Tree

    By
    Himanshu Tyagi
    -
    0
    8
    « Back to Glossary Index

    What is a Tree?

    In computer science, a tree is a hierarchical data structure that organizes data in a parent-child relationship.

    Unlike linear structures such as arrays or linked lists, where elements are arranged sequentially, a tree allows each element (called a node) to branch into multiple child nodes, forming a structure that looks like an upside-down tree.

    This branching pattern enables the efficient representation of hierarchical data—such as file systems, organizational charts, and HTML document object models—and supports efficient operations like searching, insertion, and traversal.

    Tree Structure and Terminology

    A tree consists of nodes connected by edges. The topmost node, which has no parent, is the root.

    Nodes below the root are child nodes, and the immediate predecessor of a node is its parent.

    Nodes without any children are called leaf or external nodes. Each node can have zero or more children, but only one parent.

    Trees are non-linear because data is arranged across multiple levels rather than in a single sequence.

    Key terms include:

    • Edge: A link connecting two nodes.
    • Ancestor/Descendant: An ancestor is any node on the path from the root to a given node; conversely, a descendant is any node reachable from a given node down the tree.
    • Level: The number of edges from the root to a node.
    • Height: The maximum number of edges from the root to a leaf.
    • Size: The total number of nodes in the tree.

    Basic Operations on Trees

    Common operations performed on tree data structures include:

    • Create: Initialize an empty tree or a new tree with a root node.
    • Insert: Add a new node to the tree at the appropriate location.
    • Search: Find a node containing specific data or determine whether it exists.
    • Traversal: Visit all nodes in a systematic order. The two general traversal strategies are Depth-First Search (DFS)—which explores as far as possible down each branch before backtracking—and Breadth-First Search (BFS)—which explores all nodes at the current level before moving to the next. DFS has three common orders for binary trees: in-order, pre-order, and post-order.

    Types of Trees

    Trees can be categorized by how many children each node may have and by specific ordering properties. The table below summarizes common types:

    Tree Type Maximum Children per Node Key Characteristics & Examples
    Binary Tree 2 Each node has at most two children (left and right). Binary trees are the basis for structures like binary search trees and heaps. Variants include full, complete, balanced, and degenerate binary trees.
    Binary Search Tree (BST) 2 A binary tree with a specific ordering property: for every node, the value of the left child is less, and the value of the right child is greater. This property enables efficient search, insertion, and deletion operations.
    AVL Tree 2 A self-balancing BST where the height difference between any node’s left and right subtrees is at most one. Rotations are used to restore balance after insertions or deletions.
    Ternary Tree 3 Each node can have up to three children, often distinguished as left, middle, and right.
    N-ary (Generic) Tree N (any number) Each node may have an arbitrary number of children. This is useful for representing general hierarchies such as file systems or organizational charts.

    Examples and Use Cases

    Trees appear in many areas of computing and problem solving:

    • File Systems and XML/HTML Documents: Both the folder hierarchy in an operating system and the Document Object Model (DOM) of a web page are naturally tree-structured.
    • Database Indexing and Search Structures: Balanced trees (e.g., B-trees and AVL trees) ensure efficient data retrieval by maintaining height constraints.
    • Routing and Networking: Trees represent routing tables and enable efficient pathfinding algorithms.
    • Expression Parsing: Abstract Syntax Trees (ASTs) model the hierarchical structure of expressions and programming languages.
    • Priority Queues: Heaps (a type of binary tree) implement priority queues, enabling the efficient extraction of the minimum or maximum element.
    • Artificial Intelligence: Trees model game state spaces and powerful search algorithms like minimax.

    For example, a binary search tree maintains its ordering property so that searching for a value requires traversing at most one branch at each level; this yields an average-case time complexity of .

    An AVL tree, on the other hand, ensures that its height remains balanced by performing rotations when the height difference between subtrees exceeds one, which maintains consistent performance.

    An N-ary tree might represent a company hierarchy in which a manager (node) has many direct reports (children).

    Related Concepts

    Trees are often compared with other data structures:

    • Graphs: Trees are a specific type of graph. They are acyclic (contain no cycles) and connected. Unlike general graphs, there is precisely one unique path between any two nodes, and nodes have exactly one parent (except for the root).
    • Linked Lists: A linked list is a special case of a tree where each node has at most one child, making the structure linear.
    • Forest: A forest is a collection of disjoint trees. Removing the root of a tree divides it into a forest of its subtrees.

    Conclusion

    A tree is a hierarchical, non-linear data structure composed of nodes connected by edges, with one root node and zero or more child nodes at each level.

    Trees support operations such as insertion, search, and traversal, and they provide efficient solutions for hierarchical representation, searching, and sorting.

    Understanding tree terminology—root, parent, child, leaf, height, and size—and common tree types enables computer science students to choose the right tree structure for tasks ranging from storing hierarchical data to implementing search algorithms.

    « Back to Glossary Index