3 weeks ago I showed you a A* pathfinding algorithm. It was extremely slow and sluggish and I have now made it smaller and faster, much faster.

Here is an animated gif showing you a grid 255 * 255 cells. The blue cell is the start cell and it is located almost at the top center. The red cell is the end cell and it is in the middle of the maze. I have walls in this grid, if a cell contains value 1 it is colored black with conditional formatting.

The animation shows me deleting walls and the subroutine finds a new shorter path, highlighted green.

An Event procedure removes the old path and calculates the new path if a cell is changed on this sheet. If you want to remove the even procedure, press with right mouse button on on sheet1. Press with left mouse button on "View Code..". Comment line 3:

Private Sub Worksheet_Change(ByVal Target As Range)
Application.EnableEvents = False
'Call FindShortestPath1
Application.EnableEvents = True
End Sub

You can start the path optimization manually by press with left mouse button oning the button "Find shortest path".

Button "ClearW" clears the path.

Button "Clear grid" clears everything, start and end point, walls and path.

VBA code

Sub FindShortestPath1()
'This macro shows only the final path
'The defined named range "Area" tells this mcro which cell range to use
Application.ScreenUpdating = False
Dim G() As Variant
Dim H() As Variant
Dim N() As Variant
Dim O() As Variant
Dim C() As Variant
Dim OL() As Variant
Dim CL() As Variant
Dim S() As Variant
Dim E() As Variant
Dim W() As Variant
Dim Gv() As Variant
Dim i As Single

ReDim S(0 To 1)
ReDim E(0 To 1)
ReDim W(0 To 3, 0 To 1)
ReDim OL(0 To 1, 0)
ReDim CL(0 To 1, 0)
ReDim Gv(0 To 3)

Call ClearW

Rng = Range("Area").Value

a = UBound(Rng, 1) - 1
b = UBound(Rng, 2) - 1
ReDim G(0 To a, 0 To b)
ReDim H(0 To a, 0 To b)
ReDim N(0 To a, 0 To b)
ReDim O(0 To a, 0 To b)
ReDim C(0 To a, 0 To b)

'Find start and end coordinates in cell range
For Ri = 1 To UBound(Rng, 1)
    For Ci = 1 To UBound(Rng, 2)
        If Rng(Ri, Ci) = "S" Then
            S(0) = Ri - 1
            S(1) = Ci - 1
        End If
        If Rng(Ri, Ci) = "E" Then
            E(0) = Ri - 1
            E(1) = Ci - 1
        End If
        If S(0) <> "" And E(0) <> "" Then Exit For
    Next Ci
Next Ri

'Add S to closed list
CL(0, 0) = S(0) 'row
CL(1, 0) = S(1) 'column

'Add values to closed list
W(0, 0) = -1
W(1, 0) = 1
W(2, 0) = 0
W(3, 0) = 0
W(0, 1) = 0
W(1, 1) = 0
W(2, 1) = -1
W(3, 1) = 1

Echk = False
Do Until Echk = True
    For i = 0 To UBound(CL, 2)
        For j = 0 To 3
            chk = False
            tr = CL(0, i) + W(j, 0)
            tc = CL(1, i) + W(j, 1)
        
            'Check if coordinates are less than 1 or larger than 255
            If tr < 0 Or tc < 0 Or tr > UBound(Rng, 1) - 1 Or tc > UBound(Rng, 2) - 1 Then
                chk = True
            Else
            
                'Check if new coordinates already exist on the closed list
                            On Error Resume Next
                            If C(tr, tc) = "C" Then chk = True
                            If Err <> 0 Then
                                MsgBox tr & " " & tc
                            
                                Exit Sub
                            End If
            
                'Check if coordinate is a wall
                If Rng(tr + 1, tc + 1) = 1 Then chk = True
            
                        If O(tr, tc) = "O" Then
                            chk = True
                            
                            'Calculate G, H and N
                            If G(CL(0, i), CL(1, i)) + 1 < G(tr, tc) Then
                                G(tr, tc) = G(CL(0, i), CL(1, i)) + 1
                                H(tr, tc) = Abs(tr - E(0)) + Abs(tc - E(1))
                                N(tr, tc) = G(tr, tc) + H(tr, tc)
                            End If
                        End If
                        
                'Check if coordinate is NOT on the Open list or Closed list or is a wall
                If chk = False Then
                    'Add coordinates to open list
                    O(tr, tc) = "O"
                    OL(0, UBound(OL, 2)) = tr
                    OL(1, UBound(OL, 2)) = tc
                    ReDim Preserve OL(UBound(OL, 1), UBound(OL, 2) + 1)
                    
                    'Calculate G, H and N
                    G(tr, tc) = G(CL(0, i), CL(1, i)) + 1
                    H(tr, tc) = Abs(tr - E(0)) + Abs(tc - E(1))
                    N(tr, tc) = G(tr, tc) + H(tr, tc)
                    
                    'Check if cell is End
                    If Rng(tr + 1, tc + 1) = "E" Then Echk = True
                    
                End If
            End If
        Next j
    Next i
    
    'Remove all values in closed list
    ReDim CL(0 To 1, 0)
    
    'Find cell(s) in the open list that has the smallest N and add those to the closed list
    'Find a value for Nchk
    If Echk <> True Then
    
        For i = LBound(OL, 2) To UBound(OL, 2)
            If OL(0, i) <> "" Then
                Nchk = N(OL(0, i), OL(1, i))
                Exit For
            End If
        Next i
        
        'Find smallest N
        For i = LBound(OL, 2) To UBound(OL, 2)
            If OL(1, i) <> "" Then
                If N(OL(0, i), OL(1, i)) < Nchk And N(OL(0, i), OL(1, i)) <> "" Then
                    Nchk = N(OL(0, i), OL(1, i))
                End If
            End If
        Next i
        
        'Add cell(s) from open list that has the lowest N, to closed list
        Eend = False
        For i = LBound(OL, 2) To UBound(OL, 2)
            If i <= UBound(OL, 2) Then
                On Error GoTo 0
                If OL(0, i) <> "" Then
                    If N(OL(0, i), OL(1, i)) = Nchk Then
                        Eend = True
                        
                        If CL(0, 0) <> "" Then ReDim Preserve CL(UBound(CL, 1), UBound(CL, 2) + 1)
                        
                        C(OL(0, i), OL(1, i)) = "C"
                        CL(0, UBound(CL, 2)) = OL(0, i)
                        OL(0, i) = ""
                        CL(1, UBound(CL, 2)) = OL(1, i)
                        OL(1, i) = ""
                        
                        'Remove blank values in open list
                        For j = i To UBound(OL, 2) - 1
                            OL(0, j) = OL(0, j + 1)
                            OL(1, j) = OL(1, j + 1)
                        Next j
                        ReDim Preserve OL(UBound(OL, 1), UBound(OL, 2) - 1)
                    End If
                End If
            End If
        Next i
        If Eend = False Then
            
            MsgBox "There is no free path"
            Exit Sub
        End If
    End If
Loop

'Build final path
tr = E(0)
tc = E(1)

Schk = False
Do Until Schk = True

        If C(tr + 1, tc) = "C" _
            And (Rng(tr + 2, tc + 1) <> "W" _
            And Rng(tr + 2, tc + 1) <> "1") _
            Then Gv(0) = G(tr + 1, tc)
        If C(tr, tc + 1) = "C" _
            And (Rng(tr + 1, tc + 2) <> "W" _
            And Rng(tr + 1, tc + 2) <> "1") _
            Then Gv(1) = G(tr, tc + 1)
        If C(tr - 1, tc) = "C" _
            And (Rng(tr, tc + 1) <> "W" _
            And Rng(tr, tc + 1) <> "1") _
            Then Gv(2) = G(tr - 1, tc)
        If C(tr, tc - 1) = "C" _
            And (Rng(tr + 1, tc) <> "W" _
            And Rng(tr + 1, tc) <> "1") _
            Then Gv(3) = G(tr, tc - 1)
        
        'Find smallest G
        For j = 0 To 3
            If Gv(j) <> "" Then Nf = Gv(j)
        Next j
        For j = 0 To 3
            If Gv(j) < Nf And Gv(j) <> "" Then Nf = Gv(j)
        Next j

    Select Case Nf
        Case Gv(0)
            tr = tr + 1
            Rng(tr + 1, tc + 1) = "W"
        Case Gv(1)
            tc = tc + 1
            Rng(tr + 1, tc + 1) = "W"
        Case Gv(2)
            tr = tr - 1
            Rng(tr + 1, tc + 1) = "W"
        Case Gv(3)
            tc = tc - 1
            Rng(tr + 1, tc + 1) = "W"
    End Select

    If Rng(tr + 2, tc + 1) = "S" _
        Or Rng(tr + 1, tc + 2) = "S" _
        Or Rng(tr, tc + 1) = "S" _
        Or Rng(tr + 1, tc) = "S" Then Schk = True
Loop
Range("Area") = Rng
Application.ScreenUpdating = True
End Sub

You may find these posts interesting

• Finding the shortest path – A * pathfinding
• Customize excel maze
• Solve a maze
• Build a maze
• Shortest path

Get excel *.xlsm file

Find shortest path_v4.xlsm

Pathfinding category

Finding the shortest path – A * pathfinding
Two months ago I posted some interesting stuff I found: Shortest path. Let me explain, someone created a workbook that calculated […]

Optimize pick path in a warehouse
  As you probably already are aware of I have shown you earlier a vba macro I made that finds the […]

Excel categories

Leave a Comment