/// <summary>
/// Insert a node in the Binary Search Tree
/// </summary>
/// <param name="data">data of the new tree node that needs to be inserted</param>
public void Insert(T data)
{
BinarySearchTreeNode <T> nodeToInsert = new BinarySearchTreeNode <T>(data);
// Case where the tree is empty, add the node as the head
if (Head == null)
{
Head = nodeToInsert;
}
else
{
BinarySearchTreeNode <T> currentNode = Head;
BinarySearchTreeNode <T> previousNode = null;
// Find the location where the node needs to be inserted
while (currentNode != null)
{
previousNode = currentNode;
if (currentNode.Data.CompareTo(data) <= 0)
{
currentNode = currentNode.Right;
}
else
{
currentNode = currentNode.Left;
}
}
// Insert the node to the correct location
if (previousNode.Data.CompareTo(data) <= 0)
{
previousNode.Right = nodeToInsert;
}
else
{
previousNode.Left = nodeToInsert;
}
nodeToInsert.Parent = previousNode;
}
}
/// <summary>
/// Search a BST in recursive manner.
/// The Running time should be O(h) where h is the height of the tree ~= O(log(n)) where n is the total number of nodes
/// O(h) ~= O(log(n)) is true only when the BST is balanced
/// </summary>
/// <param name="data">data which needs to be searched</param>
/// <param name="currentTreeNode">The node reference, initially head of the tree will be passed to the function</param>
/// <returns></returns>
public BinarySearchTreeNode <T> SearchBSTRecursive(T data, BinarySearchTreeNode <T> currentTreeNode)
{
if (currentTreeNode == null)
{
// base and error condition
return(null);
}
if (currentTreeNode.Data.CompareTo(data) == 0)
{
return(currentTreeNode); // The node is found
}
else if (currentTreeNode.Data.CompareTo(data) > 0)
{
// go search in left subtree
return(SearchBSTRecursive(data, currentTreeNode.Left));
}
else
{
// go search the right subtree
return(SearchBSTRecursive(data, currentTreeNode.Right));
}
}
public void Delete(T dataToDelete)
{
BinarySearchTreeNode <T> nodeToDelete = SearchBSTIterative(dataToDelete);
//Case: When the node to delete is not found in the BST
if (nodeToDelete == null)
{
return;
}
// Case 1: When the node to be deleted does not have a right node
if (nodeToDelete.Right == null)
{
if (nodeToDelete.Parent == null)
{
// This is the head node
Head = nodeToDelete.Left;
nodeToDelete.Left.Parent = null;
}
else
{
if (nodeToDelete.Parent.Left == nodeToDelete)
{
nodeToDelete.Parent.Left = nodeToDelete.Left;
if (nodeToDelete.Left != null)
{
nodeToDelete.Left.Parent = nodeToDelete.Parent.Left;
}
}
else if (nodeToDelete.Parent.Right == nodeToDelete)
{
nodeToDelete.Parent.Right = nodeToDelete.Left;
if (nodeToDelete.Left != null)
{
nodeToDelete.Left.Parent = nodeToDelete.Parent.Right;
}
}
}
}
// Case 2: When the node to be deleted has right node, but its right node does not have a left node
else if (nodeToDelete.Right.Left == null)
{
if (nodeToDelete.Parent == null)
{
// This is the head node
Head = nodeToDelete.Right;
nodeToDelete.Right.Parent = null;
nodeToDelete.Right.Left = nodeToDelete.Left;
}
else
{
if (nodeToDelete.Parent.Left == nodeToDelete)
{
nodeToDelete.Parent.Left = nodeToDelete.Right;
if (nodeToDelete.Right != null)
{
nodeToDelete.Right.Parent = nodeToDelete.Parent;
nodeToDelete.Right.Left = nodeToDelete.Left;
}
}
else if (nodeToDelete.Parent.Right == nodeToDelete)
{
nodeToDelete.Parent.Right = nodeToDelete.Right;
if (nodeToDelete.Right != null)
{
nodeToDelete.Right.Parent = nodeToDelete.Parent;
nodeToDelete.Right.Left = nodeToDelete.Left;
}
}
}
}
// Case 3: When the node to be deleted has right node and the right node has a left node, go to the
// right node and get the leftmost node and swap node to be deleted and the leftmost node.
// then delete the leftmost node
else
{
BinarySearchTreeNode <T> currentNode = nodeToDelete.Right;
// Get the left most node of the right node
while (currentNode.Left != null)
{
currentNode = currentNode.Left;
}
// swap the leftmost node and nodetodelete
nodeToDelete.Data = currentNode.Data;
// delete the leftmost node
if (currentNode.Parent.Left == currentNode)
{
currentNode.Parent.Left = null;
}
else // currentNode.Parent.Right == currentNode
{
currentNode.Parent.Right = null;
}
}
}
