"In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once."
These are algorithms used to manipulate and analyze trees, which are graphs with a hierarchical structure. Examples include tree traversal and Huffman coding.
Trees: An overview of the basic concepts and structures of trees, including terminology, types of trees, and operations performed on trees such as traversal, insertion, and deletion.
Binary Trees: A type of tree where each node can have at most two children; operations performed on binary trees such as searching, sorting, and balancing.
Binary Search Trees: A type of binary tree where the left child always contains a value less than the parent and the right child always contains a value greater than the parent.
AVL Trees: A self-balancing binary search tree where the height difference between left and right subtrees is guaranteed to be at most one.
Red-Black Trees: A self-balancing binary search tree where each node has a “color” (red or black) and strict rules are followed to maintain balance.
B-Trees: Similar to binary search trees, but nodes can have multiple children to more efficiently store data on disk.
Trie Trees: A specialized tree structure used for efficient storage and retrieval of strings, such as for automatic spelling correction or autocompletion.
Huffman Trees: A coding algorithm for data compression, where the most frequently used characters in a message are assigned shorter binary codes.
Segment Trees: A type of tree used for efficient answering of range queries, such as finding the minimum or maximum value in a set of values.
Fenwick Trees: Another type of tree used for efficient answering of range queries, but specifically for cumulative sum queries.
Suffix Trees: A data structure used to efficiently search and manipulate large strings or texts, such as in natural language processing or genome sequencing.
Interval Trees: A type of tree used for efficient searching and manipulation of intervals or ranges.
Cartesian Trees: A binary tree derived from a sequence of values, often used for efficient implementation of geometric algorithms.
Treaps: A random data structure that combines features of binary search trees and heaps, often used for efficient implementation of priority queues.
Threaded Trees: A binary tree where nodes have additional links for fast in-order, pre-order, or post-order traversal without using recursion.
Binary Search Tree (BST): A tree where the left node is smaller than the parent node, while the right node is greater.
AVL Tree: A balanced BST where the height is kept in balance by rotating nodes when necessary.
Red-Black Tree: A balanced BST where each node has a color (red or black) which determines when a node needs to be rotated.
B-Tree: A self-balancing tree structure that allows multiple nodes to be stored in one node to optimize disk accesses.
Trie (Prefix Tree): A tree structure commonly used to store strings, where each node corresponds to a letter, and the path from root to node represents a word.
Heap: A tree-based data structure where nodes are ordered according to a certain property.
Segment Tree: An efficient data structure for querying and updating ranges of elements in an array.
Fenwick Tree (Binary Indexed Tree): Another efficient data structure for querying and updating ranges of elements in an array.
Suffix Tree: A data structure used for efficient string search operations, such as finding all occurrences of a pattern within a larger string.
Cartesian Tree: A tree structure created from a sequence of values that can be used for a variety of operations, including sorting and searching.
Radix Tree (Patricia Trie): A compressed trie where nodes that have only one child are merged together.
Expression Tree: A binary tree used to represent mathematical expressions where the internal nodes are operators while the leaf nodes are operands.
Interval Tree: A data structure that stores intervals and allows for efficient queries of all the intervals that overlap with a given interval.
Huffman Tree: A binary tree used for encoding data that assigns shorter codes to characters that appear more frequently.
"Such traversals are classified by the order in which the nodes are visited."
"The following algorithms are described for a binary tree, but they may be generalized to other trees as well."
"...refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once."
"In computer science, tree traversal... is a form of graph traversal."
"...retrieving, updating, or deleting..."
"...refers to the process of visiting... each node in a tree data structure, exactly once."
"...updating... each node in a tree data structure, exactly once."
"...deleting... each node in a tree data structure, exactly once."
"...retrieving... each node in a tree data structure, exactly once."
"The following algorithms are described for a binary tree, but they may be generalized to other trees as well."
"Such traversals are classified by the order in which the nodes are visited."
"The following algorithms are described for a binary tree..."
"...also known as tree search and walking the tree..."
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