Creating a Binary Tree for a Knockout Tournament

Question

I am trying to create a binary tree for use in a knockout tournament. The tree consists of TNodes with Left and Right pointers.

This is the code that I have come up with (below); however, it runs into difficulties with the pointers in the CreateTree section.

Once this creates an empty tree of large enough size, I need to add the names on the Memo1.List to the bottoms of the tree so I can pair them up for matches.

How would I do this?

Type
    TNodePtr = ^TNode;
    TNode = Record
        Data:String;
        Left:TNodePtr;
        Right:TNodePtr;
    end;
Type
    TTree = Class
    Private
        Root:TNodePtr;
    Public
        Function GetRoot:TNodePtr;
        Constructor Create;
    end;

var
  MyTree:TTree;


function TTree.GetRoot: TNodePtr;
begin
    Result:=Root;
end;

Constructor TTree.Create;
Var NewNode:TNodePtr;
Begin
    New(NewNode);
    NewNode^.Data:='Spam';
    NewNode^.Left:=Nil;
    NewNode^.Right:=Nil;
End;

Function Power(Base:integer;Exponent:integer):Integer;  //Used for only positive powers in this program so does not need to handle negatives.
begin
        If Base = 0 then
                Power := 0
        else If Exponent = 0 then
                Power := 1
        else //If Exponent > 0 then
                Power:=Base*Power(Base, Exponent-1);
end;

Function DenToBinStr(Value:Integer):String;
Var iBinaryBit:integer;
    sBinaryString:String;
Begin
    While Value <> 0 do
        begin
        iBinaryBit:=Value mod 2;
        sBinaryString:=sBinaryString+IntToStr(iBinaryBit);
        Value:=Value div 2;
        end;
    Result:=sBinaryString;
end;

Procedure TForm1.CreateTree;
    Var iRounds, iCurrentRound, iTreeLocation, iNodeCount, iMoreString, iAddedStringLength, iStringTree:Integer;
            sBinary:String;
            NewNode, ThisNode:TNodePtr;
    begin
            iRounds:=0;
            While Power(2,iRounds) < Memo1.Lines.Count do       {Calculates numbers of rounds by using whole powers of 2}
                    iRounds:=iRounds+1;
            If iRounds > 0 then {Make sure there IS a round}
            begin
                For iCurrentRound:=1 to iRounds do     {Select the round we are currently adding nodes to}
                begin
                    iTreeLocation:=Power(2,iCurrentRound);      {Works out the number of nodes on a line}
                    For iNodeCount:= 0 to iTreeLocation do       {Selects the node we are currently working on}
                    begin
                        ThisNode:=MyTree.GetRoot;
                        sBinary:=DenToBinStr(iNodeCount);           {Gets the tree traversal to that node from the root}
                        If Length(sBinary) < iCurrentRound then  {Makes sure that the tree traversal is long enough, Fills spare spaces with Left because 0 decimal = 0 binary (we need 00 for 2nd round)}
                        begin
                            iMoreString:= iCurrentRound-Length(sBinary);
                            for iAddedStringLength := 0 to iMoreString do
                                sBinary:='0'+sBinary;
                        end;
                        iStringTree:=0;                            {Init iStringTree, iStringTree is the position along the binary string (alt the position down the tree)}
                        While iStringTree <= iCurrentRound-1 do    {While we are not at the location to add nodes to, move our variable node down the tree}
                        begin
                            If sBinary[iStringTree]='0' then
                                ThisNode:=ThisNode^.Left
                            else If sBinary[iStringTree]='1' then
                                ThisNode:=ThisNode^.Right;
                            iStringTree:=iStringTree+1;
                        end;
                        New(NewNode);                           {Create a new node once we are in position}
                        NewNode^.Data:='Spam';
                        NewNode^.Left:=Nil;
                        NewNode^.Right:=Nil;
                        If sBinary[iCurrentRound]='0' then      
                            ThisNode^.Left:=NewNode
                        else If sBinary[iCurrentRound]='1' then
                            ThisNode^.Right:=NewNode;
                        ThisNode.Data:='Spam';
                        Showmessage(ThisNode.Data);
                    end;
                end;
            end;
    {1.2Add on byes}
    {1.2.1Calculate No Of Byes and turn into count. Change each count into binary
     equivalent then flip the bits}
    //iByes:= Memo1.Lines.Count - Power(2,iRounds);
    {1.2.2Add node where 0 is left and 1 is right}

    {2THEN FILL TREE using If node.left and node.right does not exist then write
     next name from list[q] q++}
    {3THEN DISPLAY TREE}
    end;

Answer 1

Think about building the tree differently altogether by building it from the leaves. If you have a queue of nodes, you can take two nodes off the front, join them together with a new node, and add that new node to the end of the queue. Repeat until you run out of nodes, and you'll have a tournament bracket with the same number of rounds you'd get from trying to build the tree from the root.

Here's code that builds the tree and fills the leaves with names from the memo.

var
  Nodes: TQueue;
  Node: PNode;
  s: string;
begin
  Nodes := TQueue.Create;
  try
    // Build initial queue of leaf nodes
    for s in Memo1.Lines do begin
      New(Node);
      Node.Data := s;
      Node.Left := nil;
      Node.Right := nil;
      Nodes.Push(Node);
    end;

    // Link all the nodes
    while Nodes.Count > 1 do begin
      New(Node);
      Node.Left := Nodes.Pop;
      Node.Right := Nodes.Pop;
      Nodes.Push(Node);
    end;

    Assert((Nodes.Count = 1) or (Memo1.Lines.Count = 0));
    if Nodes.Empty then
      Tree := TTree.Create
    else
      Tree := TTree.Create(Nodes.Pop);
  finally
    Nodes.Free;
  end;
end;

What's nice about that code is that at no point do we know or care what level any particular node needs to be at.

If the number of competitors is not a power of two, then some of the competitors at the end of the list may get a "bye" round, and they'll be scheduled to play the winners at the top of the list. The code above has a minimal number of nodes. Your code may have a number of "spam" nodes that don't represent any actual match in the tournament.

The tree object should own the nodes it contains, so it should have a destructor, like this:

destructor TTree.Destroy;
  procedure FreeSubnodes(Node: PNode);
  begin
    if Assigned(Node.Left) then
      FreeSubnodes(Node.Left);
    if Assigned(Node.Right) then
      FreeSubnodes(Node.Right);
    Dispose(Node);
  end;
begin
  FreeSubnodes(Root);
  inherited;
end;

You'll notice I changed how the tree's constructor is called, too. If the tree is empty, it doesn't need to have any nodes. If the tree isn't empty, then we'll supply it with its nodes when we create it.

constructor TTree.Create(ARoot: PNode = nil);
begin
  inherited;
  Root := ARoot;
end;

If you have occasion to copy a tree, then you'll need to copy all its nodes, too. If you don't, then when you free one tree, the copy's root-node pointer will suddenly become invalid.

constructor TTree.Copy(Other: TTree);
  function CopyNode(Node: PNode): PNode;
  begin
    if Assigned(Node) then begin
      New(Result);
      Result.Data := Node.Data;
      Result.Left := CopyNode(Node.Left);
      Result.Right := CopyNode(Node.Right);
    end else
      Result := nil;
  end;
begin
  inherited;
  Root := CopyNode(Other.Root);
end;

Answer 2

I have actually managed to rewrite my original code to make it work individually. It appears to work at this moment in time. This is the procedure I am now using. Thanks Rob, i'll set yours as the answer since it looks like it will work better for mine and i'll look over it to learn what I can but for the purposes of not unnecessarily using others code I will use my own for now.

    Procedure TForm1.CreateTree;
Var  iRounds, iCurrentRound, iCurrentNode, iTraverseToNode:integer;
        sBinary:String;
        ThisNode, NewNode, NextNode:TNodePtr;
begin
        iRounds:=0;
        While Power(2,iRounds) < Memo1.Lines.Count do       {Calculates numbers of rounds by using whole powers of 2}
                iRounds:=iRounds+1;
        If iRounds > 0 then
        begin
                for iCurrentRound:=1 to iRounds do
                begin
                        for iCurrentNode:=0 to power(2,iCurrentRound)-1 do
                        begin
                                NextNode:=MyTree.GetRoot;
                                ThisNode:=NextNode;
                                New(NewNode);
                                NewNode.Data:='';
                                NewNode.Left:=Nil;
                                NewNode.Right:=Nil;
                                sBinary:=DenToBinStr(iCurrentNode);
                                if sBinary = '' then
                                        sBinary:='0';
                                While length(sBinary)>iCurrentNode+1 do
                                begin
                                        sBinary:='0'+sBinary;
                                end;
                                for iTraverseToNode:=1 to length(sBinary)-1 do
                                While NextNode <> nil do
                                begin
                                        if sBinary[iTraverseToNode] = '0' then
                                        begin
                                                ThisNode:=NextNode;
                                                NextNode:=NextNode.Left;
                                        end
                                        else if sBinary[iTraverseToNode] = '1' then
                                        begin
                                                ThisNode:=NextNode;
                                                NextNode:=NextNode.Right;
                                        end
                                end;
                                if sBinary[iCurrentNode+1] = '0' then
                                        ThisNode^.Left:=NewNode
                                else if sBinary[iCurrentNode+1] = '1' then
                                        ThisNode^.Right:=NewNode
                                else
                                        Showmessage('TooFar');
                                        break;
                        end;
                end;
        end;
end;

EDIT: 03/03/2010 I found a much better and simpler way of doing this recursively.

    Procedure RecursiveTree(r:integer; ThisNode: TNodePtr);
Var NewNode:TNodePtr;
begin
        If (NOT assigned(ThisNode.Left)) and (r<>0) then
        begin
                New(NewNode);
                NewNode.Left:=Nil;
                NewNode.Right:=Nil;
                NewNode.Data:='';
                ThisNode.Left:=NewNode;
                RecursiveTree(r-1,ThisNode.Left);
        end;
        If (NOT assigned(ThisNode.Right)) and (r<>0) then
        begin
                New(NewNode);
                NewNode.Left:=Nil;
                NewNode.Right:=Nil;
                NewNode.Data:='';
                ThisNode.Right:=NewNode;
                RecursiveTree(r-1,ThisNode.Right);
        end;
end;