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Must recommend for the aspirants who are preparing for Amazon, Google, Microsoft, and Top Product Based Company interview. Logicmojo focus on techniques of solving data structures & system design problems
The course curriculum is of the best quality along with the best learning experience from my tutor. Best course to prepare for MAANG companies interview. I cracked Paytm, Adobe, Intuit, and Microsoft. Finally joined Microsoft at 1.3 Cr LPA Hyderabad MS IDC
Excellent course for interview preparation, very straight to the point ,in depth coverage of every point. Nice way of explaining solutions to very complex problems in easy way. It helps me to land at Architect Position in WalmartLabs as well as VISA.
I would say the best part is the explanation by the instructor, concise and clear. Great quality of online materials and classes, it covers all algorithms and system design problems asked during interviews
Great course! Definitely helped me open some new doors in understanding how algorithms work and implementing solutions for the different exercises
The course curriculum is of best quality along with good coding problems.It's like a quick interview preparation guide
Excellent course for interview preparation, very straight to the point ,in depth coverage of every point. Nice way of explaining solutions to very complex problems in easy way
Very well-arranged course and its amazing lectures. Focus on lectures concepts & techniques than solving thousands of problems of Leetcode. Problems set in the course is more than enough for top tech companies interviews.
Learn From Basic to Advanced DSA, Problem Solving, Scalable System Design (HLD + LLD),Design Patten etc
1:1 Mentorship
7 Months Classes
Life Time Access
LIVE Classes Weekend
Projects included
Learn From Basic to Advanced Data Structures, Algorithms & Problem-Solving techniques
1:1 Mentorship
4 Months Classes
Life Time Access
LIVE Classes Weekend
Projects included
Syllabus - DSA Course
Syllabus for the DSA Course in Logicmojo is comprehensive and structured to cater to a wide range of learners. It encompasses fundamental concepts, advanced DSA and analysis, and practical problem-solving techniques. The course is designed to provide a deep understanding of both theoretical and applied aspects of data structures and algorithms, ensuring a solid foundation for aspiring professionals. Additionally, it includes hands-on projects and real-world applications to reinforce learning and skill application.
Scalable System Design with HLD + LLD
(Duration - Next 3 months)
This course is curated by leading faculties and industry leaders to provide practical learning experience with live interactive classes and projects.
Advanced DSA & Problem Solving course
(Duration - First 4 months)
This course is curated by leading faculties and industry leaders to provide practical learning experience with live interactive classes and projects.
Eligibility For Logicmojo DSA Course
Eligibility criteria must be met for candidates to qualify for the DSA Course. A mentor will call every candidate before enrollment in the course
This course is primarly designed for working professionals. Talk to our experts for profile review before joining
Fresh graduates or undergraduates from a CS/IT background are eligible for this course.
Candidates who want to improve their problem-solving skills and knowledge of DSA can join this course.
All candidates who qualify for this course are eligible to receive job assistance in top product companies.
Live Classes Will Start From 24th Feb.This is a Live Demo Session For Upcoming Batch. Initial 4 months We Focus on Data Structures, Algorithms & Problems Solving Part Where We Prepare Candidates For MAANG Companies Coding Interviews Rounds
After Completion of the 4 Months Coding Part then Next 3 Months. We Focus on Scalable System Design Part, Archirectures & Internal Design of Many Scalable System Model with HLD + LLD. We prepare Candidates for System Design Rounds.
Average Annual
Base Salary (2024)
Average Salary Growth Annual
(Service Companies --> Top Product Companies)
Software Developer
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Annual (2019-2024)
Learn fundamentals of programming and understand time complexity.
Master array, string and linked list and implement real time project on Git and GitHub.
Learn fundamentals of programming of stack and queue and its useage.
Learn fundamentals of programming the hashing/heap sort in very simpler way.
Learn fundamentals concepts of OOPs and use it real projects.
String based and mathematical competitive programming practise,Hackerank, Hackerearch Practise in Live classes
Learn fundamentals of binary tree and N-ary tree and use it project/assignements.
Learn all about building responsive websites using HTML5 and CSS3; discuss key HTML5 APIs and their use cases.
Learn fundamentals of programming the world-wide web and its key stakeholders.
Learn fundamentals of programming the world-wide web and its key stakeholders.
Learn fundamentals of programming the world-wide web and its key stakeholders.
Complete Advanced data structures like Trie, Suffix Tree, Suffix Tree, ternary search trees etc
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What Are Data Structures and Algorithms?
Data structures refer to the way data is organized in a virtual system, such as a sequence of numbers or a table of data. Meanwhile, an algorithm is a set of instructions performed by a computer to transform input into output.
How Do Data Structures and Algorithms Work Together?
1. There are numerous algorithms designed for specific tasks that operate on different data structures with the same level of computational complexity. Algorithms can be thought of as dynamic elements that interact with static data structures.
2. The expression of data in code is adaptable. Once you comprehend the construction of algorithms, you can apply this knowledge across various programming languages. In essence, it's similar to understanding the syntax of a family of related languages. Understanding the foundational principles of programming languages and their organizing principles can facilitate faster learning and easier transitioning between different languages.
How to learn DSA Steps by Steps ?
DSA courses are crucial for learning complete Data Structures and Algorithms. In the video below, we explain how you can learn DSA step by step. Understanding DSA concepts step by step, with regular practice of the problems, is essential. The video explains how we can solve problems in every topic of DSA and how much time should be spent on each topic.
Why Learn Data Structures and Algorithms ?
1. To write code that is both efficient and can handle large amounts of data, it's important to understand various data structures and algorithms. With this knowledge, you can decide which data structure and algorithm to use in different situations to create optimized and scalable code.
2. Knowing about data structures and algorithms can assist you in utilizing time and memory more effectively by enabling you to write code that runs faster and uses less storage.
3. Having knowledge of data structures and algorithms can increase your chances of finding employment opportunities, as these concepts are commonly tested in job interviews across a range of organizations, such as Google, Facebook, and others.
How you can learn data structure and Algorithms ?
1. Learn DSA from Logicmojo
Logicmojo provides a comprehensive set of tutorials on data structures and algorithms, complete with relevant examples that are easy to understand. These tutorials are designed specifically for individuals with no prior experience in computer programming who wish to explore this field.
2. Get familiar with computational complexity
Big O notation is crucial for understanding the time and space complexity of algorithms, particularly in worst-case scenarios where the input size is at its maximum. Time scales range from linear to polynomial, exponential, and logarithmic, and each represents a different level of performance and expected computation time.
The performance of algorithms can vary drastically depending on the scale. For instance, a logarithmic scale may perform well with larger data sets and inputs, while an exponential scale may result in computations that never finish in time.
3. Understand different data structures and algorithm types
Read through basic data structure and algorithm types to get a better feel for the subject.
4. Get on-the-job training
Get a job in software engineering or a role where data structures and algorithms are implemented in order to best exercise your new knowledge.
Learn DSA From Logicmojo Course
For learning DSA, you can refer multiple courses for DSA. These DSA courses will help to you understand the concepts and complete your preparation for Data Structures and Algorithms in few months.
Below we have mentioned two DSA courses to prepare for Interviews.
1. Advanced Course of Data Structures, Algorithms(DSA) & System Design: This Course is for working professionals who wants to prepare DSA to switch there profile from service to top product companies.
2. Advanced Course of Data Structures, Algorithms(DSA) & Problem Solving: This Course is for Freshers candidates who wants to prepare DSA to start there Tech carrier in top product companies.
Features of Logicmojo DSA Course
Logicmojo DSA Course is designed for both working professionals and fresher candidates to prepare for DSA & System Design interviews. Along with live classes, the DSA course is equipped with many other features, as stated below.
1.Live Interactive Classes: Weekend Live classesfrom Experts of MAANG Companies.
2. Practical Experience through Projects: All Topics in DSA & System Design teaches with practical industry based projects.
3. Live Doubt Session: Assignments & Doubts will answered in seperate weekdays Live Doubt Session By Trainer.
4. Job Assistance: : All Candidadates in DSA Course will provided with Job Assistance in Top Product based Companies.
5. Incase Missed Classes: : Attend multiple batches with multiple trainers if you miss any sessions or Topic for 1 Year subscription.
6. LifeTime Access of Content: : Access all recording in the DSA Classes for Life time.
Below image explains all features in an elaborate way.
Need of Data Structures and Algorithms.
Common Data Structures and Algorithms.
Each of these data structures has its own level of computational complexity when performing
tasks like adding items or calculating aggregate measures, such as the mean, based on the data stored within
them.
Some common categories of algorithms are:
Importance of Data Structures and Algorithms :
Dsa optimize code with complexity : DSA plays a crucial role in reducing time complexity in code. Although a problem can be approached in various ways, selecting the most optimized approach can increase productivity and solve the problem in a shorter time frame. Learning data structures and algorithms can help achieve this optimization.
DSA improves CS Fundamenetal : Data structures and algorithms are regarded as the fundamental pillars of computer science. As technology evolves, the amount of data being stored also increases. However, large volumes of data can adversely affect the processing speed of computer systems. In such scenarios, data structures can be useful as they optimize the storage and utilization of data, leading to improved processing power of the computer.
Applications of Data Structures and Algorithms
In this link we explain in detail about Application of Data Structures & Algorithms
What are Algorithms?
Algorithms are the logical procedures used to manipulate data structures in order to solve problems. There are many different types of algorithms, each with its own unique set of advantages and disadvantages. Here are some of the most common types of algorithms:
Searching Algorithms
A searching algorithm is used to find a specific element in a data structure. There are many different searching algorithms, each with its own trade-offs in terms of efficiency and simplicity.
Sorting Algorithms
A sorting algorithm is used to rearrange the elements of a data structure in a specific order, such as alphabetical or numerical..
Logicmojo offering best online data structures and algorithms course for preparing coding interviews in 2024. All tech giant companies in 2024 focus on problem-solving during interviews irrespective of the domain you are working for or you’re a fresher. Learn data structure and algorithm for experts and finish your preparation in 2-3 months. We teach data structures and algorithms in Java, Python and C++ languages with complete code explanation.
Books For Data Structures and Algorithms
A superlative, contemporary, and user-friendly treatise on data structures and algorithms, this compendium has been meticulously crafted for undergraduate scholars in computer science and information science domains. Comprising thirteen chapters, the content is the brainchild of a global consortium of accomplished pedagogues, delving into the quintessential notions of algorithms, a plethora of pivotal data structures, and the art of interface design. The tome is replete with illustrative examples and schematics, judiciously interspersed with program codes to augment the learning experience..
The best way to learn data structure and algorithm courses is to practice every problem by yourself. Practice is only key to cracking top tech company's interviews. Experienced candidates must prepare for System Design problems also. Learn System Design, Distributed System as well as oops design from experts Instructor with 12+ experience in FAANG companies.
This book receives backing from a worldwide team of writers skilled in data structures and algorithms. Through its website at http://www.cs.pitt.edu/~jung/GrowingBook/, it offers valuable insights for both educators and learners to make the most of the authors' knowledge.
Contents of the Book:
This article contains a detailed view of all common data structures and algorithms we use in our daily life programming to allow readers to become well equipped.
Listed below are the topics discussed in this article:
Data Structure is a way of collecting and organising data in such a way that we can perform operations on these data in an effective way. Data Structures is about rendering data elements in terms of some relationship, for better organization and storage. Let’s say We have some data which has, student’s name “Shivam” and his age 13. Here Shivam is of String data type and 13 is of integer data type.
In simple language, Data Structures are structures programmed to store ordered data, so that various operations can be performed on it easily. It represents the knowledge of data to be organized in memory. It should be designed and implemented in such a way that it reduces the complexity and increases the efficiency.
As we have discussed above, anything that can store data can be called as a data structure, hence Integer, Float, Boolean, Char etc, all are data structures. They are known as Primitive Data Structures. Then we also have some complex Data Structures, which are used to store large and connected data. Some examples of Abstract Data Structure are Linked List, Stack, Queue, Tree, Graph etc.
All these data structures allow us to perform different operations on data. We select these based on our requirements.
Let’s Check out each of them in detail.
Linear data structures are those whose elements are in sequential and in ordered way. For example: Array, Linked list
An array is a linear data structure representing a group of similar elements, accessed by index. Some Properties of Array Data Structures:
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.
The singly linked list is a linear data structure in which each element of the list contains a pointer which points to the next element in the list. Each node has two components: data and a pointer next which point to the next node in the list.
Below the Single LinkedList Creation Animation
class LinkedList { Node head; // head of the list /* Linked list Node*/ class Node { int data; Node next; // Constructor to create a new node // Next is by default initialized // as null Node(int d) { data = d; } } }
Doubly Linked List is just same as singly Linked List except it contains an extra pointer, typically called previous pointer, together with next pointer and data.
// Class for Doubly Linked List public class DLL { Node head; // head of list /* Doubly Linked list Node*/ class Node { int data; Node prev; Node next; // Constructor to create a new node // next and prev is by default initialized as null Node(int d) { data = d; } } }
A circular linked list is a variation of a linked list in which the last node points to the first node, completing a full circle of nodes. You can say it doesn’t have null element at the end.
What is Stack?
Stack, an abstract data structure, is a collection of objects that are inserted and removed according to the last-in-first-out (LIFO) principle. Objects can be inserted into a stack at any point of time, but only the most recently inserted (that is, “last”) object can be removed at any time.
Listed below are properties of a stack:
Following are some of the applications in which stacks play an important role.
public void push(int data) throws Exception { if (size() == capacity) throw new Exception("Stack is full."); stackArray[++top] = data; }
public int pop() throws Exception { int data; if (isEmpty()) throw new Exception("Stack is empty."); data = stackArray[top]; stackArray[top--] = Integer.MIN_VALUE; return data; }
Let n be the number of elements in the stack. The complexities of stack operations with this representation can be given as:
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:
Operations on Circular Queue:
For enQueue
For Dequeue
Below is the code implementation in Java
// Java program for insertion and // deletion in Circular Queue Using Linked List import java.util.*; class Solution { // Structure of a Node static class Node { int data; Node link; } static class Queue { Node front, rear; } // Function to create Circular queue static void enQueue(Queue q, int value) { Node temp = new Node(); temp.data = value; if (q.front == null) q.front = temp; else q.rear.link = temp; q.rear = temp; q.rear.link = q.front; } // Function to delete element from Circular Queue static int deQueue(Queue q) { if (q.front == null) { System.out.printf("Queue is empty"); return Integer.MIN_VALUE; } // If this is the last node to be deleted int value; // Value to be dequeued if (q.front == q.rear) { value = q.front.data; q.front = null; q.rear = null; } else // There are more than one nodes { Node temp = q.front; value = temp.data; q.front = q.front.link; q.rear.link = q.front; } return value; } // Function displaying the elements of Circular Queue static void displayQueue(Queue q) { Node temp = q.front; System.out.printf("\nElements in Circular Queue are: "); while (temp.link != q.front) { System.out.printf("%d ", temp.data); temp = temp.link; } System.out.printf("%d", temp.data); } /* Driver of the program */ public static void main(String args[]) { // Create a queue and initialize front and rear Queue q = new Queue(); q.front = q.rear = null; // Inserting elements in Circular Queue enQueue(q, 14); enQueue(q, 22); enQueue(q, 6); // Display elements present in Circular Queue displayQueue(q); // Deleting elements from Circular Queue System.out.printf("\nDeleted value = %d", deQueue(q)); System.out.printf("\nDeleted value = %d", deQueue(q)); // Remaining elements in Circular Queue displayQueue(q); enQueue(q, 9); enQueue(q, 20); displayQueue(q); } }
Binary Tree is a hierarchical tree data structures in which each node has at most two children, which are referred to as the left child and the right child. Each binary tree has the following groups of nodes:
Root Node: It is the topmost node and often referred to as the main node because all other nodes can be reached from the root
Left Sub-Tree, which is also a binary tree
Right Sub-Tree, which is also a binary tree
Root:Topmost node in a tree.
Parent:Every node (excluding a root) in a tree is connected by a directed edge from exactly one other node. This node is called a parent.
Child:A node directly connected to another node when moving away from the root
Leaf/External node:Node with no children.
Internal node:Node with atleast one children.
Depth of a node:Number of edges from root to the node.
Height of a node:Number of edges from the node to the deepest leaf. Height of the tree is the height of the root
A binary tree can be traversed in two ways:
Depth First Traversal: In-order (Left-Root-Right), Preorder (Root-Left-Right) and Postorder (Left-Right-Root)
Breadth First Traversal: Level Order Traversal
Time Complexity of Tree Traversal: O(n)
The maximum number of nodes at level "n" = 2^{(n-1)}.
The maximum number of nodes of Binary Tree of height "h" = 2^{(h)}.
Below is the image which gives better visualization that how maximum number of nodes of Binary tree is 2^{(h)}
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.).
Undirected Graph:
In an undirected graph, nodes are connected by edges that are all bidirectional. For example if an edge connects node 1 and 2, we can traverse from node 1 to node 2, and from node 2 to 1.
Directed Graph:
In a directed graph, nodes are connected by directed edges – they only go in one direction. For example, if an edge connects node 1 and 2, but the arrow head points towards 2, we can only traverse from node 1 to node 2 – not in the opposite direction.
To create an Adjacency list, an array of lists is used. The size of the array is equal to the number of nodes. A single index, array[i] represents the list of nodes adjacent to the ith node.
For example, we have given below.
We use Java Collections to store the Array of Linked Lists.
class Graph{ private int numVertices; private LinkedList<integer> adjLists[]; }
An Adjacency Matrix is a 2D array of size V x V where V is the number of nodes in a graph. A slot matrix[i][j] = 1 indicates that there is an edge from node i to node j.
For example, we have given below.
Here is the implementation part in Java.
public AdjacencyMatrix(int vertex){ this.vertex = vertex; matrix = new int[vertex][vertex]; }
Algorithms are deeply connected with computer science, and with data structures in particular. An algorithm is a sequence of instructions that describes a way of solving a specific problem in a finite period of time. They are represented in two ways:
Flowcharts- It is a visual representation of an algorithm’s control flow
Pseudocode– It is a textual representation of an algorithm that approximates the final source code
Note: The performance of the algorithm is measured based on time complexity and space complexity. Mostly, the complexity of any algorithm is dependent on the problem and on the algorithm itself.
Let’s explore the two major categories of algorithms in Java, which are:
Sorting algorithms are algorithms that put elements of a list in a certain order. The most commonly used orders are numerical order and lexicographical order.
Let's dive into some famous sorting algorithms.
Bubble Sort is a simple algorithm which is used to sort a given set of n elements provided in form of an array with n number of elements. Bubble Sort compares all the element one by one and sort them based on their values.
It is known as bubble sort, because with every complete iteration the largest element in the given array, bubbles up towards the last place or the highest index, just like a water bubble rises up to the water surface.
Here’s pseudocode representing Bubble Sort Algorithm (ascending sort context).
a[] is an array of size N begin BubbleSort(a[]) declare integer i, j for i = 0 to N - 1 for j = 0 to N - i - 1 if a[j] > a[j+1] then swap a[j], a[j+1] end if end for return a end BubbleSort
Worst and Average Case Time Complexity: O(n*n) (The worst-case occurs when an array is reverse sorted).
Best Case Time Complexity:O(n) (Best case occurs when an array is already sorted).
Selection sorting is a combination of both searching and sorting. The algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from the unsorted part and putting it at a proper position in the array.
Here’s pseudocode representing Selection Sort Algorithm (ascending sort context).
a[] is an array of size N begin SelectionSort(a[]) for i = 0 to n - 1 /* set current element as minimum*/ min = i /* find the minimum element */ for j = i+1 to n if list[j] < list[min] then min = j; end if end for /* swap the minimum element with the current element*/ if min != i then swap list[min], list[i] end if end for end SelectionSort
Time Complexity: O(n2) as there are two nested loops.
Auxiliary Space: O(1).
Insertion Sort is a simple sorting algorithm which iterates through the list by consuming one input element at a time and builds the final sorted array. It is very simple and more effective on smaller data sets. It is stable and in-place sorting technique.
Here’s pseudocode representing Insertion Sort Algorithm (ascending sort context).
a[] is an array of size N begin InsertionSort(a[]) for i = 1 to N key = a[ i ] j = i - 1 while ( j >= 0 and a[ j ] > key0 a[ j+1 ] = x[ j ] j = j - 1 end while a[ j+1 ] = key end for end InsertionSort
Best Case: The best case is when input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., Θ(n)).
Worst Case: The simplest worst case input is an array sorted in reverse order
Quicksort algorithm is a fast, recursive, non-stable sort algorithm which works by the divide and conquer principle. It picks an element as pivot and partitions the given array around that picked pivot.
Steps to implement Quick sortHere’s pseudocode representing Quicksort Algorithm.
QuickSort(A as array, low as int, high as int){ if (low < high){ pivot_location = Partition(A,low,high) Quicksort(A,low, pivot_location) Quicksort(A, pivot_location + 1, high) } } Partition(A as array, low as int, high as int){ pivot = A[low] left = low for i = low + 1 to high{ if (A[i] < pivot) then{ swap(A[i], A[left + 1]) left = left + 1 } } swap(pivot,A[left]) return (left)}
The complexity of quicksort in the average case is Θ(n log(n)) and in the worst case is Θ(n2).
Mergesort is a fast, recursive, stable sort algorithm which also works by the divide and conquer principle. Similar to quicksort, merge sort divides the list of elements into two lists. These lists are sorted independently and then combined. During the combination of the lists, the elements are inserted (or merged) at the right place in the list
Here’s pseudocode representing Merge Sort Algorithm
procedure MergeSort( a as array ) if ( n == 1 ) return a var l1 as array = a[0] ... a[n/2] var l2 as array = a[n/2+1] ... a[n] l1 = mergesort( l1 ) l2 = mergesort( l2 ) return merge( l1, l2 ) end procedure procedure merge( a as array, b as array ) var c as array while ( a and b have elements ) if ( a[0] > b[0] ) add b[0] to the end of c remove b[0] from b else add a[0] to the end of c remove a[0] from a end if end while while ( a has elements ) add a[0] to the end of c remove a[0] from a end while while ( b has elements ) add b[0] to the end of c remove b[0] from b end while return c end procedure
Searching is one of the most common and frequently performed actions in regular business applications. Search algorithms are algorithms for finding an item with specified properties among a collection of items. Let’s explore two of the most commonly used searching algorithms.
Linear search or sequential search is the simplest search algorithm. It involves sequential searching for an element in the given data structure until either the element is found or the end of the structure is reached. If the element is found, then the location of the item is returned otherwise the algorithm returns NULL.
Here’s pseudocode representing Linear Search in Java:
procedure linear_search (a[] , value) for i = 0 to n-1 if a[i] = value then print "Found " return i end if print "Not found" end for end linear_search
It is a brute-force algorithm. While it certainly is the simplest, it’s most definitely is not the most common, due to its inefficiency. Time Complexity of Linear search is O(N).
Binary search, also known as logarithmic search, is a search algorithm that finds the position of a target value within an already sorted array. It divides the input collection into equal halves and the item is compared with the middle element of the list. If the element is found, the search ends there. Else, we continue looking for the element by dividing and selecting the appropriate partition of the array, based on if the target element is smaller or bigger than the middle element.
Here’s pseudocode representing Binary Search in Java:
Procedure binary_search a; sorted array n; size of array x; value to be searched lowerBound = 1 upperBound = n while x not found if upperBound < lowerBound EXIT: x does not exists. set midPoint = lowerBound + ( upperBound - lowerBound ) / 2 if A[midPoint] < x set lowerBound = midPoint + 1 if A[midPoint] > x set upperBound = midPoint - 1 if A[midPoint] = x EXIT: x found at location midPoint end while end procedure
Binary Search Time Complexity
In each iteration, the search space is getting divided by 2. That means that in the current iteration you have to deal with half of the previous iteration array.
Best case could be the case where the first mid-value get matched to the element to be searched
Best Time Complexity: O(1)
Average Time Complexity: O(logn)
Worst Time Complexity: O(logn)
Since we are not using any space so space complexity will be O(1)
This brings us to the end of this ‘Data Structures and Algorithms in Java’ article. We have covered one of the most fundamental and important topics of Java. Hope you are clear with all that has been shared with you in this article.
Make sure you practice as much as possible.The knowledge of Data Structures and Algorithms forms the basis for identifying programmers, giving yet another reason for tech enthusiasts to get upscaled. While data structures help in the organization of data, algorithms help find solutions to the unending data analysis problems.
So, if you are still unaware of Data Structures and Algorithms in Python, here is a detailed article that will help you understand and implement them.
Before moving on, take a look at all the topics discussed in over here:
Linear data structures in python are those whose elements are in sequential and in ordered way. For example: Linked list, Stack, 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.
The singly linked list is a linear data structure in which each element of the list contains a pointer which points to the next element in the list. Each node has two components: data and a pointer next which point to the next node in the list.
# Node class class Node: # Function to initialize the node object def __init__(self, data): self.data = data # Assign data self.next = None # Initialize # next as null # Linked List class class LinkedList: # Function to initialize the Linked # List object def __init__(self): self.head = None
Doubly Linked List is just same as singly Linked List except it contains an extra pointer, typically called previous pointer, together with next pointer and data.
# Node of a doubly linked list class Node: def __init__(self, next=None, prev=None, data=None): self.next = next # reference to next node in DLL self.prev = prev # reference to previous node in DLL self.data = data
A circular linked list is a variation of a linked list in which the last node points to the first node, completing a full circle of nodes. You can say it doesn’t have null element at the end.
What is Stack?
Stack, an abstract data structure, is a collection of objects that are inserted and removed according to the last-in-first-out (LIFO) principle. Objects can be inserted into a stack at any point of time, but only the most recently inserted (that is, “last”) object can be removed at any time.
Listed below are properties of a stack:
Following are some of the applications in which stacks play an important role.
class Stack: def __init__(self): self.elements = [] def push(self, data): self.elements.append(data) return data
class Stack: ## ... def pop(self): return self.elements.pop()
Let n be the number of elements in the stack. The complexities of stack operations with this representation can be given as:
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:
Operations on Circular Queue:
For enQueue
For Dequeue
Below is the code implementation in Python
# Python3 program for insertion and # deletion in Circular Queue # Structure of a Node class Node: def __init__(self): self.data = None self.link = None class Queue: def __init__(self): front = None rear = None # Function to create Circular queue def enQueue(q, value): temp = Node() temp.data = value if (q.front == None): q.front = temp else: q.rear.link = temp q.rear = temp q.rear.link = q.front # Function to delete element from # Circular Queue def deQueue(q): if (q.front == None): print("Queue is empty") return -999999999999 # If this is the last node to be deleted value = None # Value to be dequeued if (q.front == q.rear): value = q.front.data q.front = None q.rear = None else: # There are more than one nodes temp = q.front value = temp.data q.front = q.front.link q.rear.link = q.front return value # Function displaying the elements # of Circular Queue def displayQueue(q): temp = q.front print("Elements in Queue are:end="") while (temp.link != q.front): print(temp.data,end = " ") temp = temp.link print(temp.data) # Driver Code if __name__ == '__main__': # Create a queue and initialize # front and rear q = Queue() q.front = q.rear = None # Inserting elements in Circular Queue enQueue(q, 14) enQueue(q, 22) enQueue(q, 6) # Display elements present in # Circular Queue displayQueue(q) # Deleting elements from Circular Queue print("Deleted value = ", deQueue(q)) print("Deleted value = ", deQueue(q)) # Remaining elements in Circular Queue displayQueue(q) enQueue(q, 9) enQueue(q, 20) displayQueue(q)
Binary Tree is a hierarchical tree data structures in which each node has at most two children, which are referred to as the left child and the right child. Each binary tree has the following groups of nodes:
Root Node: It is the topmost node and often referred to as the main node because all other nodes can be reached from the root
Left Sub-Tree, which is also a binary tree
Right Sub-Tree, which is also a binary tree
Root:Topmost node in a tree.
Parent:Every node (excluding a root) in a tree is connected by a directed edge from exactly one other node. This node is called a parent.
Child:A node directly connected to another node when moving away from the root
Leaf/External node:Node with no children.
Internal node:Node with atleast one children.
Depth of a node:Number of edges from root to the node.
Height of a node:Number of edges from the node to the deepest leaf. Height of the tree is the height of the root
A binary tree can be traversed in two ways:
Depth First Traversal: In-order (Left-Root-Right), Preorder (Root-Left-Right) and Postorder (Left-Right-Root)
Breadth First Traversal: Level Order Traversal
Time Complexity of Tree Traversal: O(n)
The maximum number of nodes at level "n" = 2^{(n-1)}.
The maximum number of nodes of Binary Tree of height "h" = 2^{(h)}.
Below is the image which gives better visualization that how maximum number of nodes of Binary tree is 2^{(h)}
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.).
Undirected Graph:
In an undirected graph, nodes are connected by edges that are all bidirectional. For example if an edge connects node 1 and 2, we can traverse from node 1 to node 2, and from node 2 to 1.
Directed Graph:
In a directed graph, nodes are connected by directed edges – they only go in one direction. For example, if an edge connects node 1 and 2, but the arrow head points towards 2, we can only traverse from node 1 to node 2 – not in the opposite direction.
To create an Adjacency list, an array of lists is used. The size of the array is equal to the number of nodes. A single index, array[i] represents the list of nodes adjacent to the ith node.
For example, we have given below.
There is a reason Python gets so much love. A simple dictionary of vertices and its edges is a sufficient representation of a graph. You can make the vertex itself as complex as you want.
graph = {'A': set(['B', 'C']), 'B': set(['A', 'D', 'E']), 'C': set(['A', 'F']), 'D': set(['B']), 'E': set(['B', 'F']), 'F': set(['C', 'E'])}
An Adjacency Matrix is a 2D array of size V x V where V is the number of nodes in a graph. A slot matrix[i][j] = 1 indicates that there is an edge from node i to node j.
For example, we have given below.
Here is the implementation part in Python.
# Adjacency Matrix representation in Python class Graph(object): # Initialize the matrix def __init__(self, size): self.adjMatrix = [] for i in range(size): self.adjMatrix.append([0 for i in range(size)]) self.size = size # Add edges def add_edge(self, v1, v2): if v1 == v2: print("Same vertex %d and %d" % (v1, v2)) self.adjMatrix[v1][v2] = 1 self.adjMatrix[v2][v1] = 1 def main(): g = Graph(5) g.add_edge(0, 1) g.add_edge(0, 2) g.add_edge(1, 2) g.add_edge(2, 0) g.add_edge(2, 3) g.print_matrix() if __name__ == '__main__': main()
Python algorithms are a set of instructions that are executed to get the solution to a given problem. Since algorithms are not language-specific, they can be implemented in several programming languages. No standard rules guide the writing of algorithms.
Let’s explore the two major categories of algorithms in Python, which are:
Sorting algorithms are algorithms that put elements of a list in a certain order. The most commonly used orders are numerical order and lexicographical order.
Let's dive into some famous sorting algorithms.
Bubble Sort is a simple algorithm which is used to sort a given set of n elements provided in form of an array with n number of elements. Bubble Sort compares all the element one by one and sort them based on their values.
It is known as bubble sort, because with every complete iteration the largest element in the given array, bubbles up towards the last place or the highest index, just like a water bubble rises up to the water surface.
Here’s pseudocode representing Bubble Sort Algorithm (ascending sort context).
a[] is an array of size N begin BubbleSort(a[]) declare integer i, j for i = 0 to N - 1 for j = 0 to N - i - 1 if a[j] > a[j+1] then swap a[j], a[j+1] end if end for return a end BubbleSort
Worst and Average Case Time Complexity: O(n*n) (The worst-case occurs when an array is reverse sorted).
Best Case Time Complexity:O(n) (Best case occurs when an array is already sorted).
Selection sorting is a combination of both searching and sorting. The algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from the unsorted part and putting it at a proper position in the array.
Here’s pseudocode representing Selection Sort Algorithm (ascending sort context).
a[] is an array of size N begin SelectionSort(a[]) for i = 0 to n - 1 /* set current element as minimum*/ min = i /* find the minimum element */ for j = i+1 to n if list[j] < list[min] then min = j; end if end for /* swap the minimum element with the current element*/ if min != i then swap list[min], list[i] end if end for end SelectionSort
Time Complexity: O(n2) as there are two nested loops.
Auxiliary Space: O(1).
Insertion Sort is a simple sorting algorithm which iterates through the list by consuming one input element at a time and builds the final sorted array. It is very simple and more effective on smaller data sets. It is stable and in-place sorting technique.
Here’s pseudocode representing Insertion Sort Algorithm (ascending sort context).
a[] is an array of size N begin InsertionSort(a[]) for i = 1 to N key = a[ i ] j = i - 1 while ( j >= 0 and a[ j ] > key0 a[ j+1 ] = x[ j ] j = j - 1 end while a[ j+1 ] = key end for end InsertionSort
Best Case: The best case is when input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., Θ(n)).
Worst Case: The simplest worst case input is an array sorted in reverse order
Quicksort algorithm is a fast, recursive, non-stable sort algorithm which works by the divide and conquer principle. It picks an element as pivot and partitions the given array around that picked pivot.
Steps to implement Quick sort
Here’s pseudocode representing Quicksort Algorithm.
QuickSort(A as array, low as int, high as int){ if (low < high){ pivot_location = Partition(A,low,high) Quicksort(A,low, pivot_location) Quicksort(A, pivot_location + 1, high) } } Partition(A as array, low as int, high as int){ pivot = A[low] left = low for i = low + 1 to high{ if (A[i] < pivot) then{ swap(A[i], A[left + 1]) left = left + 1 } } swap(pivot,A[left]) return (left)}
The complexity of quicksort in the average case is Θ(n log(n)) and in the worst case is Θ(n2).
Mergesort is a fast, recursive, stable sort algorithm which also works by the divide and conquer principle. Similar to quicksort, merge sort divides the list of elements into two lists. These lists are sorted independently and then combined. During the combination of the lists, the elements are inserted (or merged) at the right place in the list
Here’s pseudocode representing Merge Sort Algorithm
procedure MergeSort( a as array ) if ( n == 1 ) return a var l1 as array = a[0] ... a[n/2] var l2 as array = a[n/2+1] ... a[n] l1 = mergesort( l1 ) l2 = mergesort( l2 ) return merge( l1, l2 ) end procedure procedure merge( a as array, b as array ) var c as array while ( a and b have elements ) if ( a[0] > b[0] ) add b[0] to the end of c remove b[0] from b else add a[0] to the end of c remove a[0] from a end if end while while ( a has elements ) add a[0] to the end of c remove a[0] from a end while while ( b has elements ) add b[0] to the end of c remove b[0] from b end while return c end procedure
Searching is one of the most common and frequently performed actions in regular business applications. Search algorithms are algorithms for finding an item with specified properties among a collection of items. Let’s explore two of the most commonly used searching algorithms.
Linear search or sequential search is the simplest search algorithm. It involves sequential searching for an element in the given data structure until either the element is found or the end of the structure is reached. If the element is found, then the location of the item is returned otherwise the algorithm returns NULL.
Here’s pseudocode representing Linear Search in Python:
procedure linear_search (a[] , value) for i = 0 to n-1 if a[i] = value then print "Found " return i end if print "Not found" end for end linear_search
It is a brute-force algorithm. While it certainly is the simplest, it’s most definitely is not the most common, due to its inefficiency. Time Complexity of Linear search is O(N).
Binary search, also known as logarithmic search, is a search algorithm that finds the position of a target value within an already sorted array. It divides the input collection into equal halves and the item is compared with the middle element of the list. If the element is found, the search ends there. Else, we continue looking for the element by dividing and selecting the appropriate partition of the array, based on if the target element is smaller or bigger than the middle element.
Here’s pseudocode representing Binary Search in Python:
Procedure binary_search a; sorted array n; size of array x; value to be searched lowerBound = 1 upperBound = n while x not found if upperBound < lowerBound EXIT: x does not exists. set midPoint = lowerBound + ( upperBound - lowerBound ) / 2 if A[midPoint] < x set lowerBound = midPoint + 1 if A[midPoint] > x set upperBound = midPoint - 1 if A[midPoint] = x EXIT: x found at location midPoint end while end procedure
Binary Search Time Complexity
In each iteration, the search space is getting divided by 2. That means that in the current iteration you have to deal with half of the previous iteration array.
Best case could be the case where the first mid-value get matched to the element to be searched
Best Time Complexity: O(1)
Average Time Complexity: O(logn)
Worst Time Complexity: O(logn)
Since we are not using any space so space complexity will be O(1)
This brings us to the end of this ‘Data Structures and Algorithms in Python’ article. We have covered one of the most fundamental and important topics of Python. Hope you are clear with all that has been shared with you in this article.
Make sure you practice as much as possible.Knowing some fundamental data structures and algorithms both in theory and from a practical implementation perspective helps you in being a better C++ programmer, gives you a good foundation to understand standard library’s containers and algorithms inner “under the hood” mechanics, and serves as a kind of knowledge that is required in several coding interviews, as well.
In this article, Data Structures and Algorithms in C++, you’ll learn how to implement some fundamental data structures and algorithms in C++ from scratch, with a combination of theoretical introduction using animation, and practical C++ implementation code as well.
Before moving on, take a look at all the topics discussed in over here:
Data Structure is a way of collecting and organising data in such a way that we can perform operations on these data in an effective way. Data Structures is about rendering data elements in terms of some relationship, for better organization and storage. Let’s say We have some data which has, student’s name “Shivam” and his age 13. Here Shivam is of String data type and 13 is of integer data type.
In simple language, Data Structures are structures programmed to store ordered data, so that various operations can be performed on it easily. It represents the knowledge of data to be organized in memory. It should be designed and implemented in such a way that it reduces the complexity and increases the efficiency.
Linear data structures in C++ are those whose elements are in sequential and in ordered way. For example: Array, Linked list, etc
An array is a linear data structure representing a group of similar elements, accessed by index. However, one shall not confuse array with the list like data structures in languages like python. Let us see arrays are presented in C++;
// simple declaration int array[] = {1, 2, 3, 4, 5 }; // in pointer form (refers to an object stored in heap) int * array = new int[5];
Note: However, we are accustomed to the more friendly vector
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.
The singly linked list is a linear data structure in which each element of the list contains a pointer which points to the next element in the list. Each node has two components: data and a pointer next which point to the next node in the list.
class Node { public: int data; Node* next; };
Doubly Linked List is just same as singly Linked List except it contains an extra pointer, typically called previous pointer, together with next pointer and data.
/* Node of a doubly linked list */ class Node { public: int data; Node* next; // Pointer to next node in DLL Node* prev; // Pointer to previous node in DLL };
A circular linked list is a variation of a linked list in which the last node points to the first node, completing a full circle of nodes. You can say it doesn’t have null element at the end.
What is Stack?
Stack, an abstract data structure, is a collection of objects that are inserted and removed according to the last-in-first-out (LIFO) principle. Objects can be inserted into a stack at any point of time, but only the most recently inserted (that is, “last”) object can be removed at any time.
Listed below are properties of a stack:
Following are some of the applications in which stacks play an important role.
void push(int val) { if(top>=n-1) cout<<"Stack Overflow"<<endl; else { top++; stack[top]=val; } }
void pop() { if(top<=-1) cout<<"Stack Underflow"<<endl; else { cout<<"The popped element is "<< stack[top] <<endl; top--; } }
Let n be the number of elements in the stack. The complexities of stack operations with this representation can be given as:
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:
Operations on Circular Queue:
For enQueue
For Dequeue
Below is the code implementation in C++
// C++ program for insertion and // deletion in Circular Queue #include <bits/stdc++.h> using namespace std; // Structure of a Node struct Node { int data; struct Node* link; }; struct Queue { struct Node *front, *rear; }; // Function to create Circular queue void enQueue(Queue* q, int value) { struct Node* temp = new Node; temp->data = value; if (q->front == NULL) q->front = temp; else q->rear->link = temp; q->rear = temp; q->rear->link = q->front; } // Function to delete element from Circular Queue int deQueue(Queue* q) { if (q->front == NULL) { printf("Queue is empty"); return INT_MIN; } // If this is the last node to be deleted int value; // Value to be dequeued if (q->front == q->rear) { value = q->front->data; free(q->front); q->front = NULL; q->rear = NULL; } else // There are more than one nodes { struct Node* temp = q->front; value = temp->data; q->front = q->front->link; q->rear->link = q->front; free(temp); } return value; } // Function displaying the elements of Circular Queue void displayQueue(struct Queue* q) { struct Node* temp = q->front; printf("\nElements in Circular Queue are: "); while (temp->link != q->front) { printf("%d ", temp->data); temp = temp->link; } printf("%d", temp->data); } /* Driver of the program */ int main() { // Create a queue and initialize front and rear Queue* q = new Queue; q->front = q->rear = NULL; // Inserting elements in Circular Queue enQueue(q, 14); enQueue(q, 22); enQueue(q, 6); // Display elements present in Circular Queue displayQueue(q); // Deleting elements from Circular Queue printf("\nDeleted value = %d", deQueue(q)); printf("\nDeleted value = %d", deQueue(q)); // Remaining elements in Circular Queue displayQueue(q); enQueue(q, 9); enQueue(q, 20); displayQueue(q); return 0; }
Binary Tree is a hierarchical tree data structures in which each node has at most two children, which are referred to as the left child and the right child. Each binary tree has the following groups of nodes:
Root Node: It is the topmost node and often referred to as the main node because all other nodes can be reached from the root
Left Sub-Tree, which is also a binary tree
Right Sub-Tree, which is also a binary tree
Root:Topmost node in a tree.
Parent:Every node (excluding a root) in a tree is connected by a directed edge from exactly one other node. This node is called a parent.
Child:A node directly connected to another node when moving away from the root
Leaf/External node:Node with no children.
Internal node:Node with atleast one children.
Depth of a node:Number of edges from root to the node.
Height of a node:Number of edges from the node to the deepest leaf. Height of the tree is the height of the root
A binary tree can be traversed in two ways:
Depth First Traversal: In-order (Left-Root-Right), Preorder (Root-Left-Right) and Postorder (Left-Right-Root)
Breadth First Traversal: Level Order Traversal
Time Complexity of Tree Traversal: O(n)
The maximum number of nodes at level "n" = 2^{(n-1)}.
The maximum number of nodes of Binary Tree of height "h" = 2^{(h)}.
Below is the image which gives better visualization that how maximum number of nodes of Binary tree is 2^{(h)}
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.).
Undirected Graph:
In an undirected graph, nodes are connected by edges that are all bidirectional. For example if an edge connects node 1 and 2, we can traverse from node 1 to node 2, and from node 2 to 1.
Directed Graph:
In a directed graph, nodes are connected by directed edges – they only go in one direction. For example, if an edge connects node 1 and 2, but the arrow head points towards 2, we can only traverse from node 1 to node 2 – not in the opposite direction.
To create an Adjacency list, an array of lists is used. The size of the array is equal to the number of nodes. A single index, array[i] represents the list of nodes adjacent to the ith node.
For example, we have given below.
class Graph{ int numVertices; list<int> *adjLists; public: Graph(int V); void addEdge(int src, int dest); };
An Adjacency Matrix is a 2D array of size V x V where V is the number of nodes in a graph. A slot matrix[i][j] = 1 indicates that there is an edge from node i to node j.
For example, we have given below.
Here is the implementation part in C++.
#include<iostream> using namespace std; int vertArr[20][20]; //the adjacency matrix initially 0 int count = 0; void displayMatrix(int v) { int i, j; for(i = 0; i < v; i++) { for(j = 0; j < v; j++) { cout << vertArr[i][j] << " "; } cout << endl; } } void add_edge(int u, int v) { //function to add edge into the matrix vertArr[u][v] = 1; vertArr[v][u] = 1; } main(int argc, char* argv[]) { int v = 6; //there are 6 vertices in the graph add_edge(0, 4); add_edge(0, 3); add_edge(1, 2); add_edge(1, 4); displayMatrix(v); }
Algorithms are a set of instructions that are executed to get the solution to a given problem. Since algorithms are not language-specific, they can be implemented in several programming languages. No standard rules guide the writing of algorithms.
Let’s explore the two major categories of algorithms in C++, which are:
Sorting algorithms are algorithms that put elements of a list in a certain order. The most commonly used orders are numerical order and lexicographical order.
Let's dive into some famous sorting algorithms.
Bubble Sort is a simple algorithm which is used to sort a given set of n elements provided in form of an array with n number of elements. Bubble Sort compares all the element one by one and sort them based on their values.
It is known as bubble sort, because with every complete iteration the largest element in the given array, bubbles up towards the last place or the highest index, just like a water bubble rises up to the water surface.
Here’s pseudocode representing Bubble Sort Algorithm (ascending sort context).
a[] is an array of size N begin BubbleSort(a[]) declare integer i, j for i = 0 to N - 1 for j = 0 to N - i - 1 if a[j] > a[j+1] then swap a[j], a[j+1] end if end for return a end BubbleSort
Worst and Average Case Time Complexity: O(n*n) (The worst-case occurs when an array is reverse sorted).
Best Case Time Complexity:O(n) (Best case occurs when an array is already sorted).
Selection sorting is a combination of both searching and sorting. The algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from the unsorted part and putting it at a proper position in the array.
Here’s pseudocode representing Selection Sort Algorithm (ascending sort context).
a[] is an array of size N begin SelectionSort(a[]) for i = 0 to n - 1 /* set current element as minimum*/ min = i /* find the minimum element */ for j = i+1 to n if list[j] < list[min] then min = j; end if end for /* swap the minimum element with the current element*/ if min != i then swap list[min], list[i] end if end for end SelectionSort
Time Complexity: O(n2) as there are two nested loops.
Auxiliary Space: O(1).
Insertion Sort is a simple sorting algorithm which iterates through the list by consuming one input element at a time and builds the final sorted array. It is very simple and more effective on smaller data sets. It is stable and in-place sorting technique.
Here’s pseudocode representing Insertion Sort Algorithm (ascending sort context).
a[] is an array of size N begin InsertionSort(a[]) for i = 1 to N key = a[ i ] j = i - 1 while ( j >= 0 and a[ j ] > key0 a[ j+1 ] = x[ j ] j = j - 1 end while a[ j+1 ] = key end for end InsertionSort
Best Case: The best case is when input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., Θ(n)).
Worst Case: The simplest worst case input is an array sorted in reverse order
Quicksort algorithm is a fast, recursive, non-stable sort algorithm which works by the divide and conquer principle. It picks an element as pivot and partitions the given array around that picked pivot.
Steps to implement Quick sort
Here’s pseudocode representing Quicksort Algorithm.
QuickSort(A as array, low as int, high as int){ if (low < high){ pivot_location = Partition(A,low,high) Quicksort(A,low, pivot_location) Quicksort(A, pivot_location + 1, high) } } Partition(A as array, low as int, high as int){ pivot = A[low] left = low for i = low + 1 to high{ if (A[i] < pivot) then{ swap(A[i], A[left + 1]) left = left + 1 } } swap(pivot,A[left]) return (left)}
The complexity of quicksort in the average case is Θ(n log(n)) and in the worst case is Θ(n2).
Mergesort is a fast, recursive, stable sort algorithm which also works by the divide and conquer principle. Similar to quicksort, merge sort divides the list of elements into two lists. These lists are sorted independently and then combined. During the combination of the lists, the elements are inserted (or merged) at the right place in the list
Here’s pseudocode representing Merge Sort Algorithm
procedure MergeSort( a as array ) if ( n == 1 ) return a var l1 as array = a[0] ... a[n/2] var l2 as array = a[n/2+1] ... a[n] l1 = mergesort( l1 ) l2 = mergesort( l2 ) return merge( l1, l2 ) end procedure procedure merge( a as array, b as array ) var c as array while ( a and b have elements ) if ( a[0] > b[0] ) add b[0] to the end of c remove b[0] from b else add a[0] to the end of c remove a[0] from a end if end while while ( a has elements ) add a[0] to the end of c remove a[0] from a end while while ( b has elements ) add b[0] to the end of c remove b[0] from b end while return c end procedure
Searching is one of the most common and frequently performed actions in regular business applications. Search algorithms are algorithms for finding an item with specified properties among a collection of items. Let’s explore two of the most commonly used searching algorithms.
Linear search or sequential search is the simplest search algorithm. It involves sequential searching for an element in the given data structure until either the element is found or the end of the structure is reached. If the element is found, then the location of the item is returned otherwise the algorithm returns NULL.
Here’s pseudocode representing Linear Search in C++:
procedure linear_search (a[] , value) for i = 0 to n-1 if a[i] = value then print "Found " return i end if print "Not found" end for end linear_search
It is a brute-force algorithm. While it certainly is the simplest, it’s most definitely is not the most common, due to its inefficiency. Time Complexity of Linear search is O(N).
Binary search, also known as logarithmic search, is a search algorithm that finds the position of a target value within an already sorted array. It divides the input collection into equal halves and the item is compared with the middle element of the list. If the element is found, the search ends there. Else, we continue looking for the element by dividing and selecting the appropriate partition of the array, based on if the target element is smaller or bigger than the middle element.
Here’s pseudocode representing Binary Search in C++:
Procedure binary_search a; sorted array n; size of array x; value to be searched lowerBound = 1 upperBound = n while x not found if upperBound < lowerBound EXIT: x does not exists. set midPoint = lowerBound + ( upperBound - lowerBound ) / 2 if A[midPoint] < x set lowerBound = midPoint + 1 if A[midPoint] > x set upperBound = midPoint - 1 if A[midPoint] = x EXIT: x found at location midPoint end while end procedure
Binary Search Time Complexity
In each iteration, the search space is getting divided by 2. That means that in the current iteration you have to deal with half of the previous iteration array.
Best case could be the case where the first mid-value get matched to the element to be searched
Best Time Complexity: O(1)
Average Time Complexity: O(logn)
Worst Time Complexity: O(logn)
Since we are not using any space so space complexity will be O(1)
This brings us to the end of this ‘Data Structures and Algorithms in C++’ article. We have covered one of the most fundamental and important topics of C++. Hope you are clear with all that has been shared with you in this article.
We have now reached the end of this page. With the knowledge from this page, you should be able to answers your interview question confidently.
Currently, All the product companies in the world ask data structures and algorithms based problems for
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Space & Time Complexity Before starting to learn Data Structures and Algorithms, it is also very important to understand how to measure the time and space complexity of a program. Based on these complexities we optimized our solutions during interviews.
In this Data Structures and Algorithms Course (DSA Course), our main focus is to teach the candidates how to visualize recursion. Start from array till Graph, Every topic is implemented mostly in recursion. So after space and Time complexity, our main aim is to make candidates well aware of recursions with multiple examples.
Learning Data Structures and Algorithms start with Array problems. Most candidates think array problems are easy and they skip it. But initial rounds of all product companies start with arrays problems. Data Structures and Algorithms course(DSA Course) also starts with a huge list of arrays problems to cover every aspect of it.
Unquestionably, no single "optimal" programming dialect exists for mastering Data Structures and Algorithms, as these tenets transcend language boundaries. Nonetheless, certain vernaculars garner favor in academia or facilitate novices' comprehension. Here are several esteemed alternatives:
1. Python: Frequently extolled for neophytes, Python boasts straightforward syntax and legibility. This adaptable language, replete with extensive library provisions, simplifies Data Structures and Algorithm implementation. A plethora of digital materials and pedagogical guides elucidate Python and DSA principles.
2. C++: A stalwart in competitive coding and technical interviews, C++ touts formidable object-oriented programming support and furnishes granular control over memory manipulation—a crucial component when devising intricate data structures. C++ presents a more precipitous learning trajectory compared to Python, yet it yields superior performance and a profound grasp of computer memory.
3. Java: Another sought-after contender for DSA mastery, Java features a potent object-oriented programming paradigm, innate data structure endorsement via the Java Collections Framework, and automatic memory management. While Java's syntax is more prolix than Python's, it strikes an agreeable equilibrium between user-friendliness and performance.
4. JavaScript: For those entrenched in web development or prioritizing client-side programming, JavaScript emerges as an apt selection. Though not as prevalent for DSA as previously discussed languages, JavaScript's versatility and burgeoning ecosystem render it a fitting choice for acquiring data structure and algorithm knowledge.
Ultimately, the prime language for Data Structures and Algorithms hinges on individual predilections, antecedent coding familiarity, and aspirations. Python offers an excellent springboard for programming novices. Conversely, those with programming background desiring to delve into memory management and performance may find solace in C++ or Java. Irrespective of the chosen language, concentrate on assimilating the fundamental concepts and axioms, as these transcend programming language barriers.
It's the same principles we learn while solving physics, Maths problems during school days. Try to identify the techniques while solving problems and use the same techniques problems for practice. So we won't forget. In Logicmojo Data Structures and Algorithms Course, we explain techniques of solving problems, and then we have assignments attach with the lecture based on the same techniques. So you have a good hands-on with all the concepts.
Learning Data Structures and algorithms in 2024 is a step-by-step process. It's not about writing any brute force, it's about solving problems by using some algorithms in an optimized manner. Logicmojo Data Structures and Algorithms course(DSA Course) covers all in-depth concepts with full code explanations.
A DSA course, or Data Structures and Algorithms course, is an educational program that teaches students the fundamentals of data structures and algorithms. Data structures are ways of organizing and storing data, while algorithms are sets of instructions or procedures for solving problems or performing tasks in computer programming. This course is typically designed for computer science and software engineering students or professionals who want to enhance their programming skills and understanding of computational problem-solving.
A DSA course usually covers topics such as
1. Basic data structures: Arrays, linked lists, stacks, queues, and hash tables.
2. Advanced data structures: Trees, graphs, heaps, and tries.
3. Sorting algorithms: Bubble sort, selection sort, insertion sort, merge sort, and quick sort.
4. Searching algorithms: Linear search, binary search, and depth-first and breadth-first graph traversal.
5. Algorithm design techniques: Divide and conquer, dynamic programming, greedy algorithms, and backtracking.
6. Algorithm analysis: Time complexity, space complexity, and Big O notation.
Completing a DSA course can help students develop strong problem-solving skills, improve their coding efficiency, and prepare them for technical interviews or advanced courses in computer science.
A Data Structures and Algorithms (DSA) course can be beneficial for a variety of individuals. Here are some groups of people who should consider taking a DSA course:
1. Computer Science students: Students pursuing a degree in computer science or a related field should learn about data structures and algorithms as they form the foundation of computer programming and problem-solving skills.
2. Aspiring software developers/engineers: If you plan to work in software development, a strong understanding of data structures and algorithms is essential. This knowledge helps in optimizing code, improving performance, and solving complex problems efficiently.
3. Professionals looking to upskill: Current software developers or IT professionals who want to improve their skills and stay competitive in the industry should consider taking a DSA course. This can help them tackle more challenging tasks and advance their careers.
4. Competitive programming enthusiasts: Participants in competitive programming contests, such as ACM ICPC, Google Code Jam, or LeetCode, can benefit from a DSA course. Mastery of data structures and algorithms is critical for success in these competitions.
5. Job seekers in the tech industry: Many tech companies, including top firms like Google, Amazon, and Facebook, test candidates' knowledge of data structures and algorithms during the interview process. Taking a DSA course can help prepare you for these interviews and increase your chances of securing a job.
6. Educators and mentors: Computer science educators and mentors who teach programming concepts to others can benefit from a DSA course to strengthen their own understanding and effectively convey these concepts to their students.
In summary, anyone interested in computer programming, problem-solving, or a career in the technology sector can benefit from taking a Data Structures and Algorithms course. It can help build a solid foundation for further learning and career growth.
A Data Structures and Algorithms (DSA) course, at its core, delves into the fundamental principles, architectural design, execution, and dissection of an array of data structures and algorithms. While prerequisites for a DSA course may fluctuate across institutions or specific offerings, the following generally remain constant:
1. Elementary coding acumen: Acquaintance with at least one programming language (e.g., C, C++, Java, Python, or JavaScript) is crucial, as well as comprehension of programming notions such as variables, iterations, conditionals, and functions.
2. Mathematical underpinnings: Grasping the rudiments of discrete mathematics, comprising concepts like sets, relations, functions, and graphs, is paramount for decoding the theoretical facets of data structures and algorithms.
3. Analytical prowess: DSA courses mandate robust analytical and critical cogitation abilities to concoct and scrutinize a variety of algorithms and data structures.
4. Foundational computer systems knowledge: Comprehending computer architecture, memory strata, and program execution processes is advantageous for discerning the efficacy of algorithms and data structures.
5. Data structures familiarity: Although the course elucidates data structures, possessing a rudimentary comprehension of prevalent data structures such as arrays, linked lists, stacks, and queues can facilitate a swifter mastery of the concepts.
6. Antecedent coursework (if applicable): Certain institutions may necessitate the completion of particular prerequisite courses prior to DSA course enrollment. These might encompass introductory programming, discrete mathematics, or computer systems courses.
For programming novices, contemplate enrolling in an elementary programming course or exploring tutorials and practice quandaries online before diving into a DSA course. This approach ensures a robust foundation in programming and problem-solving aptitudes, indispensable for flourishing in the realm of DSA.
A Data Structures and Algorithms (DSA) course typically covers a variety of topics that are fundamental to computer science and programming. Some of the key topics covered in a DSA course include:
1. Introduction to Data Structures and Algorithms: Basic concepts, algorithm analysis, time and space complexity, Big O notation.
2. Arrays: Static and dynamic arrays, multi-dimensional arrays, operations, and applications.
3. Linked Lists: Singly linked lists, doubly linked lists, circular linked lists, operations, and applications.
4. Stacks: Implementation, operations (push, pop, peek), and applications.
5. Queues: Implementation, operations (enqueue, dequeue, front, rear), priority queues, circular queues, and applications.
6. Trees: Binary trees, binary search trees, balanced trees (AVL, Red-Black), tree traversal techniques (in-order, pre-order, post-order), and applications.
7. Graphs: Representation (adjacency matrix, adjacency list), graph traversal algorithms (BFS, DFS), shortest path algorithms (Dijkstra, Bellman-Ford), minimum spanning tree algorithms (Prim, Kruskal), and applications.
8. Hashing: Hash functions, hash tables, collision resolution techniques (chaining, open addressing), and applications.
9. Sorting Algorithms: Bubble sort, selection sort, insertion sort, merge sort, quick sort, heap sort, counting sort, radix sort, and their time complexities.
10. Searching Algorithms: Linear search, binary search, interpolation search, and their time complexities.
11. Recursion: Basics of recursion, recursive algorithms, and examples (factorial, Fibonacci series, Tower of Hanoi).
12. Dynamic Programming: Introduction to dynamic programming, memoization, top-down and bottom-up approaches, examples (Fibonacci series, longest common subsequence, 0/1 knapsack problem).
13. Greedy Algorithms: Introduction to greedy algorithms, examples (fractional knapsack problem, minimum spanning tree, Huffman coding).
14. Backtracking: Introduction to backtracking, examples (N-Queens problem, graph coloring problem, Hamiltonian cycle).
15. Divide and Conquer: Introduction to divide and conquer, examples (merge sort, quick sort, Strassen's matrix multiplication).
These topics provide a solid foundation for understanding the principles and techniques used in designing and analyzing efficient algorithms and data structures, which are essential for solving complex problems in computer science and programming.
Imbibing the erudition of Data Structures and Algorithms (DSA) can yield multifarious boons, especially for those captivated by computer science, software engineering, or affiliated domains. Here are some pivotal merits to consider:
1. Improved problem-solving skills : DSA courses teach you how to analyze and solve complex problems methodically, making you a more effective problem solver in various domains.
2. Strong foundation in computer science: Understanding data structures and algorithms is fundamental to computer science. A DSA course lays the groundwork for more advanced topics and helps you develop a solid understanding of key principles.
3. Enhanced programming skills: DSA courses typically involve hands-on coding exercises, which help you become more proficient in your chosen programming language and enable you to write more efficient, maintainable code.
4. Better performance in technical interviews: Many tech companies assess candidates' knowledge of data structures and algorithms during interviews. A strong grasp of DSA concepts can give you an edge in the competitive job market.
5. Increased career opportunities: A thorough understanding of DSA concepts can open doors to various roles in software development, data science, and other technology fields.
6. Improved software performance: Learning how to choose the right data structure or algorithm for a particular task can lead to significant performance improvements in software applications.
7: Scalability and optimization: DSA courses help you understand how to build scalable systems and optimize resource usage, which is essential for handling large datasets or high-traffic applications.
8. Interdisciplinary applications: DSA concepts are applicable across various disciplines, including artificial intelligence, machine learning, and bioinformatics, making this knowledge valuable in diverse fields.
9. Lifelong learning : A DSA course lays the foundation for continuous learning in computer science and serves as a stepping stone to explore more advanced topics in the future.
10. Community and networking: By taking a DSA course, you can connect with like-minded individuals, share ideas, and build a professional network that can benefit your career in the long run
A Data Structures and Algorithms (DSA) course, at its core, delves into the fundamental principles, architectural design, execution, and dissection of an array of data structures and algorithms. While prerequisites for a DSA course may fluctuate across institutions or specific offerings, the following generally remain constant:
The duration of a Data Structures and Algorithms (DSA) course can vary greatly depending on the institution, course format, and the student's prior knowledge and dedication. A typical DSA course in a university or college setting may last for one semester, which is about 12 to 16 weeks. However, online courses and boot camps can have different timeframes, ranging from a few weeks to several months.
If you are self-studying, the time it takes to complete a DSA course can depend on your own pace and the amount of time you dedicate to learning. It's important to consider that mastering data structures and algorithms requires practice and hands-on experience, so allocating time for exercises and projects is crucial. In general, self-paced DSA learning can take anywhere from a few weeks to several months, depending on your commitment and available time.