Tree (data structure) Totally Explained

Everything about Tree Data Structure totally explained

In computer science, a tree is a widely-used data structure that emulates a tree structure with a set of linked nodes. It is an acyclic and connected graph. Most of the literatures also include the constraint that a graph's edges must be undirected to be a tree. In addition to these three constraints, some literature indicates that a graph's edges should be un-weighted to be a tree.

Nodes

A node may contain a value or a condition or represent a separate data structure or a tree of its own. Each node in a tree has zero or more child nodes, which are below it in the tree (by convention, trees grow down, not up as they do in nature). A node that has a child is called the child's parent node (or ancestor node, or superior). A node has at most one parent. The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree. The depth of a node is the length of the path to its root (for example, its root path).

Root nodes

The topmost node in a tree is called the root node. Being the topmost node, the root node won't have parents. It is the node at which operations on the tree commonly begin (although some algorithms begin with the leaf nodes and work up ending at the root). All other nodes can be reached from it by following edges or links. (In the formal definition, each such path is also unique). In diagrams, it's typically drawn at the top. In some trees, such as heaps, the root node has special properties. Every node in a tree can be seen as the root node of the subtree rooted at that node.

Leaf nodes

Nodes at the bottommost level of the tree are called leaf nodes. Since they're at the bottommost level, they don't have any children.

Internal nodes

An internal node or inner node is any node of a tree that has child nodes and is thus not a leaf node.

Subtrees

A subtree is a portion of a tree data structure that can be viewed as a complete tree in itself. Any node in a tree T, together with all the nodes below it, comprise a subtree of T. The subtree corresponding to the root node is the entire tree; the subtree corresponding to any other node is called a proper subtree (in analogy to the term proper subset).

Tree ordering

There are two basic types of trees. In an unordered tree, a tree is a tree in a purely structural sense — that's to say, given a node, there's no order for the children of that node. A tree on which an order is imposed — for example, by assigning different natural numbers to each edge leading to a node's children — is called an edge-labeled tree or an ordered tree with data structures built upon them being called ordered tree data structures.
Ordered trees are by far the most common form of tree data structure. Binary search trees are one kind of ordered tree.

Tree representations

There are many different ways to represent trees; common representations represent the nodes as records allocated on the heap (not to be confused with the heap data structure) with pointers to their children, their parents, or both, or as items in an array, with relationships between them determined by their positions in the array (for example, binary heap).

Trees as graphs

In graph theory, a tree is a connected acyclic graph. A rooted tree is such a graph with a vertex singled out as the root. In this case, any two vertices connected by an edge inherit a parent-child relationship. An acyclic graph with multiple connected components or a set of rooted trees is sometimes called a forest.
Traversal methods
Stepping through the items of a tree, by means of the connections between parents and children, is called walking the tree, and the action is a walk of the tree. Often, an operation might be performed when a pointer arrives at a particular node. A walk in which each parent node is traversed before its children is called a pre-order walk; a walk in which the children are traversed before their respective parents are traversed is called a post-order walk.
Common operations

Enumerating all the items
Searching for an item
Adding a new item at a certain position on the tree
Deleting an item
Removing a whole section of a tree (called pruning)
Adding a whole section to a tree (called grafting)
Finding the root for any node

Common uses

Manipulate hierarchical data
Make information easy to search (see tree traversal)
Manipulate sorted lists of data
As a workflow for compositing digital images for visual effectsFurther Information
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