A skew tree, also known as a self-balancing binary search tree, is a type of data structure that organizes its elements in a hierarchical manner. It is similar to other binary search trees but differs in its balancing strategy.
Introduction to Skew Trees
A binary search tree (BST) is a data structure that stores elements in a sorted manner, allowing for efficient searching, insertion, and deletion operations. However, if the elements are not inserted in a balanced manner, the tree can become skewed and lose its efficiency.
A skew tree addresses this issue by implementing a balancing strategy that ensures the height of the tree remains as small as possible. This balancing strategy involves performing rotations on the tree during insertion and deletion operations.
Structure of Skew Trees
Like other binary search trees, each node in a skew tree has at most two children: a left child and a right child. The key property of a skew tree is that the right subtree always has smaller or equal height compared to the left subtree.
The following HTML code demonstrates how to create an unordered list to represent the structure of a skew tree:
- The root node
- The left subtree (with smaller elements)
- The right subtree (with larger or equal elements)
Operations on Skew Trees
Skew trees support various operations such as insertion, deletion, and searching. These operations are performed based on the key value associated with each node.
To insert an element into an empty skew tree or an existing skew tree:
- Create a new node with the given element.
- If the tree is empty, make the new node the root.
- If the element is smaller than the root’s key, insert it into the left subtree.
- If the element is larger than or equal to the root’s key, insert it into the right subtree.
- Perform a skew operation on the root.
To delete an element from a skew tree:
- Search for the node with the given element.
- If found, perform a skew operation on its parent and remove it from the tree.
To search for an element in a skew tree:
- If the tree is empty, return “Element not found.”
- If the element matches with the root’s key, return “Element found.”
- If the element is smaller than the root’s key, search in the left subtree.
- If the element is larger than or equal to the root’s key, search in the right subtree.
Advantages of Skew Trees
The use of skew trees offers several advantages:
- Balanced Structure: Skew trees maintain balance by ensuring that no path from root to leaf differs in length by more than one. This property improves overall performance and efficiency of operations.
- Space Efficiency: Skew trees require less memory compared to other self-balancing binary search trees like AVL trees or red-black trees. This makes them suitable for memory-constrained environments.
A skew tree is a self-balancing binary search tree that maintains balance by performing rotations during insertion and deletion operations. It ensures that the right subtree has smaller or equal height compared to the left subtree, resulting in a balanced structure.
Skew trees offer advantages such as balanced structure and space efficiency. They are widely used in situations where memory is limited, and efficient search, insertion, and deletion operations are required.