Trees, BSTs & Balanced Trees
Trees are hierarchical data structures with nodes connected by edges, starting from a root. Binary Search Trees (BSTs) are specialized trees where each node has at most two children, and the left child’s value is less than its parent while the right child’s value is greater. Balanced Trees, such as AVL or Red-Black Trees, are BSTs that automatically maintain minimal height, ensuring efficient operations like search, insert, and delete.
Trees, BSTs & Balanced Trees
Trees are hierarchical data structures with nodes connected by edges, starting from a root. Binary Search Trees (BSTs) are specialized trees where each node has at most two children, and the left child’s value is less than its parent while the right child’s value is greater. Balanced Trees, such as AVL or Red-Black Trees, are BSTs that automatically maintain minimal height, ensuring efficient operations like search, insert, and delete.
💡 Key Takeaways
- Understand fundamental tree concepts such as root, nodes, edges, leaves, and hierarchical structure.
- Explain Binary Search Trees where left descendants are smaller and right descendants are larger, enabling efficient searches, inserts, and deletes.
- Describe common BST operations (insert, search, delete) and their average time complexities, assuming a balanced tree.
- Understand balanced trees (e.g., AVL, red-black) and why balancing keeps operation times near logarithmic.
- Learn tree traversal methods (in-order, pre-order, post-order) and how they are used to process or output tree data.
❓ Frequently Asked Questions
What is a tree in computer science?
A tree is a hierarchical data structure with nodes connected by edges, rooted at a single root. Each node may have children, and there are no cycles.
What defines a Binary Search Tree (BST) and its key rule?
A BST is a binary tree where each node has at most two children; all values in the left subtree are less than the node's value, and all values in the right subtree are greater. Some variants handle duplicates by placing them on one side.
What is a balanced tree and why is it important?
A balanced tree keeps its height small relative to the number of nodes, ensuring fast operations. Examples include AVL trees, Red-Black trees, and B-trees.
What is a self-balancing BST and how does it affect performance?
A self-balancing BST automatically rebalances after insertions or deletions to maintain near logarithmic height, keeping searches, insertions, and deletions close to O(log n) time.