Whether you are a veteran coder or an aspiring one, you will need to master data structures. These abstract concepts are integral to all kinds of computer processes, from matrix manipulation to machine learning & data mining. Data structures are the most effective and efficient ways to store data so that different operations can be carried out.

There are different types of data structures in computer science, each with its traits & features. This data structure __programming help__ article offers a concise overview of all the major kinds of data structures alongside examples of certain operations carried out.

Let’s begin.

**Non-Primitive Data Structures: The Fundamentals**

**Non-Primitive Data Structures: The Fundamentals**

Data structures are a way to store data and often encapsulate information regarding the storage framework and the operations supported. Those operations via which their data can be accessed/manipulated are clubbed together to represent a mathematical model referred to as abstract data types (ADTs).

ADTs define the logical specification/abstraction; *data structures are the logical implementations or representations of those abstract data types.*

**Basic data structures**such as arrays, linked lists, dynamic arrays, and hash tables are*sequential or linear data structures.**Advanced data structures, such as trees, graphs, etc., are**non-sequential**.*

are the simplest data structures and most suited for basic static operations, but they are not so good in dynamic processes. Traversing the entire array, and retrieving, inserting, and removing elements at a particular location are generally supported.*Arrays*

use pointer nodes to store the memory addresses of subsequent or the data next in sequence. The pointer values of nodes can be manipulated to link to other data in the sequence. Insertion and removal are two fundamental operations for linked lists.*Linked lists*

- The first node points to the data located at the
of the linked list, the initial memory pointer. Stacks and queues are two of the most commonly used linked lists.*head*

support LIFO (*Stacks*-based operations, wherein the previous item to be inserted is also the first to be removed from the list. The head, thus, points to the final element inserted, and insertion & deletion are done at the same end.*last in, first out)*

* *

supports FIFO (*Queue*-based operations, where the first item to be inserted is also the first to be removed. Queues are double-ended, wherein elements enqueue at one end and dequeue at the other.*first in, first out)*

combine the best features of both stacks and queues. Elements can be inserted and deleted at both ends of the linked list.*Double-ended queues*

are those whose sizes can be changed as items are inserted or removed. The ratio of items to space available is a key factor, and extra spaces are allocated when it is equal to one. Shadow copies of the data set within the existing array are done onto the newly allocated space.*Dynamic arrays*

Data structure programming requires a thorough understanding and clear concepts about the features of different data structures & how to implement them for various purposes. Diligent practice and cracking tough programming assignments are essential for developing superb skills & expert programming __assignment help____ online__ from major programming help services.

Let us now take a look at some advanced forms of data structures.

**Non-Linear Data Structures**

**Non-Linear Data Structures**

Search trees, balanced search trees, heaps, tries, binary heaps, hash tables, tries, etc., are some examples of advanced data structures. Unfortunately, we need more time or space to discuss extensively in-depth each type. Thus, we will mull over the fundamental structures that are modified & manipulated to design enhanced versions of advanced data structures.

**Binary Trees**

Search trees store objects that are identified by key values. The keys are generally in sequence and are used to guide access to objects/elements in trees. Trees have roots from where the search starts and are fundamental to most data structure types. They support different kinds of modifications and variations & serve as building blocks for much more complex data structures.

- Trees store elements in a hierarchical fashion. The top element is the root, and every other element has a parent except it. Including the root, elements in an array can have 0 to more children.

- Nodes have a direct parent-child relationship. Nodes that have the same parent are siblings. Complete binary trees store data from left to right; left child nodes must be filled before their right sibling.

- A search tree can have multiple levels, and the maximum level of nodes in a search tree is also known as the tree’s height, which is the number of edges from the root to the furthest or lowest node.

- The depth or level of a particular node is its distance or the number of edges from the root to that node. Leave the nodes at the lowest level or with the maximum depth.

- When implemented in a programming language, an element in a binary search tree stores data and points to two different locations/elements, that is, its children. In some cases, data objects may only reside in the leaf nodes.

- The generic binary search tree model can be empty, consist of only a leaf, or comprise a root node that leads to non-empty sub-trees. Children nodes on the left have a lower key value than their parent, while those on the right are higher.

- Nodes of binary trees generally comprise three components àthe key, a pointer to the right child, and a pointer to the left child.

- Binary search trees are ordered versions of binary trees that exhibit the
*binary search tree property**à.*

* *

- All nodes in the left subtree of a BST have key values LESS THAN or EQUAL TO their parent node.

- Nodes in the right subtree have key values GREATER THAN the preceding or parent node.

- Irrespective of how a binary search tree is implemented, they all must comprise interfaces for finding the root & the size of a tree, finding the parent & children of a node, etc.

Binary trees can be tough to master in one go. Think deeply, read more, and solve your data structure assignments diligently. Find out more about binary trees from this article from Stanford University.

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**Graphs **

Graphs are data structures that, you guessed it, use vertices and edges to store data optimally. The graph’s edges represent the relationships between the data/entities stored in the vertices.

- A graph can be represented as a pair consisting of vertices and edges ->
**G =(V, E)** - Set of vertices are also known as nodes à
**V =(V1, V2, V3,…..VN)** - Similarly, we have a set of edges à
**E = (E1, E2,E3,…EN)** - Every edge must comprise a pair of vertices à
**E= (V**_{i}**, V**_{j}We can, thus, consider edges to be information that establishes some connection between the information stored in the nodes.**).** - Graphs can be directed or Directed graphs can signify dependent or cascading relationships, while the edges of undirected graphs exhibit mutual, two-way dependencies. +

Interested in learning more about graphs? Check out these lecture notes from the University of Washington, Seattle.

**Heaps**

Heaps are data structures based on binary trees (not on binary search trees, as they are not ordered). They exhibit excellent dynamic properties & come in handy when the elements to be sorted are unknown beforehand.

Heaps, also called binary heaps, are built upon complete binary trees. The root node is assigned an index value **i=1, **and all subsequent left child nodes are assigned index values

**& right child node**

*2i*

*2i+1**For a binary tree to be complete, given indices must be contiguous.*

*.*Heaps can be of two types: **min heap **and

*max heap.*are complete binary trees where the values stored in the nodes increase progressively from the root to the leaves; the root stores the lowest value & the children hold progressively larger values. Child nodes must store lower values than their parent, with left child node values being lower than right child values.**Min heaps**

are the opposite, with the root storing the maximum value and subsequent nodes holding lower values.**Max heaps**

Well, that’s all the space we have for today. Hope this write comes up of some use to anyone who goes through it. Excelling in data structures and algorithms takes time & hard work—look for expert programming help online to shore up your learning and score top grades.

All the best!

** Author-Bio:** Aaron Benjamin is a back-end developer with a major software outsourcing firm in Nebraska, USA. He is also a part-time tutor and programming assignment helper with AllEssayWriter.com, a leading global programming assignment writing help service.