I'm trying to get round to writing more often and to do my own research with some interesting and complicated algorithms. Given to my great passion for different types of algorithms, in AI , I have found one very interesting and here you can get it build with Delphi 2010. With this solution, you'll be able to add values to the leaves and run the algorithm to find the nodes that will be evaluated and others that will be pruned. I've used my little framework to build the

**structure**(using a GDI render) and then only focus on the algorithm that was the important part.**Alpha-beta pruning**is a*search algorithm*which seeks to reduce the number of nodes that are evaluated in the search tree by the minimax algorithm. It is a search with adversary algorithm used commonly for machine playing of two-player games (Tic-tac-toe, Chess, Go, etc.). It stops completely evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further. Alpha-beta pruning is a sound optimization in that it does not change the result of the algorithm it optimizes (Algorithmist.com).The pseudo-code is quite simple, and it looks like this:

The structure of the application is very simple and the most difficult part is the simulation process where you need to draw every step of the algorithm.

You can download the application from here (

**Thundax Alpha-beta pruning**) and play with it to understand how the algorithm works.This video shows the execution of the program:

The code of the algorithm is explained as follows:

The code of the algorithm is explained as follows:

**Alpha-beta algorithm:**

function TViewMinimax.alphabeta(Node: TNode; alpha: integer; beta: integer): integer; var i: integer; ret: integer; begin if Node.isLeaf then ret := Node.Value else begin for i := 0 to Node.children.Count - 1 do begin alpha := max(alpha, -alphabeta(Node.children.Items[i], -beta, -alpha)); case Node.player of tMAX: begin Node.Value := alpha; SetAlpha(Node, alpha); Node.visited := true; end; tMIN: begin Node.Value := -alpha; SetBeta(Node, alpha); Node.visited := true; end; end; if beta <= alpha then Break; end; ret := alpha; end; result := ret; end;

**Drawing the nodes by using a pre-order method for iterating the binary tree:**

procedure TViewMinimax.Draw; begin preorder(Self.FMinimax.root); end; procedure TViewMinimax.preorder(root: TNode); begin if Assigned(root) then begin if root.children.Count > 0 then begin DrawLine(root, root.children.Items[0]); DrawLine(root, root.children.Items[1]); preorder(root.children.Items[0]); preorder(root.children.Items[1]); end; DrawRectangle(root); end; end; procedure TViewMinimax.DrawRectangle(Node: TNode); begin Fcanvas.Font.Name := 'Arial'; Fcanvas.Brush.Style := bsSolid; if Node.visited then Fcanvas.Brush.Color := clRed else Fcanvas.Brush.Color := clWhite; if Node.selected then Fcanvas.Brush.Color := clGreen; Fcanvas.Pen.Width := 2; Fcanvas.Pen.Color := clBlack; Fcanvas.Rectangle(Node.position.x - gap, Node.position.y - gap, Node.position.x + gap, Node.position.y + gap); Fcanvas.TextOut(Node.position.x - 5, Node.position.y - 5, Inttostr(Node.Value)); Fcanvas.Brush.Color := clWhite; if (Node.isLeaf) and (Node.Order <> 0) then Fcanvas.TextOut(Node.position.x - 5, Node.position.y + 15, Inttostr(Node.Order)); if not Node.isLeaf then begin case Node.player of tMAX: begin if Node.alpha <> 0 then Fcanvas.TextOut(Node.position.x - 65, Node.position.y - 10, Inttostr(Node.Order) + ': a=' + Inttostr(Node.alpha)); if Node.newAlpha <> 0 then Fcanvas.TextOut(Node.position.x - 65, Node.position.y + 5, Inttostr(Node.NewOrder) + ': a=' + Inttostr(Node.newAlpha)); end; tMIN: begin if Node.beta <> 0 then Fcanvas.TextOut(Node.position.x - 65, Node.position.y - 10, Inttostr(Node.Order) + ': ß=' + Inttostr(Node.beta)); if Node.Newbeta <> 0 then Fcanvas.TextOut(Node.position.x - 65, Node.position.y + 5, Inttostr(Node.NewOrder) + ': ß=' + Inttostr(Node.Newbeta)); end; end; if Node.text <> '' then begin Fcanvas.Brush.Color := clyellow; if (Node.newAlpha = 0) and (Node.Newbeta = 0) then Fcanvas.TextOut(Node.position.x - 53, Node.position.y + 5, Node.text) else Fcanvas.TextOut(Node.position.x - 53, Node.position.y + 20, Node.text) end; end; end;

**Setting up the Minimax Algorithm:**

procedure TForm1.Start1Click(Sender: TObject); var vminimax: TViewMinimax; minimax: TMinimax; words: TStringList; alpha, beta: integer; begin minimax := TMinimax.Create; if Edit1.Text <> '' then begin words := TStringList.Create; SplitTextIntoWords(Edit1.Text, words); minimax.AddNumbers(words); end; minimax.CreateTree; Memo1.Lines.Clear; Image1.Canvas.Brush.color := clwhite; Image1.Canvas.Rectangle(0, 0, Image1.Width, Image1.Height); vminimax := TViewMinimax.Create(Self.Image1.Canvas, minimax, Memo1); if CheckBox1.Checked then vminimax.time := 1000 else vminimax.time := 0; alpha := alphavalue; beta := betavalue; vminimax.Draw; Self.Image1.Canvas.TextOut(951, 25 - 5, 'MAX'); Self.Image1.Canvas.TextOut(951, 127 - 5, 'MIN'); Self.Image1.Canvas.TextOut(951, 228 - 5, 'MAX'); Self.Image1.Canvas.TextOut(951, 328 - 5, 'MIN'); Start1.Enabled := false; CheckBox1.Enabled := false; vminimax.alphabeta(minimax.root, alpha, beta); vminimax.Draw; Start1.Enabled := true; CheckBox1.Enabled := true; FreeAndNil(words); FreeAndNil(minimax); FreeAndNil(vminimax); end;

**Splitting the text into numbers (comma separated values):**

procedure SplitTextIntoWords(const S: string; words: TstringList); var startpos, endpos: Integer; begin Assert(Assigned(words)); words.Clear; startpos := 1; while startpos <= Length(S) do begin while (startpos <= Length(S)) and (S[startpos] = ',') do Inc(startpos); if startpos <= Length(S) then begin endpos := startpos + 1; while (endpos <= Length(S)) and not (S[endpos] = ',') do Inc(endpos); words.Add(Copy(S, startpos, endpos - startpos)); startpos := endpos + 1; end; end; end;

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