Fixed: binary tree deletion
This commit is contained in:
parent
0820da418a
commit
48f62eeab7
@ -102,8 +102,25 @@ begin
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// 16
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// 5 25
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// 1
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//FTree.Delete(10);
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//CheckTree('16-5-1-25');
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FTree.Delete(10);
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CheckTree('16-5-1-25');
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// 16
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// 1 25
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FTree.Delete(5);
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CheckTree('16-1-25');
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// 16
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// 1
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FTree.Delete(25);
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CheckTree('16-1');
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// 1
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FTree.Delete(16);
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CheckTree('1');
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FTree.Delete(1);
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CheckTree('');
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CustomTearDown();
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end;
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211
X2UtTrees.pas
211
X2UtTrees.pas
@ -21,13 +21,22 @@ type
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* who their parent is. It costs 4 bytes... but that's only 4 megabytes
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* overhead for each million nodes, not much of a burden nowadays.
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*}
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RX2BTNode = ^PX2BTNode;
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TX2BTLinks = array[0..11] of Byte;
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PX2BTNode = ^TX2BTNode;
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TX2BTNode = record
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Key: Cardinal;
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Parent: PX2BTNode;
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Left: PX2BTNode;
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Right: PX2BTNode;
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case Boolean of
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True:
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(
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Parent: PX2BTNode;
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Left: PX2BTNode;
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Right: PX2BTNode;
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);
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False:
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(
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Links: TX2BTLinks;
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);
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end;
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@ -37,17 +46,17 @@ type
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*}
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TX2BTCustomCursor = class(TObject)
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private
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FRoot: RX2BTNode;
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FRoot: PX2BTNode;
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protected
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function GetCurrentNode(): RX2BTNode; virtual; abstract;
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function GetCurrentNode(): PX2BTNode; virtual; abstract;
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function GetEof(): Boolean; virtual; abstract;
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public
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constructor Create(const ARoot: RX2BTNode); virtual;
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constructor Create(const ARoot: PX2BTNode); virtual;
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procedure First(); virtual; abstract;
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procedure Next(); virtual; abstract;
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property CurrentNode: RX2BTNode read GetCurrentNode;
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property CurrentNode: PX2BTNode read GetCurrentNode;
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property Eof: Boolean read GetEof;
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end;
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@ -61,9 +70,9 @@ type
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*}
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TX2BTDefaultCursor = class(TX2BTCustomCursor)
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private
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FNode: RX2BTNode;
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FNode: PX2BTNode;
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protected
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function GetCurrentNode(): RX2BTNode; override;
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function GetCurrentNode(): PX2BTNode; override;
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function GetEof(): Boolean; override;
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public
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procedure First(); override;
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@ -80,29 +89,31 @@ type
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private
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FCursor: TX2BTCustomCursor;
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FRoot: PX2BTNode;
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FLastNode: RX2BTNode;
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FLastNode: PX2BTNode;
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function GetRoot(): RX2BTNode;
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function GetCurrentKey(): Cardinal;
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function GetEof(): Boolean;
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protected
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procedure CursorNeeded();
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procedure InvalidateCursor();
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property Root: RX2BTNode read GetRoot;
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//property Root: PX2BTNode read FRoot write FRoot;
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protected
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// Methods which don't really need to be virtual
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// (if you have a good reason; share it with me so I can make it
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// virtual, until then it's kept normal for performance reasons)
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procedure ClearNodes();
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function FindLowestNode(const ANode: RX2BTNode): RX2BTNode;
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function FindHighestNode(const ANode: RX2BTNode): RX2BTNode;
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function FindNode(const AKey: Cardinal; out AParent: RX2BTNode): RX2BTNode;
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function FindNodeOnly(const AKey: Cardinal): RX2BTNode;
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function FindLowestNode(const ANode: PX2BTNode): PX2BTNode;
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function FindHighestNode(const ANode: PX2BTNode): PX2BTNode;
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function FindNode(const AKey: Cardinal; out AParent: PX2BTNode): PX2BTNode;
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function FindNodeOnly(const AKey: Cardinal): PX2BTNode;
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function LeftChild(const ANode: PX2BTNode): Boolean;
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function RightChild(const ANode: PX2BTNode): Boolean;
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procedure SwapNodes(const ANode1, ANode2: PX2BTNode);
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// Virtual methods (commonly needed in descendants)
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function GetCursorClass(): TX2BTCursorClass; virtual;
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@ -112,7 +123,7 @@ type
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procedure InsertNode(const AKey: Cardinal); virtual;
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procedure DeleteNode(const AKey: Cardinal); virtual;
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procedure DeleteCleanNode(const ANode: PX2BTNode); virtual;
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procedure DeleteCleanNode(var ANode: PX2BTNode); virtual;
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public
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constructor Create(); virtual;
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destructor Destroy(); override;
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@ -173,9 +184,6 @@ type
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end;
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implementation
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uses
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Dialogs;
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resourcestring
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RSBTKeyExists = 'The key "%d" already exists in the tree.';
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RSBTKeyNotFound = 'The key "%d" could not be found in the tree.';
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@ -210,25 +218,25 @@ begin
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if Eof then
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raise EBTCursorEof.Create(RSBTCursorEof);
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if Assigned(FNode^^.Left) then
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if Assigned(FNode^.Left) then
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// Node has a left child
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FNode := @FNode^^.Left
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else if Assigned(FNode^^.Right) then
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FNode := FNode^.Left
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else if Assigned(FNode^.Right) then
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// Node has a right child
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FNode := @FNode^^.Right
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FNode := FNode^.Right
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else
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begin
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// Traverse up the path. If we encounter a left direction, it means we
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// can attempt to search the right part of that parent node.
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repeat
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pChild := FNode^;
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FNode := @FNode^^.Parent;
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pChild := FNode;
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FNode := FNode^.Parent;
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if Assigned(FNode^) then
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if Assigned(FNode) then
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begin
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if (FNode^^.Left = pChild) and Assigned(FNode^^.Right) then
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if (FNode^.Left = pChild) and Assigned(FNode^.Right) then
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begin
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FNode := @FNode^^.Right;
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FNode := FNode^.Right;
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break;
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end;
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end else
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@ -248,7 +256,7 @@ end;
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function TX2BTDefaultCursor.GetEof;
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begin
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Result := (not Assigned(FNode)) or (not Assigned(FNode^));
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Result := not Assigned(FNode);
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end;
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@ -279,7 +287,7 @@ end;
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function TX2BinaryTree.Exists;
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begin
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Result := Assigned(FindNodeOnly(AKey)^);
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Result := Assigned(FindNodeOnly(AKey));
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end;
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procedure TX2BinaryTree.Insert;
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@ -313,14 +321,10 @@ procedure TX2BinaryTree.AllocateNode;
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begin
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GetMem(ANode, SizeOf(TX2BTNode));
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FillChar(ANode^, SizeOf(TX2BTNode), #0);
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ShowMessage('Allocating: ' + IntToStr(Integer(ANode)));
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end;
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procedure TX2BinaryTree.DeallocateNode;
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begin
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ShowMessage('Deallocating: ' + IntToStr(Integer(ANode)));
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FreeMem(ANode, SizeOf(TX2BTNode));
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ANode := nil;
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end;
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@ -332,7 +336,7 @@ var
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pParent: PX2BTNode;
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begin
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pNode := Root^;
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pNode := FRoot;;
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while Assigned(pNode) do
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begin
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@ -361,7 +365,7 @@ begin
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end;
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FLastNode := nil;
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Root^ := nil;
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FRoot := nil;
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end;
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@ -369,23 +373,25 @@ function TX2BinaryTree.FindHighestNode;
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begin
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Result := ANode;
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while Assigned(Result^) and Assigned(Result^^.Right) do
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Result := @Result^^.Right;
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while Assigned(Result) and Assigned(Result^.Right) do
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Result := Result^.Right;
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end;
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function TX2BinaryTree.FindLowestNode;
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begin
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Result := ANode;
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while Assigned(Result^) and Assigned(Result^^.Left) do
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Result := @Result^^.Left;
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while Assigned(Result) and Assigned(Result^.Left) do
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Result := Result^.Left;
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end;
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function TX2BinaryTree.FindNode;
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var
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pNode: PX2BTNode;
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begin
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// Quick check; was this node found previously
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if Assigned(FLastNode) and Assigned(FLastNode^) and
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(FLastNode^^.Key = AKey) then
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if Assigned(FLastNode) and (FLastNode^.Key = AKey) then
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begin
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Result := FLastNode;
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exit;
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@ -393,28 +399,31 @@ begin
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AParent := nil;
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FLastNode := nil;
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Result := nil;
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pNode := FRoot;
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Result := Root;
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while Assigned(Result^) do
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if AKey = Result^^.Key then
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break
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else
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while Assigned(pNode) do
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if AKey = pNode^.Key then
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begin
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AParent := Result;
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Result := pNode;
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break;
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end else
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begin
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AParent := pNode;
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if AKey < Result^^.Key then
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Result := @Result^^.Left
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if AKey < pNode^.Key then
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pNode := pNode^.Left
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else
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Result := @Result^^.Right;
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pNode := pNode^.Right;
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end;
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if Assigned(Result^) then
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if Assigned(Result) then
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FLastNode := Result;
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end;
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function TX2BinaryTree.FindNodeOnly;
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var
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pDummy: RX2BTNode;
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pDummy: PX2BTNode;
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begin
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Result := FindNode(AKey, pDummy);
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@ -433,34 +442,81 @@ begin
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end;
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procedure TX2BinaryTree.SwapNodes;
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procedure FixLinks(const ANode, AOld: PX2BTNode);
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begin
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if Assigned(ANode^.Parent) then
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if ANode^.Parent^.Left = AOld then
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ANode^.Parent^.Left := ANode
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else
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ANode^.Parent^.Right := ANode;
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if Assigned(ANode^.Left) then
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ANode^.Left^.Parent := ANode;
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if Assigned(ANode^.Right) then
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ANode^.Right^.Parent := ANode;
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end;
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var
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pBuffer: TX2BTLinks;
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begin
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pBuffer := ANode1.Links;
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ANode1.Links := ANode2.Links;
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ANode2.Links := pBuffer;
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FixLinks(ANode1, ANode2);
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FixLinks(ANode2, ANode1);
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if FRoot = ANode1 then
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FRoot := ANode2
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else if FRoot = ANode2 then
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FRoot := ANode1;
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end;
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procedure TX2BinaryTree.InsertNode;
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var
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pNode: RX2BTNode;
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pParent: RX2BTNode;
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pNode: PX2BTNode;
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pParent: PX2BTNode;
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begin
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pNode := FindNode(AKey, pParent);
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if Assigned(pNode^) then
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if Assigned(pNode) then
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raise EBTKeyExists.CreateFmt(RSBTKeyExists, [AKey]);
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AllocateNode(pNode^);
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InvalidateCursor();
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AllocateNode(pNode);
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FLastNode := pNode;
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pNode^^.Key := AKey;
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if not Assigned(FRoot) then
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FRoot := pNode;
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pNode^.Key := AKey;
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if Assigned(pParent) then
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pNode^^.Parent := pParent^;
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begin
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pNode^.Parent := pParent;
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if AKey < pParent^.Key then
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pParent^.Left := pNode
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else
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pParent^.Right := pNode;
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end;
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end;
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procedure TX2BinaryTree.DeleteNode;
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var
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pNode: RX2BTNode;
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pNode: PX2BTNode;
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pLowest: PX2BTNode;
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begin
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//! Implement DeleteNode
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pNode := FindNodeOnly(AKey);
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if not Assigned(pNode^) then
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if not Assigned(pNode) then
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raise EBTKeyNotFound.CreateFmt(RSBTKeyNotFound, [AKey]);
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InvalidateCursor();
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// If the node to be deleted has either one or no branch, it can simply be
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// taken out of the chain. If it has two branches, find the lowest key on
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// the right branch and swap it.
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@ -472,13 +528,14 @@ begin
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// 2 5 | >>> 2 5
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// 1 3 4 6 | 1 3 6
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// +----+
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if Assigned(pNode^^.Left) and Assigned(pNode^^.Right) then
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if Assigned(pNode^.Left) and Assigned(pNode^.Right) then
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begin
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exit;
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pLowest := FindLowestNode(pNode^.Right);
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SwapNodes(pNode, pLowest);
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end;
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// At this point, the node is a leaf node or has only one branch
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DeleteCleanNode(pNode^);
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DeleteCleanNode(pNode);
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end;
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procedure TX2BinaryTree.DeleteCleanNode;
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@ -510,15 +567,22 @@ begin
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if Assigned(pChild) then
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pChild^.Parent := pParent;
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pChild := ANode;
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DeallocateNode(pChild);
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if ANode = FRoot then
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FRoot := pChild;
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DeallocateNode(ANode);
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end;
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procedure TX2BinaryTree.CursorNeeded;
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begin
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if not Assigned(FCursor) then
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FCursor := GetCursorClass().Create(Root);
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FCursor := GetCursorClass().Create(FRoot);
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end;
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procedure TX2BinaryTree.InvalidateCursor;
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begin
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FreeAndNil(FCursor);
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end;
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@ -528,17 +592,12 @@ begin
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end;
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function TX2BinaryTree.GetRoot;
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begin
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Result := @FRoot;
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end;
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function TX2BinaryTree.GetCurrentKey;
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begin
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if Eof then
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raise EBTCursorEof.Create(RSBTCursorEof);
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Result := FCursor.CurrentNode^^.Key;
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Result := FCursor.CurrentNode^.Key;
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end;
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function TX2BinaryTree.GetEof;
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