//find the node with the given identifier among descendants of parent and parent
//uses pre-order traversal
//O(log(n)) worst O(n) for unbalanced tree
private TreapTreeNode <T> Find(TreapTreeNode <T> parent, T value)
{
if (parent == null)
{
return(null);
}
if (parent.Value.CompareTo(value) == 0)
{
return(parent);
}
var left = Find(parent.Left, value);
if (left != null)
{
return(left);
}
var right = Find(parent.Right, value);
if (right != null)
{
return(right);
}
return(null);
}
private void deleteLeftNode(TreapTreeNode <T> node)
{
//root
if (node.Parent == null)
{
Root.Left.Parent = null;
Root = Root.Left;
return;
}
else
{
//node is left child of parent
if (node.IsLeftChild)
{
node.Parent.Left = node.Left;
}
//node is right child of parent
else
{
node.Parent.Right = node.Left;
}
node.Left.Parent = node.Parent;
}
}
//O(log(n)) worst O(n) for unbalanced tree
private void delete(TreapTreeNode <T> node, T value)
{
var compareResult = node.Value.CompareTo(value);
//node is less than the search value so move right to find the deletion node
if (compareResult < 0)
{
if (node.Right == null)
{
throw new Exception("Item do not exist");
}
delete(node.Right, value);
}
//node is less than the search value so move left to find the deletion node
else if (compareResult > 0)
{
if (node.Left == null)
{
throw new Exception("Item do not exist");
}
delete(node.Left, value);
}
else
{
var parent = node.Parent;
//node is a leaf node
if (node.IsLeaf)
{
deleteLeaf(node);
}
else
{
//case one - right tree is null (move sub tree up)
if (node.Left != null && node.Right == null)
{
deleteLeftNode(node);
}
//case two - left tree is null (move sub tree up)
else if (node.Right != null && node.Left == null)
{
deleteRightNode(node);
}
//case three - two child trees
//replace the node value with maximum element of left subtree (left max node)
//and then delete the left max node
else
{
var maxLeftNode = FindMax(node.Left);
node.Value = maxLeftNode.Value;
//delete left max node
delete(node.Left, maxLeftNode.Value);
}
}
}
}
/// <summary>
/// Initialize the BST with given sorted keys.
/// Time complexity: O(n).
/// </summary>
/// <param name="sortedCollection">The initial sorted collection.</param>
public TreapTree(IEnumerable <T> sortedCollection, IComparer <T> comparer = null) : this(comparer)
{
BSTHelpers.ValidateSortedCollection(sortedCollection, this.comparer);
var nodes = sortedCollection.Select(x => new TreapTreeNode <T>(null, x, rndGenerator.Next())).ToArray();
Root = (TreapTreeNode <T>)BSTHelpers.ToBST(nodes);
BSTHelpers.AssignCount(Root);
heapify(Root);
}
/// <summary>
/// Initialize the BST with given sorted keys.
/// Time complexity: O(n).
/// </summary>
/// <param name="sortedKeys">The sorted keys.</param>
public TreapTree(IEnumerable <T> collection) : this()
{
ValidateCollection(collection);
var nodes = collection.Select(x => new TreapTreeNode <T>(null, x, rndGenerator.Next())).ToArray();
Root = (TreapTreeNode <T>)ToBST(nodes);
assignCount(Root);
heapify(Root);
}
private TreapTreeNode <T> FindMin(TreapTreeNode <T> node)
{
if (node.Left == null)
{
return(node);
}
return(FindMin(node.Left));
}
private TreapTreeNode <T> FindMax(TreapTreeNode <T> node)
{
if (node.Right == null)
{
return(node);
}
return(FindMax(node.Right));
}
private int getHeight(TreapTreeNode <T> node)
{
if (node == null)
{
return(-1);
}
return(Math.Max(getHeight(node.Left), getHeight(node.Right)) + 1);
}
private TreapTreeNode <T> findMax(TreapTreeNode <T> node)
{
while (true)
{
if (node.Right == null)
{
return(node);
}
node = node.Right;
}
}
private TreapTreeNode <T> findMin(TreapTreeNode <T> node)
{
while (true)
{
if (node.Left == null)
{
return(node);
}
node = node.Left;
}
}
/// <summary>
/// Time complexity: O(log(n))
/// </summary>
public void Insert(T value)
{
if (Root == null)
{
Root = new TreapTreeNode <T>(null, value, rndGenerator.Next());
return;
}
var newNode = insert(Root, value);
heapify(newNode);
}
//reorder the tree node so that heap property is valid
private void heapify(TreapTreeNode <T> node)
{
while (node.Parent != null)
{
if (node.Priority < node.Parent.Priority)
{
node = node.IsLeftChild ? rightRotate(node.Parent) : leftRotate(node.Parent);
}
else
{
break;
}
}
}
private void deleteLeaf(TreapTreeNode <T> node)
{
//if node is root
if (node.Parent == null)
{
Root = null;
}
//assign nodes parent.left/right to null
else if (node.IsLeftChild)
{
node.Parent.Left = null;
}
else
{
node.Parent.Right = null;
}
}
/// <summary>
/// Rotates the current root left and returns new root
/// </summary>
private TreapTreeNode <T> leftRotate(TreapTreeNode <T> currentRoot)
{
var prevRoot = currentRoot;
var rightLeftChild = prevRoot.Right.Left;
var newRoot = currentRoot.Right;
//make right child as root
prevRoot.Right.Parent = prevRoot.Parent;
if (prevRoot.Parent != null)
{
if (prevRoot.Parent.Left == prevRoot)
{
prevRoot.Parent.Left = prevRoot.Right;
}
else
{
prevRoot.Parent.Right = prevRoot.Right;
}
}
//move prev root as left child of current root
newRoot.Left = prevRoot;
prevRoot.Parent = newRoot;
//move left child of right child of prev root to right child of left child of new root
newRoot.Left.Right = rightLeftChild;
if (newRoot.Left.Right != null)
{
newRoot.Left.Right.Parent = newRoot.Left;
}
newRoot.Left.UpdateCounts();
newRoot.Right.UpdateCounts();
newRoot.UpdateCounts();
if (prevRoot == Root)
{
Root = newRoot;
}
return(newRoot);
}
/// <summary>
/// Rotates current root right and returns the new root node
/// </summary>
/// <param name="currentRoot"></param>
/// <returns></returns>
private TreapTreeNode <T> RightRotate(TreapTreeNode <T> currentRoot)
{
var prevRoot = currentRoot;
var leftRightChild = prevRoot.Left.Right;
var newRoot = currentRoot.Left;
//make left child as root
prevRoot.Left.Parent = prevRoot.Parent;
if (prevRoot.Parent != null)
{
if (prevRoot.Parent.Left == prevRoot)
{
prevRoot.Parent.Left = prevRoot.Left;
}
else
{
prevRoot.Parent.Right = prevRoot.Left;
}
}
//move prev root as right child of current root
newRoot.Right = prevRoot;
prevRoot.Parent = newRoot;
//move right child of left child of prev root to left child of right child of new root
newRoot.Right.Left = leftRightChild;
if (newRoot.Right.Left != null)
{
newRoot.Right.Left.Parent = newRoot.Right;
}
if (prevRoot == Root)
{
Root = newRoot;
}
return(newRoot);
}
//O(log(n)) always
private TreapTreeNode <T> insert(
TreapTreeNode <T> currentNode, T newNodeValue)
{
var compareResult = currentNode.Value.CompareTo(newNodeValue);
//current node is less than new item
if (compareResult < 0)
{
//no right child
if (currentNode.Right == null)
{
//insert
currentNode.Right = new TreapTreeNode <T>(currentNode, newNodeValue, rndGenerator.Next());
return(currentNode.Right);
}
else
{
return(insert(currentNode.Right, newNodeValue));
}
}
//current node is greater than new node
else if (compareResult > 0)
{
if (currentNode.Left == null)
{
//insert
currentNode.Left = new TreapTreeNode <T>(currentNode, newNodeValue, rndGenerator.Next());
return(currentNode.Left);
}
else
{
return(insert(currentNode.Left, newNodeValue));
}
}
else
{
throw new Exception("Item exists");
}
}
//find the node with the given identifier among descendants of parent and parent
//uses pre-order traversal
private TreapTreeNode <T> find(TreapTreeNode <T> parent, T value)
{
while (true)
{
if (parent == null)
{
return(null);
}
if (comparer.Compare(parent.Value, value) == 0)
{
return(parent);
}
var left = find(parent.Left, value);
if (left != null)
{
return(left);
}
parent = parent.Right;
}
}
private void delete(TreapTreeNode <T> node, T value)
{
while (true)
{
if (node != null)
{
var compareResult = comparer.Compare(node.Value, value);
//node is less than the search value so move right to find the deletion node
if (compareResult < 0)
{
node = node.Right ?? throw new Exception("Item do not exist");
continue;
}
//node is less than the search value so move left to find the deletion node
if (compareResult > 0)
{
node = node.Left ?? throw new Exception("Item do not exist");
continue;
}
}
//node is a leaf node
if (node != null && node.IsLeaf)
{
deleteLeaf(node);
}
else
{
//case one - right tree is null (move sub tree up)
if (node?.Left != null && node.Right == null)
{
deleteLeftNode(node);
}
//case two - left tree is null (move sub tree up)
else if (node?.Right != null && node.Left == null)
{
deleteRightNode(node);
}
//case three - two child trees
//replace the node value with maximum element of left subtree (left max node)
//and then delete the left max node
else
{
if (node != null)
{
var maxLeftNode = findMax(node.Left);
node.Value = maxLeftNode.Value;
//delete left max node
node = node.Left;
value = maxLeftNode.Value;
}
continue;
}
}
break;
}
node.UpdateCounts(true);
}
internal TreapTreeNode(TreapTreeNode <T> parent, T value, int priority)
{
Parent = parent;
Value = value;
Priority = priority;
}
internal TreapTreeNode(TreapTreeNode <T> parent, T value, int priority)
{
this.Parent = parent;
this.Value = value;
this.Priority = priority;
}
