A tree is a fundamental data structure in computer science that organizes elements hierarchically. It consists of nodes connected by edges, where each node can have zero or more child nodes. Trees are used in a wide range of applications, including file systems, databases, hierarchical structures, and more. In this tutorial, we'll cover the basics of trees, their terminology, types of trees, tree traversal, and common operations.
A tree is a non-linear data structure that represents a hierarchical relationship between elements. It consists of nodes and edges, where each node contains data and may have zero or more child nodes. The topmost node is called the root, and nodes without children are called leaves.
Basic Tree Terminologies
- Node: A fundamental element of a tree that holds data and references to its child nodes.
- Root: The topmost node of the tree, from which all other nodes are descended.
- Parent: A node that has child nodes.
- Child: A node that is directly connected to another node when moving away from the root.
- Leaf: A node with no children.
- Depth: The distance between a node and the root.
- Height: The length of the longest path from a node to a leaf.
- Siblings: Nodes that share the same parent.
- Subtree: A portion of a tree that is itself a tree.
- Binary Tree: A tree in which each node has at most two children.
Types of Trees
- Binary Tree: A tree where each node has at most two children: a left child and a right child.
- Binary Search Tree (BST): A binary tree where for each node, all nodes in the left subtree are smaller, and all nodes in the right subtree are larger.
- AVL Tree: A self-balancing binary search tree where the height difference between the left and right subtrees of any node is at most one.
- Red-Black Tree: A self-balancing binary search tree with additional properties to ensure balanced structure.
- Heap: A binary tree used to implement priority queues with efficient insertion and deletion.
- Trie: A tree used to store a dynamic set of strings, commonly used for fast prefix matching.
Common Operations
- Insertion: Adding a new node to the tree.
- Deletion: Removing a node from the tree.
- Search: Finding a specific node in the tree.
- Traversal: Visiting all nodes in a specific order.
- Height/Depth: Calculating the height or depth of the tree.
- Balancing: Ensuring the tree remains balanced (e.g., AVL or Red-Black trees).
- Minimum/Maximum: Finding the minimum or maximum element in the tree.
Tree Implementations
Trees can be implemented using various data structures, including linked structures and arrays. Some common implementations include:
- Linked Structure: Each node contains data and references to its child nodes.
- Array Representation: Nodes are stored in an array, and parent-child relationships are determined by indices.
- Binary Heap: A specialized binary tree used for priority queues.
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