()) test.All(Function(v) v = test(0))
        Dim xLength = input.GetLength(0)
        Dim yLength = input.GetLength(1)

        If xLength >= 3 AndAlso yLength >= 3 Then
            If isValid({i(0, 0), i(1, 1), i(1, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("0,0", "R"c, 3))
            ElseIf isValid({i(1, 0), i(2, 1), i(2, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("1,0", "R"c, 3))
            ElseIf isValid({i(2, 0), i(1, 1), i(1, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("2,0", "L"c, 3))
            ElseIf isValid({i(1, 0), i(0, 1), i(0, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("1,0", "L"c, 3))
            ElseIf isValid({i(0, 0), i(1, 1), i(2, 1)}) Then
                Return Tuple.Create(True, Tuple.Create("0,0", "D"c, 3))
            ElseIf isValid({i(0, 1), i(1, 2), i(2, 2)}) Then
                Return Tuple.Create(True, Tuple.Create("0,1", "D"c, 3))
            ElseIf isValid({i(0, 1), i(1, 0), i(2, 0)}) Then
                Return Tuple.Create(True, Tuple.Create("0,1", "U"c, 3))
            ElseIf isValid({i(0, 2), i(1, 1), i(2, 1)}) Then
                Return Tuple.Create(True, Tuple.Create("0,2", "U"c, 3))
            End If
        End If

        Return Tuple.Create(False, Tuple.Create("None", "."c, 0))
    End Function
End Module

And here is the tuple class I used.
BTW: I converted the it from C# to VB.NET from a question on StackOverflow

Imports System.Collections.Generic

Public Class Tuple(Of T1, T2, T3)
    Inherits Tuple(Of T1, T2)
    Implements IEqualityComparer(Of Tuple(Of T1, T2, T3))

    Private _third As T3

    Public Sub New(ByVal item1 As T1, ByVal item2 As T2, ByVal item3 As T3)
        MyBase.New(item1, item2)
        _third = item3
    End Sub

    Public Property Item3() As T3
        Get
            Return _third
        End Get
        Private Set(ByVal value As T3)
            _third = value
        End Set
    End Property

    Public Overloads Function Equals(ByVal x As Tuple(Of T1, T2, T3), ByVal y As Tuple(Of T1, T2, T3)) As Boolean Implements IEqualityComparer(Of Tuple(Of T1, T2, T3)).Equals
        Return EqualityComparer(Of T1).[Default].Equals(x.Item1, y.Item1) AndAlso EqualityComparer(Of T2).[Default].Equals(x.Item2, y.Item2) AndAlso EqualityComparer(Of T3).[Default].Equals(x.Item3, y.Item3)
    End Function

    Public Overrides Function Equals(ByVal obj As Object) As Boolean
        Return TypeOf obj Is Tuple(Of T1, T2, T3) AndAlso Equals(Me, DirectCast(obj, Tuple(Of T1, T2, T3)))
    End Function

    Public Overloads Function GetHashCode(ByVal obj As Tuple(Of T1, T2, T3)) As Integer Implements IEqualityComparer(Of Tuple(Of T1, T2, T3)).GetHashCode
        Return EqualityComparer(Of T1).[Default].GetHashCode(Item1) Xor EqualityComparer(Of T2).[Default].GetHashCode(Item2) Xor EqualityComparer(Of T3).[Default].GetHashCode(Item3)
    End Function

    Public Shared Shadows Operator =(ByVal left As Tuple(Of T1, T2, T3), ByVal right As Tuple(Of T1, T2, T3)) As Boolean
        If DirectCast(left, Object) Is Nothing AndAlso DirectCast(right, Object) Is Nothing Then
            Return True
        End If

        Return left.Equals(right)
    End Operator

    Public Shared Shadows Operator <>(ByVal left As Tuple(Of T1, T2, T3), ByVal right As Tuple(Of T1, T2, T3)) As Boolean
        If DirectCast(left, Object) Is Nothing AndAlso DirectCast(right, Object) Is Nothing Then
            Return False
        End If

        Return Not left.Equals(right)
    End Operator
End Class

Public Class Tuple(Of T1, T2)
    Implements IEqualityComparer(Of Tuple(Of T1, T2))

    Public Property Item1() As T1
        Get
            Return _first
        End Get
        Private Set(ByVal value As T1)
            _first = value
        End Set
    End Property
    Private _first As T1

    Public Property Item2() As T2
        Get
            Return _second
        End Get
        Private Set(ByVal value As T2)
            _second = value
        End Set
    End Property
    Private _second As T2

    Public Sub New(ByVal item1 As T1, ByVal item2 As T2)
        _first = item1
        _second = item2
    End Sub

    Public Overloads Function Equals(ByVal x As Tuple(Of T1, T2), ByVal y As Tuple(Of T1, T2)) As Boolean Implements IEqualityComparer(Of Tuple(Of T1, T2)).Equals
        Return EqualityComparer(Of T1).[Default].Equals(x.Item1, y.Item1) AndAlso EqualityComparer(Of T2).[Default].Equals(x.Item2, y.Item2)
    End Function

    Public Overrides Function Equals(ByVal obj As Object) As Boolean
        Return TypeOf obj Is Tuple(Of T1, T2) AndAlso Equals(Me, DirectCast(obj, Tuple(Of T1, T2)))
    End Function

    Public Overloads Function GetHashCode(ByVal obj As Tuple(Of T1, T2)) As Integer Implements IEqualityComparer(Of Tuple(Of T1, T2)).GetHashCode
        Return EqualityComparer(Of T1).[Default].GetHashCode(Item1) Xor EqualityComparer(Of T2).[Default].GetHashCode(Item2)
    End Function

    Public Shared Operator =(ByVal left As Tuple(Of T1, T2), ByVal right As Tuple(Of T1, T2)) As Boolean
        If DirectCast(left, Object) Is Nothing AndAlso DirectCast(right, Object) Is Nothing Then
            Return True
        End If

        Return left.Equals(right)
    End Operator

    Public Shared Operator <>(ByVal left As Tuple(Of T1, T2), ByVal right As Tuple(Of T1, T2)) As Boolean
        If DirectCast(left, Object) Is Nothing AndAlso DirectCast(right, Object) Is Nothing Then
            Return False
        End If

        Return Not left.Equals(right)
    End Operator
End Class

Public MustInherit Class Tuple
    <DebuggerStepThrough()> _
    Public Shared Function Create(Of T1, T2)(ByVal first As T1, ByVal second As T2) As Tuple(Of T1, T2)
        Return New Tuple(Of T1, T2)(first, second)
    End Function

    <DebuggerStepThrough()> _
    Public Shared Function Create(Of T1, T2, T3)(ByVal first As T1, ByVal second As T2, ByVal third As T3) As Tuple(Of T1, T2, T3)
        Return New Tuple(Of T1, T2, T3)(first, second, third)
    End Function

End Class

Running the application give this output:

INPUT:
   |  A  B  C  D  E  F  G  H
---+------------------------
  1|  1  3  2  4  1  1  2  1
  2|  1  2  5  3  2  1  3  4
  3|  2  1  5  4  3  2  5  4
  4|  3  5  1  5  2  4  1  2
  5|  4  2  5  1  5  2  4  2
  6|  2  3  2  2  5  1  3  1
  7|  2  1  5  4  3  2  5  4
  8|  3  5  1  3  2  4  1  2


SOLUTION:
Move B4 R for a match of 4
Move D4 L for a match of 4
Move B3 L for a match of 3
Move B5 D for a match of 3
Move C3 D for a match of 3
Move C5 U for a match of 3
Move D4 D for a match of 3
Move E4 R for a match of 3
Move F3 L for a match of 3

This program can work with any board size. The program is based on the way I search for matches in the game (which I suppose is brute-force).

Edit
It appears the solver was not able to find matches on the first gem (see sample below).

5, 2, 5
2, 5, 3
1, 5, 4

If the algorithm were applied on the sample above, no matches would be found.

I’ve fixed that now. There is now an IsMatchOnFirst() method to handle those cases.
See the updated code for changes.