## A quicker A * pathfinding algorithm

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

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