"In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes."
A hierarchical data structure that consists of nodes connected by edges. Trees are used in many applications where high-level organization of data is required, such as file systems or network routing algorithms.
Binary Trees: A tree data structure where each node has at most two children nodes.
Binary Search Trees: A binary tree data structure where the left sub-tree of a node contains only nodes with keys less than the node’s key and the right sub-tree of a node contains only nodes with keys greater than the node’s key.
AVL Trees: A self-balancing binary search tree data structure that maintains the height balance of the binary search tree.
Red-Black Trees: A self-balancing binary search tree data structure where each node is either red or black and the root node is always black.
B-Trees: A tree data structure that can have more than two children at each node, designed to minimize the number of disk accesses required in large databases.
Trie Trees: A tree data structure that represents a collection of strings, with each node representing a common prefix among a group of strings.
Suffix Trees: A tree data structure that represents all the suffixes of a given string.
Segment Trees: A tree data structure used in range query and update problems; each node represents a range of indices and stores information about the corresponding segment.
Fenwick Trees: A tree data structure used for efficient range query and update operations on an array of numbers.
Heap Data Structure: A tree data structure that can be used to implement priority queues and sorting algorithms.
Huffman Coding Trees: A tree data structure representing a variable-length encoding scheme for a set of characters based on their frequencies.
Spanning Trees: A sub-graph of a graph that is a tree and contains all the vertices of the original graph.
Minimum Spanning Trees: A spanning tree of a weighted undirected graph that has the lowest weight.
Maximum Spanning Trees: A spanning tree of a weighted undirected graph that has the highest weight.
Tries: A data structure that stores a set of strings, allowing for efficient searching and prefix matching.
Tree Traversals: Methods of visiting all the nodes in a tree data structure in a particular order, such as Pre-order, In-order, and Post-order traversals.
Tree Balancing Techniques: Methods of balancing a tree data structure, including AVL trees, red-black trees, and tree rotations.
Binary Tree Representation: Representing a binary tree data structure as an array or linked list.
Applications of Tree Data Structures: Examples of real-world applications of tree data structures, such as file systems, decision trees, and game trees.
Binary Tree: A tree with at most two children for every node.
AVL Tree: A self-balancing binary search tree in which the heights of the two child subtrees at any node differ by at most one.
Red-Black Tree: A self-balancing binary search tree in which each node is either red or black, and the root is always black.
B-Tree: A self-balancing search tree in which each node can have more than two children.
Trie: A tree-like data structure used to store associative arrays where keys are usually strings.
Heap: A complete binary tree where all nodes follow the heap property: either the parent node is greater than its children (max-heap) or smaller than its children (min-heap).
Splay Tree: A self-adjusting binary search tree in which recently accessed nodes are moved closer to the root.
2-3 Tree: A self-balancing search tree in which each internal node has either one or two keys.
Quadtree: A tree structure in which each internal node has four children, used to partition a two-dimensional space recursively.
Octree: A tree structure in which each internal node has eight children, used to partition a three-dimensional space recursively.
Patricia Tree: A space-optimized trie in which nodes with a single child are merged into that child.
Interval Tree: A tree data structure used for finding overlapping intervals.
Fenwick Tree: A binary indexed tree used to efficiently calculate prefix sums and to perform range queries.
Segment Tree: A binary tree used to store information about intervals or segments. It can be used for efficient range queries and updates.
R-Tree: A tree structure used for indexing spatial information such as points and rectangles.
Huffman Tree: A binary tree used for efficient data compression by assigning shorter codewords to more frequently occurring symbols.
And many more!: "And many more!" refers to the extension of tree structures to various types of trees beyond the commonly studied binary trees, including ternary trees, quad trees, B-trees, and more.
"Each node in the tree can be connected to many children (depending on the type of tree) but must be connected to exactly one parent."
"except for the root node, which has no parent (i.e., the root node is the top-most node in the tree hierarchy)."
"These constraints mean there are no cycles or 'loops' (no node can be its own ancestor)."
"Each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal."
"In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes in a single straight line."
"Binary trees are a commonly used type, which constrain the number of children for each parent to at most two."
"When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory."
"A value or pointer to other data may be associated with every node in the tree, or sometimes only with the leaf nodes."
"The ADT can be represented in a number of ways, including a list of parents with pointers to children, a list of children with pointers to parents, or a list of nodes and a separate list of parent-child relations."
"Representations might also be more complicated, for example using indexes or ancestor lists for performance."
"Tress as used in computing are similar to but can be different from mathematical constructs of trees in graph theory, trees in set theory, and trees in descriptive set theory."