## Binary trees data structure

Contents

- Binary trees data structure
- What is the structure of a tree like?
- What operations can be performed on a tree data structure?
- What is the shape or structure of a binary tree?
- Examples of trees in programming
- What is a hierarchical tree structure?
- What is the cellular structure of a tree?
- What are the methods for traversing a tree?
- Types of data structure trees
- What are the applications of trees?
- What are binary trees and what are the basic operations and examples?
- What does a complete binary tree look like?
- Trees data structure examples

In graph theory, the following definition is used: “A binary tree is a connected, acyclic, undirected graph such that the degree of each vertex is not greater than 2”. Thus there is only one path between a pair of nodes.

In the case of a quasi-complete binary tree (or a complete tree), a simple integer array can be used with as many positions as the tree should have nodes. The information of the location of the node in the tree is implicit to each position in the array. Thus, if a node is at position i, its children are at positions 2i+1 and 2i+2, while its parent (if it has one), is at position truncation((i-1)/2) (assuming the root is at position zero). This method benefits from more compact storage and better reference locality, particularly during a preorder run. The structure for this case would therefore be:

In this type of traversal, a certain action (perhaps simply screen printing the key value of that node) is performed on the current node and then the left subtree is processed, and when completed, the right subtree is processed. Another way to understand the path with this method would be to follow the order: root node, left node, right node.

## What is the structure of a tree like?

Every tree has at least one trunk, which supports the entire structure of the tree, and ends in a crown, formed by the series of branches that arise from the trunk, and which are also subdivided into other thinner branches, where the leaves and growth buds are located.

## What operations can be performed on a tree data structure?

As in any data structure there are two basic operations, insertion and deletion.

## What is the shape or structure of a binary tree?

In a language with records and references, binary trees are typically built with a structure of nodes and pointers in which data is stored, each of these nodes has a reference or pointer to a left node and a right node called children.

### Examples of trees in programming

In computer science and informatics, a tree is a widely used abstract data type (ADT) that mimics the hierarchical structure of a tree, with a value at the root and subtrees with a parent node, represented as a set of linked nodes.

As a data structure, a linked tree is a group of nodes, where each node has a value and a list of references to other nodes (its children). This data structure actually defines a directed network,[1] because it can have loops or several references to the same node, just like a linked list. Then there is also the requirement that no two references point to the same node (that each node has at most a single parent, and in fact they all do, except for the root), and a tree that violates this is a corrupt tree.

Because of the use of references to trees in the data structure of a linked tree, we often speak of trees in which they are implicitly being represented by references to the root node, since this is usually the way they are actually implemented. For example, instead of an empty tree, one can have a null reference: a tree is never empty, but a reference to a tree can be null.

### What is a hierarchical tree structure?

A hierarchical database is a type of database management system that, as the name implies, stores information in a hierarchical structure that links records in a tree-like structure, where one mode of information can have several child modes, and so on.

### What is the cellular structure of a tree?

Although plants and animals are eukaryotes, plant cells differ in some ways from animal cells ( Figure below ). Plant cells have a large central vacuole, are surrounded by a cell wall, and have chloroplasts, which are the organelles of photosynthesis.

### What are the methods for traversing a tree?

Basically three ways can be used to traverse a binary tree, preorder, inorder, postorder. In the preorder order it is traversed as follows: root, left subtree, right subtree. In the inorder order it is traversed as follows: left subtree, root, right subtree.

### Types of data structure trees

Every tree has at least one trunk, which is the one that supports the whole structure of the tree, and which ends in a crown, formed by the series of branches that arise from the trunk, and which are also subdivided into other thinner ones, where the leaves and the growth buds are located. When there is no branching, as in the case of palm trees, which only have a tuft of large leaves at the top, we do not speak of a trunk but of a stipe.

– Heartwood: layer present only in some species. Hard, dead inner tissue, which due to the stratification of resinous substances acquires a dark color and an enormous resistance to rotting.

Regarding the thickness of the trunk, the baobab, a typical tree of the African bush savannah, exceeds thirty meters in circumference. Eucalyptus trees, native to Australia, exceed six meters in diameter.

### What are the applications of trees?

Trees are nonlinear and dynamic structures used in many computational applications, especially in the construction of compilers, data mining, computational linguistics,… A tree is a structure in which each node can point (chain) to one or more nodes.

### What are binary trees and what are the basic operations and examples?

Full binary tree: is one in which all nodes have two children and all leaves are at the same level. – Each node, except the leaves, has the maximum number of children it can have. The nodes of the tree are structures that store the data, and pointers to the subtrees of that node.

### What does a complete binary tree look like?

Complete binary tree: A binary tree of height k is said to be complete if it is filled to height k-1 and the last level is occupied from left to right.

### Trees data structure examples

Trees are, without a doubt, one of the non-linear data structures used in computer science, both to solve hardware and software problems. The trees of directories are organizations quite employed by any user or programmer of a computer. They also play a good role in decision making, valid as a decision tree.

Family trees and organizational charts are common examples. Among other applications, trees are used to analyze electrical circuits and to represent the structure of mathematical formulas, as well as to organize information in databases, to represent the syntactic structure of a source program in compilers and for decision making.

Trees are data structures very similar to doubly linked lists, in the sense that they have pointers pointing to other elements, but they do not have a logical structure of linear or sequential type like those, but branched. They have a tree-like appearance, hence their name.