Logicmojo - Updated Dec 12, 2024

Many a times Computer Science graduates devalue the importance of learning data structures and algorithms considering it as complicated, irrelevant or a waste of time.
However they soon get a reality check when they enter the real-world for job hunting. Big Companies like Amazon, Google, Microsoft often ask questions related to algorithms and data structures to check the problem-solving abilities of the candidates.
DSA provides a simple approach to evaluate problem-solving skills, coding skills and clarity of thought of a candidate.

The knowledge of data structures and algorithms forms the basis for identifying programmers, giving yet another reason for tech enthusiasts to get upscaled as well as upskilled.

There are both simple and complex data structures; they are designed to organize data in a way that makes it useful for a certain function. Fundamentally, data structures aim to provide information in a way that is understandable and accessible to both machines and people.

As per the technical definition: “Data structures are defined and orderly set of data arranged to make a process easier to follow.“

A variety of data values and the connections among them make up a data structure. Programs can efficiently store and analyze data thanks to data structures. There are numerous distinct data structures, and each has benefits and drawbacks of its own. Data structures including arrays, lists, trees, and graphs are some of the most popular ones.

Data structures are like hands for algorithms to make a recipe. Using a combination of data structure and algorithms, we can improve the performance of the program drastically. Any programming language's data structure is a fundamental idea that is required for algorithmic design.

**Hands = Data Structure**

**Recipe Book = Algorithm**

Data structures are like hands that organize data, and algorithms are like recipes that process data.

Using the right data structure and algorithm can drastically improve the performance of a program.

Data structures are essential for efficient and effective programming.

A data structure is a method of arranging data in order to make it more useful. Data Structure word used efficiently in this context, which refers to both space and time.

We can list the following as data structure operations:

1. a complex abstraction, such as the addition or deletion of items from a list.

2. searching and sorting a list's contents.

3. accessing the list item with the highest priority.

The data structure is referred to as an **Abstract Data Type (ADT)** whenever it performs these operations.

A stack, for example, is an ADT (abstract data type) that is implemented using either arrays or a linked list data structure. As a result, we infer that some data structure is required to implement a specific ADT.

An ADT specifies what should be done, while a data structure specifies how it should be done. To put it another way, ADT provides the blueprint, whereas data structure provides the implementation. Now the challenge is: how does one figure out the data structure to utilise for which ADT?

Although several data structures can be expressed in a single ADT, the different implementations are evaluated in terms of time and space. The Stack ADT, for example, can be built using both arrays and linked lists. Assume the array provides time efficiency while the linked list provides space efficiency; hence, the one best suited to the present user's requirements will be chosen.

When you're looking for an answer to your question, one of the most crucial things to discover is what data structure is. What is the benefit of data structure?

Data structures provide numerous benefits to IT-related processes, particularly as applications become more complex and the amount of data available grows. The following are some of the reasons why data structures are so important.

**Efficiency:** If the choice of a data structure for implementing a particular ADT is proper, it makes the program very efficient in terms of time and space.

**Reusability:** The data structure provides reusability means that multiple client programs can use the data structure

**Abstraction:** The data structure specified by an ADT also provides the level of abstraction. The client cannot see the internal working of the data structure,
so it does not have to worry about the implementation part. The client can only see the interface.

Data structure and algorithms rank among the most crucial components in computer science. We can organize and store data using data structures, and process it meaningfully using algorithms. Developing your knowledge of data structures and algorithms will make you a better programmer. You'll be able to create more dependable and effective code. Additionally, you'll be quicker and more efficient at problem-solving.

The following steps should be followed while selecting a data structure:

1. Analyzing the issue is the first step in figuring out the fundamental operations that must be supported. Examples of basic operations include adding a data item to the data structure, removing a data item from the data structure, and locating a specific data item.

2. Identify and quantify the resource limitations for each operation.

3. Establish which data structure best satisfies these demands.

Developers should think about the answers to the following three questions when choosing a data structure for a program or application:

**Supported operations: **What are the program's required functions and operations? Processes between the data types not included in the
table can be executed if the underlying data type of an attribute can be converted into one of the kinds for which an operation is supported.

**Complexity analysis: **What is the maximum level of computing performance that can be tolerated? A data structure with operations that execute in time proportional to the number of items
handled (Big O Notation: O(n)) will be faster than one with operations that execute in time proportional to the square of the number of items managed O(n^{2}).

**Programming elegance: **Is the data structure's organisation and functional interface simple to use? An elegant program is one of those things that is easy to recognize but hard to define.
It avoids using obfuscation and instead makes good use of language. It is concise without using difficult code.

**Data structures** are crucial tools in software development and data management, providing efficient ways to work with abstract data types.
They play a vital role in the creation of well-designed software, effective algorithms, and seamless data exchange between various
applications.

**Storing data:**Data structures are instrumental in storing information within database management systems. This involves defining attributes and associated structures to house records efficiently.**Managing resources and services:**They are used for managing core operating system resources and services, encompassing memory allocation, file directory administration, and process scheduling.**Ordering and sorting:**Data structures come into play when organizing and arranging data, whether it's character strings or objects with specific priorities.**Indexing:**Data structures facilitate indexing data, making it easier to locate specific items within a database.**Searching:**Creating indexes with data structures accelerates the process of finding particular items within a dataset.**Scalability:**Big data applications utilize data structures to allocate and manage data storage across distributed sites, ensuring optimal performance and scalability.

Here are some additional examples of data structures:

**Arrays:**Arrays are employed to store lists of items in a specific order.**Linked lists:**Linked lists store lists of items in arbitrary orders.**Hash tables:**Hash tables hold collections of key-value pairs.**Trees:**Trees serve as data structures for hierarchical data storage.**Graphs:**Graphs are used to represent interconnected data, such as social networks or roadmaps.

Understanding data structures empowers developers to write more efficient and effective software.

Data structures serve as a systematic means to organize data efficiently. Understanding their key characteristics is vital for data management and processing:

**Linear or Non-Linear:**Data structures can be categorized as either linear or non-linear. Linear structures, such as arrays and lists, organize data sequentially. Non-linear structures, like graphs and trees, arrange data in more complex, interconnected patterns.**Static and Dynamic:**Data structures can be static or dynamic. Static structures have fixed formats and sizes, with predetermined memory allocations. Dynamic structures, on the other hand, can adapt to changing data requirements as they allocate and deallocate memory as needed.**Time Complexity:**Effective data structures aim to optimize time complexity. The execution time of a program should be minimized to enhance performance. Reducing execution time leads to more efficient data processing and improved device responsiveness.**Correctness:**Every data structure should adhere to a specific interface, which defines its set of operations and behavior. Implementing data structures accurately within their interfaces ensures reliable data management and processing.**Space Complexity:**Efficient memory management is crucial. Data structures should minimize space utilization to avoid wastage and ensure optimal device functionality. Effective space management contributes to the efficient use of available resources.

These characteristics guide the design and selection of data structures, enabling data to be organized and processed in ways that meet specific requirements, whether for simple linear sequences or complex interconnected networks of data.

A data structure is used for processing, retrieving, storing, and organizing data in addition to structuring it.

Here are some Terminologies that will help you understand data structure:

**Data:** Values that is collected and organized.

**Data item:** A single piece of information.

**Group item:** A collection of related data items.

**Elementary item:** A data item that cannot be further divided.

**Entity:** A real-world object or concept that is represented in a database.

**Entity set:** A collection of similar entities.

**Field:** A single characteristic of an entity.

**Record:** A complete set of data about an entity.

**File:** A collection of related records.

A data structure provides a structured collection of variables that are variously related to one another. It serves as the foundation for a programming tool that denotes the relationships between the data items and enables effective data processing by programmers.

There are two types of Data Structures:-

1. Primitive Data Structures

2. Non-primitive Data Structures

⮞ **Primitive data structures** are those that come pre-built into programs and are made up of characters and numbers that can be directly edited or
used by machine-level instructions.
Due to the fact that they include characters that cannot be further subdivided, these data types are also known as simple data types.

Primitive data structures that can only carry one value include data types like **int, char, float, double,** and **pointer**.

⮞ **Non-primitive data structures** are complicated data structures descended from primitive data structures that are inaccessible to machine-level
instructions and cannot be directly modified or used. The non-primitive data types have been further divided into two distinct categories:

Linear Data Structures

Non Linear Data Structures

Data structures are divided into two categories:

**Linear Data Structures can be classified as:-** A linear data structure is one that maintains a linear link between each of its data items. With the exception of the first and last data elements, the data are arranged sequentially, with each element consisting of its predecessors and successors. In the case of memory, it may not always be the case, as the organization may not be sequential.

**Static Data Structures**are data structures that have their size stated and fixed at compile time and can't be modified later.

**Example**– Arrays**Dynamic data structures**are data structures whose size is not specified at compile time and can be determined at runtime based on requirements.

**Example**– Linked Lists, Stacks, and Queues

**Non Linear Data Structures:** Non-linear data structures are those in which the placement of data items is not linear or sequential. We cannot explore every
element of a non-linear data structure in a single operation.

**Example** Trees and graphs are two examples of non-linear data structures.

**Data types** are the fundamental building blocks of data structures and computer programs. The most common data types include:

**Boolean:**Stores logical values, such as`true`

or`false`

.**Integer:**Stores whole numbers, such as`1`

,`2`

, and`3`

.**Floating-point number:**Stores real numbers, such as`3.14`

and`1.6e2`

.**Fixed-point number:**Stores real numbers as digits to the left and right of the decimal point.**Character:**Stores a single character, such as`'a'`

or`'1'`

.**Pointer:**Stores a reference to another value in memory.**String:**Stores a sequence of characters, such as`"Hello, world!"`

.

Programming languages use data types to define the types of data that can be stored and manipulated. For example, a variable declared as an integer can only store whole numbers.

The kind of operations that will be necessary or the kinds of algorithms that will be used in a given situation will decide the data structure type that is employed. Let’s first list the different types of data structures, and then we’ll cover them one by one:

• Arrays

• Stacks

• Queues

• Linked Lists

• Trees

• Graphs

• Tries (they are effectively trees, but it’s still good to call them out separately).

• Hash Tables

An **Array** is the simplest and most widely used data structure. Other data structures like stacks and queues are derived from arrays.

Each data element is assigned a positive numerical value called the Index, which corresponds to the position of that item in the array. The majority of languages define the starting index of the array as 0.

**Array are of three types:**

1. One-Dimensional Array

2. Two-Dimensional Array

3. Multidimensional Array

**Insert** — Inserts an element at given index

**Get** — Returns the element at given index

**Delete** — Deletes an element at given index

**Size** — Get the total number of elements in array

⮞ Merge two sorted arrays

⮞ Search Rotated Array

⮞ Rearrange positive and negative values in an array

⮞ First non-repeating integers in an array

We are all familiar with the famous Undo option, which is present in almost every application. Ever wondered how it works? The idea: you store the previous states of your work (which are limited to a specific number) in the memory in such an order that the last one appears first. This can’t be done just by using arrays. That is where the Stack comes in handy.

A real-life example of Stack could be a pile of books placed in a vertical order. In order to get the book that’s somewhere in the middle,
you will need to remove all the books placed on top of it. This is how the **LIFO (Last In First Out)** method works.

**Push** — Inserts an element at the top

**Pop** — Returns the top element after removing from the stack

**isEmpty** — Returns true if the stack is empty

**Top** — Returns the top element without removing from the stack

⮞ Largest Rectangle in the Histogram

⮞ Evaluate postfix expression using a stack

⮞ Check balanced parentheses in an expression

⮞ Find Maximum size rectangle in Binary Sub-matrix

Queues are also another type of abstract data structure. Unlike a stack, the queue is a collection of objects that are inserted and removed according to the **first-in-first-out (FIFO) principle**.

Listed below are properties of a queue:

Often referred to as the first-in-first-out list

Supports two most fundamental methods **enqueue(e)**: Insert element e, at the rear of the queue **dequeue()**: Remove and return the element from the front of the queue

**Basic Operations on Queue**

When an element is inserted in a queue, the concept is called **EnQueue**.

When an element is removed from the queue, the concept is called **DeQueue**.

DeQueueing an empty queue is called **underflow (treat as Exception)**

EnQueuing an element in a full queue is called **overflow (treat as Exception)**.

⮞ Implement stack using a queue

⮞ Sliding Window Problem using deque Data Structure

⮞ Generate binary numbers from 1 to n using a queue

A linked list is a linear data structure with the collection of multiple nodes, where each element stores its own data and a pointer to the location of the next element. The last link of linked List points to null. An element in Linked List is called node. The first node is called head. The last node is called tail.

Linked lists are used to implement file systems, hash tables, and adjacency lists.

• **Singly linked list** — Traversal of items can be done in the forward direction only.

• **Doubly linked list** — Traversal of items can be done in both forward and backward directions. Nodes consist of an additional pointer known as prev, pointing to the previous node.

• **Circular linked lists** — Linked lists where the prev pointer of the head points to the tail and the next pointer of the tail points to the head.

**Basic operations of Linked List:**

**InsertAtEnd**- Inserts given element at the end of the linked list

**InsertAtHead**- Inserts given element at the start/head of the linked list

**Delete**- Deletes given element from the linked list

**DeleteAtHead**- Deletes first element of the linked list

**Search**- Returns the given element from a linked list

**isEmpty**- Returns true if the linked list is empty

⮞ Detect loop in a linked list

⮞ Reverse k node group in Linked list

⮞ Remove duplicates from a linked list

**What is graph (data structure)?**

A graph is a common data structure that consists of a finite set of **nodes (or vertices)** and a set of **edges** connecting them.

A **pair (x,y)** is referred to as an **edge**, which communicates that the x vertex connects to the y vertex.

Graphs are used to solve real-life problems that involve representation of the **problem space as a network**. Examples of networks include telephone networks, circuit networks, social networks (like LinkedIn, Facebook etc.).

Graphs in graph theory can take various forms and exhibit distinct characteristics. These types of graphs serve different purposes and are essential in various applications:

**Null Graph:**Also known as the order zero graph, a null graph contains no edges and consists solely of isolated vertices. It is essentially an empty graph.**Trivial Graph:**A trivial graph is formed by a single vertex, making it the smallest possible graph.**Finite Graph:**A graph is considered finite when the number of vertices and edges in the graph is limited or countable.**Infinite Graph:**An infinite graph is characterized by having an unlimited number of vertices and edges.**Directed Graph (Digraph):**In a directed graph or digraph, all edges connecting vertices have a defined direction, indicating their starting and ending points. These edges are directed, unlike in undirected graphs.**Simple Graph:**A simple graph has only one edge connecting any pair of nodes or vertices, representing one-to-one relationships between components.**Multigraph:**When multiple edges connect two vertices in a graph, it is referred to as a multigraph. Multigraphs do not have self-loops, meaning edges that loop back to the same vertex.**Complete Graph:**A complete graph is a simple graph where each pair of vertices is connected by an edge, resulting in each vertex having a degree of n-1. It represents a fully interconnected graph.**Pseudograph:**A pseudograph contains self-loops in addition to other edges, allowing vertices to be connected to themselves.**Regular Graph:**A regular graph is a simple graph in which every vertex has the same degree, meaning they all have an equal number of edges connected to them.**Bipartite Graph:**Bipartite graphs can be partitioned into two non-empty disjoint sets of vertices, denoted as V1(G) and V2(G), with edges connecting vertices from one set to the other. This structure is useful for certain applications.**Weighted Graph:**In a weighted graph, each edge is labeled with a value or weight, indicating the cost or significance of traversing that edge. These weights provide additional information for various algorithms.**Connected Graph:**A graph is considered connected if there is a path connecting any vertex to any other vertex within the graph.**Disconnected Graph:**A disconnected graph is one where there are no edges connecting its vertices, resulting in isolated components.**Cyclic Graph:**A graph is termed cyclic if it contains at least one graph cycle, which is a closed path through the graph.**Acyclic Graph:**An acyclic graph is one that does not contain any cycles, making it a tree-like structure.**Acyclic Directed Graph (DAG):**A directed acyclic graph (DAG) features directed edges and has no cycles. It is a valuable structure for various applications, including data processing and task scheduling.**Subgraph:**A subgraph is a subset of vertices and edges in one graph, forming a smaller graph contained within another graph. It inherits properties from the parent graph.

⮞ Breadth First Search

⮞ Depth First Search

⮞ Topological Sorting (Important)

Breadth-First Search algorithm is a graph traversing technique, where you select a random initial node (source or root node) and start traversing the graph layer-wise in such a way that all the nodes and their respective children nodes are visited and explored.

Now let’s take a look at the steps involved in traversing a graph by using Breadth-First Search:

• Take an Empty Queue.

• Select a starting node (visiting a node) and insert it into the Queue.

• Provided that the Queue is not empty, extract the node from the Queue and insert its child nodes (exploring a node) into the Queue.

• Print the extracted node.

The algorithm depth-first search searches or traverses a graph or tree data structure. Starting at a chosen root node (which can be any node in a graph data structure), the algorithm explores each feasible branch until it has to backtrack up to unexplored nodes.

Now let’s take a look at the steps involved in traversing a graph by using Depth-First Search:

• Visit the adjacent unvisited vertex. Mark it as visited. Display it. Push it in a stack.

• If no adjacent vertex is found, pop up a vertex from the stack. (It will pop up all the vertices from the stack, which do not have adjacent vertices.)

• Repeat Rule 1 and Rule 2 until the stack is empty.

For a Directed Acyclic Graph (DAG), topological sorting is a linear ordering of vertices in which vertex u occurs before v in the ordering for any directed edge u v. If the graph is not a DAG, topological sorting is not possible.

Now let’s take a look at the steps involved in topological Sorting:

• Enqueue the vertices with the in-degree of 0.

• While the queue is not empty dequeue a vertex. Add this vertex to the result.

• Decrement the in-degree of all its neighboring vertices by 1 in the array “local”.

• Enqueue the neighboring vertices with the in-degree of 0.

⮞ Implement Breadth and Depth First Search

⮞ Find the shortest path between two vertices

⮞ Check if a graph is a tree or not

A tree is a hierarchical data structure consisting of vertices (nodes) and edges that connect them. Trees are similar to graphs, but the key point that differentiates a tree from the graph is that a cycle cannot exist in a tree.

Data structures can be organized into various types of trees, each with unique characteristics and applications. These tree structures facilitate efficient data management and retrieval:

**General Tree:**In a general tree, hierarchy is not constrained, meaning that a node can have an unlimited number of children. All other tree types are subsets of general trees, making them highly versatile for various applications.**Binary Tree:**A binary tree is a tree structure where each parent node has, at most, two child nodes. This binary nature means each node can have zero, one, or two child nodes. Binary trees are widely used, and various modifications, such as AVL trees, binary search trees (BST), and red-black trees (RBT), are derived from this structure.**Binary Search Tree (BST):**BST is a type of binary tree where each node has, at most, two child nodes. It is named for its primary function: searching. BST enables efficient searches in O(log(n)) time, making it a valuable structure for tasks like searching and retrieval.**AVL Tree:**The AVL tree is a self-balancing binary search tree, invented by Adelson-Velsky and Landis. It maintains balance by assigning balancing factors to each node. Balancing factors of -1, 0, or 1 indicate the right balance. When adding a new node, rotations are performed to ensure balance. Common operations in AVL trees, such as viewing, insertion, and removal, have a time complexity of O(log(n)).**B Tree:**The B Tree is a more generalized binary search tree. It is referred to as a height-balanced m-way tree, with 'm' indicating the order of the tree. B Trees allow multiple keys and more than two child nodes per node. Unlike other binary trees, B Tree's leaf nodes may not be at the same level, and ensuring equal height of all leaf nodes is essential for its functionality.

⮞ Find kth maximum value in a binary search tree

⮞ LCA of given nodes in binary tree

⮞ Find the height of a binary tree

⮞ Find the Diameter of a binary tree

Trie is an efficient information retrieval data structure. Using Trie, search complexities can be brought to optimal limit (key length). If we store keys in binary search tree,
a well balanced BST will need time proportional to M * log N, where M is maximum string length and N is number of keys in tree. Using Trie, we can search the key in **O(M) time**.

Every node of Trie consists of multiple branches. Each branch represents a possible character of keys. We need to mark the last node of every key as end of word node. A Trie node field isEndOfWord is used to distinguish the node as end of word node. A simple structure to represent nodes of the English alphabet can be as following,

struct TrieNode { struct TrieNode *children[ALPHABET_SIZE]; // isEndOfWord is true if the node represents // end of a word bool isEndOfWord; };

⮞ Sort elements of an array using Trie

⮞ Auto Complete Suggestion

⮞ Count total number of words in Trie

Hashing is a process used to uniquely identify objects and store each object at some pre-calculated unique index called its “key.” So, the object is stored in the form of a “key-value” pair, and the collection of such items is called a “dictionary.” Each object can be searched using that key. There are different data structures based on hashing, but the most commonly used data structure is the hash table.

The performance of hashing data structure depends upon these three factors:

**Hash Function**

**Size of the Hash Table**

**Collision Handling Method**

1. The data being hashed completely determines the hash value.

2. All of the input data is used by the hash function.

3. The hash function distributes the data "uniformly" across all possible hash values.

4. For similar strings, the hash function generates very different hash values.

⮞ Design and Implement LRU cache->Imp

⮞ Group Anagrams Together

⮞ Four Sum Problem

We have learned lot about " What is Data Structure and it types", now lets learn about where it is applicable.

Data structures is the core of software development, any efficient method to a given problem is contingent on how effectively data is arranged. Hash tables are used to build identifier lookups in compiler implementations.The B-tree data structures are appropriate for use in databases.

The following are some of the most important areas where data structures are used:

**Artificial Intelligence:**Data structures are vital for managing and optimizing large volumes of data in AI applications, facilitating efficient pattern recognition, decision-making, and problem-solving algorithms.**Compiler Design:**Data structures like hash tables play a crucial role in compiler implementations, enabling efficient identifier lookups and symbol table management during code compilation.**Machine Learning:**Data structures are essential for organizing and processing training datasets, enabling machine learning algorithms to classify, predict, and learn from data effectively.**Database Design and Management:**Databases rely on data structures like B-trees to ensure efficient data retrieval, insertion, and modification, maintaining the integrity and performance of database systems.**Blockchain:**Data structures underpin the decentralized nature of blockchain technology, helping record and secure transaction data in a tamper-resistant and distributed ledger format.**Numerical and Statistical Analysis:**Data structures support numerical and statistical analysis by organizing data for various computational tasks, such as simulations, optimization, and data-driven insights.**Operating System Development:**Data structures are fundamental components in OS development, providing efficient memory management, process scheduling, file system organization, and interprocess communication.**Image & Speech Processing:**Data structures assist in representing, processing, and analyzing multimedia data, contributing to applications like image recognition, speech synthesis, and digital signal processing.**Cryptography:**Cryptographic algorithms rely on data structures to securely store keys and manage encrypted data, ensuring the confidentiality and integrity of sensitive information.

The actual reason behind your learning can improve your knowledge in the domain accordingly. For example, some people learn them particularly to suffice job interviews, few to make their resumes look better, etc. While others might learn to ace competitive programming. Regardless of the reason for learning data structures and algorithms, there are benefits pertaining to knowledge. The following are some of those benefits.

This means that a programmer can write the correct code if they knew both data structures and algorithms.

There can many different types of loop statements based on the desired outcome. However, there are for core types that are:

1. For

2. While/do

3. Repeat/until

4. Infinite looping

Here you need to arrange and keep everything (data) in such a structure that whenever you need to search something you get that easily and as soon as possible.

Now take the example of a library. If you need to find a book on Algorithm from a library, you will go to the Programing section first, then the Algorithm books section. If these books are not organized in this manner and just distributed randomly then it will be frustrating to find a specific book. So data structures refer to the way we organize information on our computer. Computer scientists process and look for the best way we can organize the data we have, so it can be better processed based on the input provided.

**Note**: Knowing the many types of data structures available aids the programmer in determining which data structure is ideal for solving an issue quickly. It's not only about getting an issue to work; it's also about getting it to work efficiently.

Here is the most hot topic that is going among all the passionate Software Engineers out there, How can I get into my dream Company? It can be any Top Product companies ( Google, Facebook, Amazon, Microsoft, Flipkart) or any Great Start-up.

Hold on, But that is not that simple. you can read tons of stories, but you have to figure out the one which works for you guys. So this is not going to give straight forward answer

This is the story of every newbie ☠️ who is unfamiliar with the interview procedure at the top tech companies. The interviews for technical roles in some of the tech giants like Google, Facebook, Amazon, Microsoft is more focused on measuring the knowledge of Data Structures and Algorithms of the candidates. The main reason behind this is Data Structures and Algorithms improves the problem-solving ability of a candidate to a great extent

“Choosing the best possible data structure or algorithm to solve a problem affects the time and space complexity of the solution, which the interviewer is looking for”

These skills not only help a student in getting a highly-paid job but helps him to sustain in this ever-growing software industry.

**Searching**

In the ideal case scenario, while searching for an element in a hash map, the element is found directly at the position given by its key. So all we have to do now
is compute the hash key and retrieve the element. This is accomplished in a constant amount of time. As a result, **the best case complexity is O(1)**.

In the worst-case scenario, the hash map is completely full. To get a search result in the case of open addressing for collisions, we'll have to go over the complete hash map and check every element. In the case of chaining, all of the elements will be contained in a single linked list. To produce good search results, the search algorithm must traverse the full linked list and examine every node.

Because all items are checked one by one, the **worst-case complexity rises to O(n)**. In the worst-case scenario, linear searching is likewise O(n),
whereas binary searching keeps the order of log n.

**Insertion & Deletion**

Both insertion and deletion have O(n) complexity in the worst-case scenario. Because of a collision, all nodes are connected to the same linked list.

The above are the top eight data structures that part of "What is Data Structure?" & you should definitely know before walking into a coding interview. If you are looking for resources on data structures for coding interviews, look at the interactive & challenge based courses: learning Data Structures and Algorithms Concepts

**Good luck and happy learning!**

Let's explore the concept of a data structure. Essentially, a data structure is a systematic way of assembling data. Its primary function is to store data on a computer in such a way that it can be efficiently used. There are numerous types of data structures, including lists, which keep items in a sequential order; arrays, another type of ordered sequence; trees, which arrange items in a hierarchical fashion; graphs, which maintain information about the relationships between items; and files, which hold related data.

Having discussed what a data structure is and its definition, let's consider an example. Suppose you wish to record a person's name and age. You could employ two distinct variables for this purpose: one for the name and another for the age. This approach is referred to as an array. An array, as a kind of data structure, enables the concurrent storage of several pieces of information.

Data structures are specific methods of arranging and storing data within a computer system to enable efficient access and modification. They encompass arrays, linked lists, stacks, queues, trees, and graphs. The selection of a data structure typically relies on the application's characteristics and the types of operations needed.

Having grasped the concept of data structures, it's essential to understand their importance – they play a crucial role because they enable us to sort data in a manner that facilitates easy access and modification. Here are some of the key benefits that data structures offer:

1. One of the significant perks of data structures is their ability to arrange data in a manner that makes accessing, modifying, and storing it a breeze.

2. Another major advantage of data structures is their capacity to help us discover and recognize connections between various data pieces.

3. Data structures are incredibly versatile, capable of storing a diverse range of information - from numbers and text to images, and even intricate entities like database records or programs.