private void RightRotation()
{
// c (this)
// /
// b
// /
// a
//
// becomes
// b
// / \
// a c
// Note: RightRotation is basically the opposite of LeftRotation
AVLTreeNode <TNode> newRoot = Left;
// replace the current root with the new root
ReplaceRoot(newRoot);
// take ownership of left's right child as left (now parent)
Left = newRoot.Right;
// the new root takes this as it's right
newRoot.Right = this;
}
public bool Remove(T value)
{
AVLTreeNode <T> current;
current = Find(value);
if (current == null)
{
return(false);
}
AVLTreeNode <T> treeToBalance = current.Parent;
Count--;
if (current.Right == null)
{
if (current.Parent == null)
{
Head = current.Left;
if (Head != null)
{
Head.Parent = null;
}
}
else
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
current.Parent.Left = current.Left;
}
else if (result < 0)
{
current.Parent.Right = current.Left;
}
}
}
else if (current.Right.Left == null)
{
current.Right.Left = current.Left;
if (current.Parent == null)
{
Head = current.Right;
if (Head != null)
{
Head.Parent = null;
}
}
else
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
current.Parent.Left = current.Right;
}
else if (result < 0)
{
current.Parent.Right = current.Right;
}
}
}
else
{
AVLTreeNode <T> leftmost = current.Right.Left;
while (leftmost.Left != null)
{
leftmost = leftmost.Left;
}
leftmost.Parent.Left = leftmost.Right;
leftmost.Left = current.Left;
leftmost.Right = current.Right;
if (current.Parent == null)
{
Head = leftmost;
if (Head != null)
{
Head.Parent = null;
}
}
else
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
current.Parent.Left = leftmost;
}
else if (result < 0)
{
current.Parent.Right = leftmost;
}
}
}
if (treeToBalance != null)
{
treeToBalance.Balance();
}
else
{
if (Head != null)
{
Head.Balance();
}
}
return(true);
}
public bool Remove(T value)
{
AVLTreeNode <T> current;
current = Find(value); // находим узел с удаляемым значением
if (current == null) // узел не найден
{
return(false);
}
AVLTreeNode <T> treeToBalance = current.Parent; // баланс дерева относительно узла родителя
Count--; // уменьшение колиества узлов
// Вариант 1: Если удаляемый узел не имеет правого потомка
if (current.Right == null) // если нет правого потомка
{
if (current.Parent == null) // удаляемый узел является корнем
{
Head = current.Left; // на место корня перемещаем левого потомка
if (Head != null)
{
Head.Parent = null; // убераем ссылку на родителя
}
}
else // удаляемый узел не является корнем
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// Если значение родительского узла больше значения удаляемого,
// сделать левого потомка удаляемого узла, левым потомком родителя.
current.Parent.Left = current.Left;
}
else if (result < 0)
{
// Если значение родительского узла меньше чем удаляемого,
// сделать левого потомка удаляемого узла - правым потомком родительского узла.
current.Parent.Right = current.Left;
}
}
}
// Вариант 2: Если правый потомок удаляемого узла не имеет левого потомка, тогда правый потомок удаляемого узла
// становится потомком родительского узла.
else if (current.Right.Left == null) // если у правого потомка нет левого потомка
{
current.Right.Left = current.Left;
if (current.Parent == null) // текущий элемент является корнем
{
Head = current.Right;
if (Head != null)
{
Head.Parent = null;
}
}
else
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// Если значение узла родителя больше чем значение удаляемого узла,
// сделать правого потомка удаляемого узла, левым потомком его родителя.
current.Parent.Left = current.Right;
}
else if (result < 0)
{
// Если значение родительского узла меньше значения удаляемого,
// сделать правого потомка удаляемого узла - правым потомком родителя.
current.Parent.Right = current.Right;
}
}
}
// Вариант 3: Если правый потомок удаляемого узла имеет левого потомка,
// заместить удаляемый узел, крайним левым потомком правого потомка.
else
{
// Нахожление крайнего левого узла для правого потомка удаляемого узла.
AVLTreeNode <T> leftmost = current.Right.Left;
while (leftmost.Left != null)
{
leftmost = leftmost.Left;
}
// Родительское правое поддерево становится родительским левым поддеревом.
leftmost.Parent.Left = leftmost.Right;
// Присвоить крайнему левому узлу, ссылки на правого и левого потомка удаляемого узла.
leftmost.Left = current.Left;
leftmost.Right = current.Right;
if (current.Parent == null)
{
Head = leftmost;
if (Head != null)
{
Head.Parent = null;
}
}
else
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// Если значение родительского узла больше значения удаляемого,
// сделать крайнего левого потомка левым потомком родителя удаляемого узла.
current.Parent.Left = leftmost;
}
else if (result < 0)
{
// Если значение родительского узла, меньше чем значение удаляемого,
// сделать крайнего левого потомка, правым потомком родителя удаляемого узла.
current.Parent.Right = leftmost;
}
}
}
if (treeToBalance != null)
{
treeToBalance.Balance();
}
else
{
if (Head != null)
{
Head.Balance();
}
}
return(true);
}
/// <summary>
/// Removes all items from the tree
/// </summary>
public void Clear()
{
_head = null;
_count = 0;
}
/// <summary>
/// Removes the first occurance of the specified value from the tree.
/// </summary>
/// <param name="value">The value to remove</param>
/// <returns>True if the value was removed, false otherwise</returns>
public bool Remove(T value)
{
AVLTreeNode <T> current;
// Find the node to remove
current = Find(value);
// If no such node, then just return false
if (current == null)
{
return(false);
}
AVLTreeNode <T> treeToBalance = current.Parent;
_count--;
// Case 1: If current has no right child, then
// current's left replaces current
if (current.Right == null)
{
// The node to be removed is the head node
if (current.Parent == null)
{
_head = current.Left;
if (_head != null)
{
_head.Parent = null;
}
}
else
{
// This is to determine after the current's left replaces current,
// it should be the left child or the right child of current's parent node.
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// if parent value is greater than current value
// make the current's left child a left child of parent
current.Parent.Left = current.Left;
}
else if (result < 0)
{
// if parent value is less than current value
// make the current's left child a right child of parent
current.Parent.Right = current.Left;
}
}
}
// Case 2: If current's right child has no left child, then current's
// right child replaces current
// first we move current's left child to its right child's left child since it has no left child.
// the reason we can do this is because current's right must be bigger than current, but
// current's left must be smaller than current, so it's safe to make such move.
else if (current.Right.Left == null)
{
current.Right.Left = current.Left;
if (current.Parent == null)
{
_head = current.Right;
if (_head != null)
{
_head.Parent = null;
}
}
else
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// if parent value is greater than current value
// make the current's right child a left child of parent
current.Parent.Left = current.Right;
}
else if (result < 0)
{
// if parent value is less than current value
// make the current right child a right child of parent
current.Parent.Right = current.Right;
}
}
}
// Case 3: current's right has a left child, then replace current with current's
// right child's left-most child.
// Seems complicated but the reason is actually straightforward.
// Current's right must be bigger than current, and current's right's left-most node
// must be the least bigger value compared to current, so it needs to be replaced by
// that value.
else
{
// Find the right's left-most child
// start with current.Right.Left as first
AVLTreeNode <T> leftmost = current.Right.Left;
while (leftmost.Left != null)
{
leftmost = leftmost.Left;
}
// if the leftmost node has a right child, make that right child
// as leftmost's parent's left child
leftmost.Parent.Left = leftmost.Right;
// assign leftmost's left and right to current's left and right children
leftmost.Left = current.Left;
leftmost.Right = current.Right;
if (current.Parent == null)
{
_head = leftmost;
if (_head != null)
{
_head.Parent = null;
}
}
else
{
int result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// if parent value is greater than current value
// make leftmost the parent's left child
current.Parent.Left = leftmost;
}
else if (result < 0)
{
// if parent value is less than current value
// make leftmost the parent's right child
current.Parent.Right = leftmost;
}
}
}
// Removal done, need to consider balancing
if (treeToBalance != null)
{
treeToBalance.Balance();
}
else
{
if (_head != null)
{
_head.Balance();
}
}
return(true);
}
//Vi node la dai luong nguoi dung khoi tao nen cac phep toan so sanh phari duoc cai dat
public int CompareTo(object obj)
{
AVLTreeNode <T> node = obj as AVLTreeNode <T>;
return(this.Value.CompareTo(node.Value));
}
private AVLTreeNode <T> Remove(AVLTreeNode <T> node, T value)
{
//Neu cay rong
if (node == null)
{
return(null);
}
else
{
AVLTreeNode <T> parent = new AVLTreeNode <T>(value);
if (node.Value.CompareTo(value) > 0)//Truong hop gia tri can xoa nho hon node dang xet->tim tren cay con trai
{
node.LeftChild = Remove(node.LeftChild, value);
if (balance_factor(node) == -2)//Cay lech phai
{
if (balance_factor(node.RightChild) <= 0)
{
node = RotateRR(node);
}
else
{
node = RotateRL(node);
}
}
}
else if (node.Value.CompareTo(value) < 0)//Truong hop gia tri can xoa lon hon node dang xet->tim tren cayy con phai
{
node.RightChild = Remove(node.RightChild, value);
if (balance_factor(node) == 2)//Cay lech trai
{
if (balance_factor(node.LeftChild) >= 0)
{
node = RotateLL(node);
}
else
{
node = RotateLR(node);
}
}
}
///Neu tim duoc nodee can xet
else
{
if (node.RightChild != null)
{
//delete its inorder successor
parent = node.RightChild;
while (parent.LeftChild != null)
{
parent = parent.LeftChild;
}
node.Value = parent.Value; //Gan lai gia tri node hien hanh
node.RightChild = Remove(node.RightChild, parent.Value);
if (balance_factor(node) == 2) //Tai can bang cay
{
if (balance_factor(node.LeftChild) >= 0)
{
node = RotateLL(node);
}
else
{
node = RotateLR(node);
}
}
}
else
{ //if node.left != null
return(node.LeftChild);
}
}
}
return(node);
}
private bool CheckRemove(AVLTreeNode <T> node, T value)
{
if (node == null)
{
return(false);
}
if (node.Value.Equals(value))
{
if (node.IsLeaf) // no children
{
if (node.Parent.LeftChild == node)
{
node.Parent.LeftChild = null;
}
else
{
node.Parent.RightChild = null;
}
node.Parent = null;
}
else if (node.CheckLeftChild && node.CheckRightChild) // 2 children
{
// Tìm successor node
AVLTreeNode <T> replacementNode = node.RightChild;
while (replacementNode.CheckLeftChild)
{
replacementNode = replacementNode.LeftChild;
}
node.Value = replacementNode.Value;
Remove(replacementNode, replacementNode.Value);
}
else // one child
{
AVLTreeNode <T> subNode;
if (node.CheckLeftChild)
{
subNode = node.LeftChild;
}
else
{
subNode = node.RightChild;
}
if (Root == (subNode))
{
Root = subNode;
}
subNode.Parent = node.Parent;
if (node.Parent.LeftChild == node)
{
node.Parent.LeftChild = subNode;
}
else
{
node.Parent.RightChild = subNode;
}
}
return(true);
}
else
{
if (node.Value.CompareTo(value) > 0)
{
return(CheckRemove(node.LeftChild, value));
}
else
{
return(CheckRemove(node.RightChild, value));
}
}
}
/// <summary>
/// Removes the first occurance of the specified value from the tree.
/// </summary>
/// <param name="value">The value to remove</param>
/// <returns>True if the value was removed, false otherwise</returns>
public bool Remove(T value)
{
var current = Find(value);
if (current == null)
{
return(false);
}
var treeToBalance = current.Parent;
Count--;
// Case 1: If current has no right child, then current's left replaces current
if (current.Right == null)
{
if (current.Parent == null)
{
_head = current.Left;
if (_head != null)
{
_head.Parent = null;
}
}
else
{
var result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// if parent value is greater than current value make the current left child a left child of parent
current.Parent.Left = current.Left;
}
else if (result < 0)
{
// if parent value is less than current value make the current left child a right child of parent
current.Parent.Right = current.Left;
}
}
}
// Case 2: If current's right child has no left child, then current's right child
// replaces current
else if (current.Right.Left == null)
{
current.Right.Left = current.Left;
if (current.Parent == null)
{
_head = current.Right;
if (_head != null)
{
_head.Parent = null;
}
}
else
{
var result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// if parent value is greater than current value make the current right child a left child of parent
current.Parent.Left = current.Right;
}
else if (result < 0)
{
// if parent value is less than current value make the current right child a right child of parent
current.Parent.Right = current.Right;
}
}
}
// Case 3: If current's right child has a left child, replace current with current's
// right child's left-most child
else
{
// find the right's left-most child
var leftmost = current.Right.Left;
while (leftmost.Left != null)
{
leftmost = leftmost.Left;
}
// the parent's left subtree becomes the leftmost's right subtree
leftmost.Parent.Left = leftmost.Right;
// assign leftmost's left and right to current's left and right children
leftmost.Left = current.Left;
leftmost.Right = current.Right;
if (current.Parent == null)
{
_head = leftmost;
if (_head != null)
{
_head.Parent = null;
}
}
else
{
var result = current.Parent.CompareTo(current.Value);
if (result > 0)
{
// if parent value is greater than current value make leftmost the parent's left child
current.Parent.Left = leftmost;
}
else if (result < 0)
{
// if parent value is less than current value make leftmost the parent's right child
current.Parent.Right = leftmost;
}
}
}
if (treeToBalance != null)
{
treeToBalance.Balance();
}
else
{
_head?.Balance();
}
return(true);
}
public AVLTreeNode(TNode value, AVLTreeNode <TNode> parent, AVLTree <TNode> tree)
{
Value = value;
Parent = parent;
_tree = tree;
}
public bool Remove(T value)
{
var compare = value.CompareTo(Value);
if (compare == 0)
{
if (LeftHand == null && RightHand == null)
{
if (Parent != null)
{
if (Parent.LeftHand == this)
{
Parent.LeftHand = null;
}
else
{
Parent.RightHand = null;
}
Parent.Reconstruct(true);
}
else
{
AVLTree.RootNode = null;
}
}
else
{
if (LeftHand == null || RightHand == null)
{
AVLTreeNode child = LeftHand ?? RightHand;
if (Parent != null)
{
if (Parent.LeftHand == this)
{
Parent.LeftHand = child;
}
else
{
Parent.RightHand = child;
}
child.Parent = Parent;
child.Parent.Reconstruct(true);
}
else
{
AVLTree.RootNode = child;
AVLTree.RootNode.Parent = null;
}
}
else
{
AVLTreeNode replace = LeftHand;
while (replace.RightHand != null)
{
replace = replace.RightHand;
}
T tempValue = Value;
Value = replace.Value;
replace.Value = tempValue;
return(replace.Remove(replace.Value));
}
}
Parent = LeftHand = RightHand = null;
return(true);
}
if (compare < 0)
{
return(LeftHand == null ? false : LeftHand.Remove(value));
}
else
{
return(RightHand == null ? false : RightHand.Remove(value));
}
}
void Reconstruct(bool recursive)
{
Count = 1;
int leftLevel = 0;
int rightLevel = 0;
if (LeftHand != null)
{
leftLevel = LeftHand.Level;
Count += LeftHand.Count;
}
if (RightHand != null)
{
rightLevel = RightHand.Level;
Count += RightHand.Count;
}
if (leftLevel - rightLevel > 1)
{
int leftNext = LeftHand.LeftHand == null ? 0 : LeftHand.LeftHand.Level;
int rightNext = LeftHand.RightHand == null ? 0 : LeftHand.RightHand.Level;
if (leftNext >= rightNext)
{
LeftHand.Elevate();
Reconstruct(true);
}
else
{
AVLTreeNode pivot = LeftHand.RightHand;
pivot.Elevate();
pivot.Elevate();
pivot.LeftHand.Reconstruct(false);
pivot.RightHand.Reconstruct(true);
}
}
else if (rightLevel - leftLevel > 1)
{
int leftNext = RightHand.LeftHand == null ? 0 : RightHand.LeftHand.Level;
int rightNext = RightHand.RightHand == null ? 0 : RightHand.RightHand.Level;
if (rightNext >= leftNext)
{
RightHand.Elevate();
Reconstruct(true);
}
else
{
var pivot = RightHand.LeftHand;
pivot.Elevate();
pivot.Elevate();
pivot.LeftHand.Reconstruct(false);
pivot.RightHand.Reconstruct(true);
}
}
else
{
Level = Math.Max(leftLevel, rightLevel) + 1;
if (Parent != null && recursive)
{
Parent.Reconstruct(true);
}
}
}
