Tree (data structure)
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
See Also[edit | edit source]
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