Difference between revisions of "AVL Tree"

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m (Text replace - "Delphi>" to "syntaxhighlight>")
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   Node:=Tree.FindKey(Pointer(Filename),@CompareFilenameWithMyData);
 
   Node:=Tree.FindKey(Pointer(Filename),@CompareFilenameWithMyData);
  
 +
end;
 +
</syntaxhighlight>
 +
 +
=Associative arrays using AVL trees=
 +
 +
An associative array is an array where instead of an index an different key is used. For example a string.
 +
The unit AvgLvlTree implements several associative arrays using AVL trees:
 +
 +
*TStringToStringTree: string to string, you can choose case sensitive or case insensitive or provide your own string comparison function
 +
*TStringToPointerTree: As TStringToStringTree but to arbitrary pointers, which might be objects
 +
 +
Here is an example demonstrating how to use a TStringToStringTree:
 +
 +
<syntaxhighlight>
 +
uses
 +
  AvgLvlTree;
 +
var
 +
  NameToValue: TStringToStringTree;
 +
  S2SItem: PStringToStringItem;
 +
begin
 +
  // create
 +
  NameToValue:=TStringToStringTree.Create(false); // false = Names are compared case insensitive via ''AnsiCompareText''
 +
 +
  // set values
 +
  NameToValue['First'] := 'One';
 +
  NameToValue['Second'] := 'Two';
 +
 +
  // get values
 +
  writeln('First=',NameToValue['first']); // writes one
 +
  writeln('Second=',NameToValue['second']); // writes two
 +
  writeln('Third=',NameToValue['second']); // write the empty string
 +
 +
  // check if a key is defined
 +
  writeln('First exists: ',NameToValue.Contains('first')); // gives true
 +
  writeln('Third exists: ',NameToValue.Contains('third')); // gives false
 +
 +
  // enumerate all values
 +
  for S2SItem in NameToValue do
 +
    writeln('Name=',S2SItem^.Name,' Value=',S2SItem^.Value);
 +
 +
  // free
 +
  NameToValue.Free;
 
end;
 
end;
 
</syntaxhighlight>
 
</syntaxhighlight>

Revision as of 00:04, 27 March 2012

TAVLTree

Implemented in the FCL unit avl_tree. This is the predecessor of TAvgLvlTree.

TAvgLvlTree

Where to get: Unit AvgLvlTree of Lazarus package LazUtils of the Lazarus sources.

The AVL trees - Average Level Trees are sorted self balancing binary trees. Similar to a list like TPFList a TAvgLvlTree can store arbitrary data (Pointer), but contrary to TFPList the tree is always sorted and balanced. Therefore searching is very fast. Features:

  • You can define your own compare function or method.
  • Searching an item or key takes O(log(n))
  • Inserting an item takes O(log(n))
  • Deleting an item takes O(log(n))
  • Finding the lowest or highest item takes log(n)
  • Finding the sucessor or predecessor item takes O(log(n))
  • Iterating through all items in order takes O(n)
  • Enumerators for running from lowest to highest and highest to lowest
  • Supports duplicates
  • Keeps duplicates order stable.
  • It is not thread safe, but it does not use any global variables. So it can be used in threads just like TFPList.

Creating a tree

By default the tree is sorted for the pointers. That means similar to TFPList you can add any pointers or objects:

uses AvgLvlTree; // in package lazutils

Tree:=TAvgLvlTree.Cteate;
Tree.Add(AnObject1);
Tree.Add(AnObject2);
...
// If you want to know if an item is already in the tree use Find:
if Tree.Find(AnObject1)<>nil then
  writeln('AnObject is in the tree');
...
// To remove an item from the tree use:
Tree.Remove(AnObject1);

To create a tree for your custom data you only need a compare function. The following example demonstrates how to sort TMyData objects via their Filenames:

uses AvgLvlTree; // in package lazutils
type
  TMyData = class
  public
    Filename: string;
    Content: string;
  end;

function CompareMyData(Data1, Data2: Pointer): integer;
begin
  Result:=CompareFilenames(TMyData(d1).Filename,TMyData(d2).Filename);
end;

...
var
  MyData1: TMyData;
  Tree: TAvgLvlTree;
begin
  Tree:=TAvgLvlTree.Create(@CompareMyData);

  MyData1:=TMyData.Create;
  MyData1.Filename:='SomeFile';
  Tree.Add(MyData1);
end;

Enumerating all items of a tree

This will enumerate from lowest to highest:

var
  MyData: TMyData;
begin
  for Node in Tree do begin
    MyData:=TMyData(Node.Data);
    writeln(MyData.Filename);
  end;
end;

This will enumerate from highest to lowest:

var
  MyData: TMyData;
begin
  for Node in Tree.GetEnumeratorHighToLow do begin
    MyData:=TMyData(Node.Data);
    writeln(MyData.Filename);
  end;
end;


Searching items

You can search an item with the same key:

var
  Node: TAvgLvlTreeNode;
begin
  MyData.Filename:='test';
  Node:=Tree.Find(MyData); // finds a node with a Filename = 'test'
                 // Note: The above function CompareFilenames works case insensitive under Windows
                 // so under Windows it can find a node with Filename 'TEST'
end;

Note: Find will find a node where your compare function returns 0.

You can also search directly with a filename, without creating a TMyData. The function FindKey takes as arguments a key (here: the filename) and a special compare function:

function CompareFilenameWithMyData(Filename, MyData: Pointer): integer;
begin
  Result:=CompareFilenames(String(Filename),TMyData(MyData).Filename);
end;

...
var
  Filename: string;
  Node: TAvgLvlTreeNode;
begin
  Filename:='Test';
  Node:=Tree.FindKey(Pointer(Filename),@CompareFilenameWithMyData);

end;

Associative arrays using AVL trees

An associative array is an array where instead of an index an different key is used. For example a string. The unit AvgLvlTree implements several associative arrays using AVL trees:

  • TStringToStringTree: string to string, you can choose case sensitive or case insensitive or provide your own string comparison function
  • TStringToPointerTree: As TStringToStringTree but to arbitrary pointers, which might be objects

Here is an example demonstrating how to use a TStringToStringTree:

uses
  AvgLvlTree;
var
  NameToValue: TStringToStringTree;
  S2SItem: PStringToStringItem;
begin
  // create
  NameToValue:=TStringToStringTree.Create(false); // false = Names are compared case insensitive via ''AnsiCompareText''

  // set values
  NameToValue['First'] := 'One';
  NameToValue['Second'] := 'Two';

  // get values
  writeln('First=',NameToValue['first']); // writes one
  writeln('Second=',NameToValue['second']); // writes two
  writeln('Third=',NameToValue['second']); // write the empty string

  // check if a key is defined
  writeln('First exists: ',NameToValue.Contains('first')); // gives true
  writeln('Third exists: ',NameToValue.Contains('third')); // gives false

  // enumerate all values
  for S2SItem in NameToValue do 
    writeln('Name=',S2SItem^.Name,' Value=',S2SItem^.Value);

  // free
  NameToValue.Free;
end;