Tree (data structure)

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Tree_(computer_science)

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Tree (data structure)

A tree is a widely used abstract data type (ADT) that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes. A tree data structure is a collection of nodes connected by edges, where each node contains a value or data and may have a reference to other nodes, known as its children.

Structure

A tree consists of nodes and edges. The topmost node is called the root, and each node (except the root) is connected by a single edge to exactly one other node, which is its parent. A node that has no children is called a leaf node. Nodes that have the same parent are called siblings.

Types of Trees

There are several types of trees, each with its own properties and applications:

• Binary tree: A tree in which each node has at most two children, referred to as the left child and the right child.
• Binary search tree (BST): A binary tree in which the left subtree of a node contains only nodes with values less than the node's value, and the right subtree only nodes with values greater than the node's value.
• AVL tree: A self-balancing binary search tree where the difference in heights between the left and right subtrees cannot be more than one for all nodes.
• Red-black tree: A self-balancing binary search tree where each node contains an extra bit for denoting the color of the node, either red or black.
• B-tree: A self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time.
• Trie: A tree-like data structure that stores a dynamic set of strings, where the keys are usually strings.

Operations

Common operations on a tree data structure include:

• Insertion: Adding a node to the tree.
• Deletion: Removing a node from the tree.
• Traversal: Visiting all the nodes in a specific order. Common traversal methods include pre-order traversal, in-order traversal, and post-order traversal.
• Searching: Finding a node in the tree that contains a specific value.

Applications

Trees are used in various applications, including:

• File systems: Organizing files and directories.
• Databases: Implementing indexes for efficient data retrieval.
• Network routing: Representing hierarchical network structures.
• Artificial intelligence: Representing decision processes in algorithms like decision trees.

Related Pages

• Graph (abstract data type)
• Heap (data structure)
• Linked list
• Priority queue
• Hash table

See Also

• Tree traversal
• Self-balancing binary search tree
• Data structure