## Mastering Backtracking: A Comprehensive Guide to Solving Complex Problems in DAA

Learn the general method of backtracking in DAA and how to apply it to solve complex problems. Understand the concept, algorithm, and examples of backtracking.

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## General Method of Backtracking in DAA: A Comprehensive Guide

Backtracking is a fundamental concept in computer science, particularly in the field of Design and Analysis of Algorithms (DAA). It is a powerful technique used to solve complex problems by systematically exploring all possible solutions. In this blog post, we will delve into the general method of backtracking in DAA, its applications, and examples.

## What is Backtracking?

Backtracking is a problem-solving strategy that involves recursively exploring all possible solutions to a problem. It is a form of brute force approach that systematically generates all possible solutions and checks if any of them satisfy the problem's constraints. The backtracking algorithm is particularly useful for solving constraint satisfaction problems, where the goal is to find a solution that satisfies a set of constraints.

## The General Method of Backtracking

The general method of backtracking involves the following steps:

## 1. Choose a Variable

Select a variable from the problem's domain. This variable will be used to generate possible solutions.

## 2. Generate a Possible Solution

Generate a possible solution by assigning a value to the chosen variable.

## 3. Constraint Checking

Check if the generated solution satisfies the problem's constraints. If it does, then recursively explore the solution space by assigning values to the remaining variables.

## 4. Backtrack

If the generated solution does not satisfy the constraints, then backtrack by undoing the last assignment and exploring alternative solutions.

Repeat steps 2-4 until a solution is found or all possible solutions have been explored.

## Examples of Backtracking Algorithms

1. n-queens problem.

The N-Queens problem is a classic example of a backtracking algorithm. The problem involves placing N queens on an NxN chessboard such that no queen attacks another. The backtracking algorithm works by placing queens one by one on the board, checking for conflicts, and backtracking when a conflict is found.

Sudoku is another popular puzzle that can be solved using backtracking. The algorithm works by filling in the puzzle grid one cell at a time, checking for validity, and backtracking when an invalid solution is found.

## 3. Traveling Salesman Problem

The Traveling Salesman Problem is a classic problem in computer science that involves finding the shortest possible tour that visits a set of cities and returns to the starting city. The backtracking algorithm works by generating all possible tours and checking for the shortest tour.

## Advantages of Backtracking

1. guaranteed solution.

Backtracking guarantees a solution to the problem, provided the problem has a solution.

## 2. Flexibility

Backtracking can be used to solve a wide range of problems, from simple puzzles to complex optimization problems.

## 3. Easy to Implement

Backtracking algorithms are relatively easy to implement, especially for small problems.

## Disadvantages of Backtracking

1. computational complexity.

Backtracking algorithms can be computationally expensive, especially for large problems.

## 2. Space Complexity

Backtracking algorithms require a significant amount of memory to store the solution space.

## 3. Difficulty in Handling Constraints

Backtracking algorithms can struggle to handle complex constraints, leading to inefficient solutions.

## Real-World Applications of Backtracking

1. cryptography.

Backtracking is used in cryptography to break certain encryption algorithms.

## 2. Scheduling

Backtracking is used in scheduling algorithms to find the optimal schedule for a set of tasks.

## 3. Resource Allocation

Backtracking is used in resource allocation algorithms to allocate resources efficiently.

In conclusion, backtracking is a powerful technique used to solve complex problems in computer science. The general method of backtracking involves choosing a variable, generating a possible solution, constraint checking, backtracking, and repeating the process until a solution is found. Backtracking has numerous advantages, including guaranteed solutions, flexibility, and ease of implementation. However, it also has disadvantages, including high computational complexity, space complexity, and difficulty in handling constraints. Despite these limitations, backtracking has numerous real-world applications in cryptography, scheduling, and resource allocation.

- Design and Analysis of Algorithms
- Basics of Algorithms
- DAA - Introduction to Algorithms
- DAA - Analysis of Algorithms
- DAA - Methodology of Analysis
- DAA - Asymptotic Notations & Apriori Analysis
- DAA - Time Complexity
- DAA - Master's Theorem
- DAA - Space Complexities
- Divide & Conquer
- DAA - Divide & Conquer Algorithm
- DAA - Max-Min Problem
- DAA - Merge Sort Algorithm
- DAA - Binary Search
- DAA - Strassen's Matrix Multiplication
- DAA - Karatsuba Algorithm
- DAA - Towers of Hanoi
- Greedy Algorithms
- DAA - Greedy Algorithms
- DAA - Travelling Salesman Problem
- DAA - Prim's Minimal Spanning Tree
- DAA - Kruskal's Minimal Spanning Tree
- DAA - Dijkstra's Shortest Path Algorithm
- DAA - Map Colouring Algorithm
- DAA - Fractional Knapsack
- DAA - Job Sequencing with Deadline
- DAA - Optimal Merge Pattern
- Dynamic Programming
- DAA - Dynamic Programming
- DAA - Matrix Chain Multiplication
- DAA - Floyd Warshall Algorithm
- DAA - 0-1 Knapsack Problem
- DAA - Longest Common Subsequence Algorithm
- DAA - Travelling Salesman Problem using Dynamic Programming
- Randomized Algorithms
- DAA - Randomized Algorithms
- DAA - Randomized Quick Sort Algorithm
- DAA - Karger's Minimum Cut Algorithm
- DAA - Fisher-Yates Shuffle Algorithm
- Approximation Algorithms
- DAA - Approximation Algorithms
- DAA - Vertex Cover Problem
- DAA - Set Cover Problem
- DAA - Travelling Salesperson Approximation Algorithm
- Sorting Techniques
- DAA - Bubble Sort Algorithm
- DAA - Insertion Sort Algorithm
- DAA - Selection Sort Algorithm
- DAA - Shell Sort Algorithm
- DAA - Heap Sort Algorithm
- DAA - Bucket Sort Algorithm
- DAA - Counting Sort Algorithm
- DAA - Radix Sort Algorithm
- DAA - Quick Sort Algorithm
- Searching Techniques
- DAA - Searching Techniques Introduction
- DAA - Linear Search
- DAA - Interpolation Search
- DAA - Jump Search
- DAA - Exponential Search
- DAA - Fibonacci Search
- DAA - Sublist Search
- DAA - Hash Table
- Graph Theory
- DAA - Shortest Paths
- DAA - Multistage Graph
- DAA - Optimal Cost Binary Search Trees
- Heap Algorithms
- DAA - Binary Heap
- DAA - Insert Method
- DAA - Heapify Method
- DAA - Extract Method
- Complexity Theory
- DAA - Deterministic vs. Nondeterministic Computations
- DAA - Max Cliques
- DAA - Vertex Cover
- DAA - P and NP Class
- DAA - Cook's Theorem
- DAA - NP Hard & NP-Complete Classes
- DAA - Hill Climbing Algorithm
- DAA Useful Resources
- DAA - Quick Guide
- DAA - Useful Resources
- DAA - Discussion
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary

## Design and Analysis of Algorithms Tutorial

Daa online compiler or editor, why design and analysis of algorithms, design strategies, analysis of algorithms, applications of daa, who should learn daa, prerequisites to learn daa, daa jobs and opportunities, frequently asked questions about daa.

An Algorithm is a sequence of steps to solve a problem. It acts like a set of instructions on how a program should be executed. Thus, there is no fixed structure of an algorithm. Design and Analysis of Algorithms covers the concepts of designing an algorithm as to solve various problems in computer science and information technology, and also analyse the complexity of these algorithms designed.

The main aim of designing an algorithm is to provide a optimal solution for a problem. Not all problems must have similar type of solutions; an optimal solution for one problem may not be optimal for another. Therefore, we must adopt various strategies to provide feasible solutions for all types of problems.

This tutorial introduces the fundamental concepts of Designing Strategies, Complexity analysis of Algorithms, followed by problems on Graph Theory and Sorting methods. This tutorial also includes the basic concepts on Complexity theory.

In this tutorial, we will provide online compilers and editors to execute programs of all algorithms. The code is written in four different programming languages: C, C++, Java, Python. This will eliminate the need to install a local setup for all these languages.

For instance, let us execute the code for a simple linear search algorithm to work with these online compilers.

One computer problem might have several versions of a solution. In this case, every approach taken to solve the computer problem is correct. However, choosing the best-suited solution will improve the efficiency of the program.

There might be a misconception that smaller algorithms are best-suited solutions in most cases. But, a feasible solution is not based on the length of algorithm, but the one with efficient complexity (time and space complexity).

We study Design and Analysis of Algorithms to analyse the complexity of all the versions of a solution to a computer problem.

There are various types of strategies in order to design algorithms for various problems. Some of them are listed as follows −

- Greedy Approach
- Divide & Conquer Approach
- Dynamic Programming Approach
- Randomization Approach
- Approximation Approach
- Recursive Approach
- Branch and Bound Approach

In this tutorial, we will see various algorithms of each approach to solve various problems.

To analyse the feasibility of an algorithm designed, we calculate the complexity of it. This is represented in three notations, called asymptotic notations. Asymptotic notations are as follows −

- Worst-Case Scenario − Big Oh and Little Oh Notations
- Best-Case Scenario − Big Omega and Little Omega Notations
- Average-Case Scenario − Theta Notation

Each solution is analysed in all scenarios of the problem, and the solution having the best worst-case is said to be optimal. Thus, providing an efficient algorithm.

There are applications of Design and Analysis of Algorithms (DAA) in a wide range of fields. Here are some of the common fields where it is used:

- Computer programming: Used in computer programming to solve problems efficiently. This includes developing algorithms for sorting, searching, and manipulating data structures.
- Big data processing: Also used to develop and analyse algorithms for operations such as data mining, machine learning, and natural language processing, in order to handle large sets of data.
- Networking: Network protocols and algorithms are developed for routing, flow control, congestion control, and network security. DAA is used to design and analyse these algorithms.
- Artificial intelligence: Used to design and analyse algorithms for tasks in Artificial Intelligence such as computer vision, speech recognition, and natural language understanding.
- Scientific computing: DAA in scientific computing is used to develop algorithms for operations like numerical integration, optimization, and simulation.
- Game development: In game development, we use design and analysis of algorithms for pathfinding, collision detection, and physics simulation.
- Cryptography: DAA is also used in the design and analysis of cryptographic algorithms, such as RSA and AES, which are used to secure data transmission and storage.

This tutorial has been designed for students pursuing a degree in any computer science, engineering, and/or information technology related fields. It attempts to help students to grasp the essential concepts involved in algorithm design.

The readers should have basic knowledge of programming and mathematics. The readers should know data structure very well. Moreover, it is preferred if the readers have basic understanding of Formal Language and Automata Theory.

Many top companies are actively recruiting experts in Design and Analysis of Algorithms, and they offer roles such as Software Engineer, Data Scientist, Machine Learning Engineer, and more. These companies need individuals who can solve complex problems, analyse data, and design algorithms to drive their business forward. Here is the list of few such companies −

- JPMorgan Chase
- Goldman Sachs
- Johnson & Johnson

The demand for DAA professionals is continually growing across various sectors. By developing expertise in these areas, you can open up a wide range of career opportunities in some of the world's leading companies.

To get started, there are user-friendly tutorials and resources available to help you master DAA. These materials are designed to prepare you for technical interviews and certification exams, and you can learn at your own pace, anytime and anywhere.

There are many Frequently Asked Questions (FAQs) on Design and Analysis of Algorithms due to the complex nature of this concept. In this section, we will try to answer some of them briefly.

An algorithm is a set of instructions to solve a problem by performing calculations, data processing, or automating reasoning tasks. However, there are always multiple solutions to solving a problem. Design and Analysis of Algorithms provides various ways to design efficient algorithms to solve a problem by analysing their complexities.

Algorithm analysis is an important part of computational complexity theory. The complexity theory provides a theoretical estimation for the required algorithm resources to solve a computational problem. For instance, most algorithms are designed to work with input data of variable length. Analysis of algorithms determines the amount of time and space taken to execute such algorithms.

Here are the summarized list of tips which you can follow to learn Analysis of Algorithms.

- Follow our tutorial step by step from the very beginning.
- Read more articles, watch online courses or buy reference books on Algorithm Analysis to enhance your knowledge.
- Try to design a small algorithm for a simple problem to check your knowledge in these concepts.

As algorithms are not language specific, using any programming language that you are comfortable with is recommended.

Our basic aim while designing an algorithm is to maintain the efficiency of the solution. Algorithms are used in almost all areas of computing. Hence, learning how to design an efficient algorithm is important.

To test the implementation of an algorithm, feed it with diverse types of inputs and observe the outputs generated. If the time taken by the algorithm to be executed and space complexity are efficient even in worst case inputs, your algorithm is feasible.

Time complexity of an algorithm, in general, is simply defined as the time taken by an algorithm to implement each statement in the code. Time complexity can be influenced by various factors like the input size, the methods used and the procedure. An algorithm is said to be the most efficient when the output is produced in the minimal time possible.

Space complexity is a function describing the amount of memory (space) an algorithm takes in terms of the amount of input to the algorithm. So, it is usually computed by combining the auxiliary space and the space used by input values.

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## Algorithm Design Techniques in DAA

When it comes to solve problems, especially in computer science, algorithms are something that play a crucial role. An algorithm is a set of rules for solving a certain problem quickly. But the question is how to design an algorithm to solve that problem? So IT professionals are upgrading their knowledge and developing different approaches to construct an effective algorithm to fulfil the expanding demands of industry. Different algorithm design techniques and their applications are discussed in this article.

## Brute-Force Search

It is a simple approach of addressing a problem that relies on huge processing power and testing of all possibilities to improve efficiency. Suppose you forgot the combination of a 4-digit padlock and to avoid purchasing the new one, you have to open the lock using brute-force search method. You will have to try all possible 4-digit combinations from 0 to 9 to unlock it. That combination could be anything between 0000 to 9999, hence there are 10,000 combinations. So we can say that in the worst case, you have to try 10, 000 times to find your actual combination.

Brute Force Search for combination of padlock

The time complexity of brute force is O(mn), which can also be written as O(n*m). This means that if we need to search a string of “n” characters in a string of “m” characters, then it would take “n*m” tries.

Divide and Conquer

Divide and conquer algorithm works on top-down approach and is preferred for large problems. As the name says divide and conquer, it follows following steps:

Step 1: Divide the problem into several subproblems.

Step 2: Conquer or solve each sub-problem.

Step 3: Combine each sub-problem to get the required result.

Divide and Conquer solve each subproblem recursively, so each subproblem will be the smaller original problem.

Greedy Algorithm

In Greedy Algorithm, resources are divided in a loop depending on the maximum and immediate availability at any given stage of execution. This method is used to solve optimization problems in which set of input values are given, that are required either to be increased or decreased according to the objective. Greedy Algorithm always chooses the option, which appears to be the best at the moment. That is why it is known as greedy algorithm. It may not always give the optimized solution. There are two stages to solve the problem using greedy algorithm:

- Examining the list of Items.
- Optimization

This means that a greedy algorithm selects the best immediate option and does not rethink its decisions. When it comes to optimizing a solution, this simply implies that the greedy solution will seek out local optimum solutions, which could be multiple, and may skip a global optimal solution. For example, greedy algorithm in animation below aims to locate the path with the largest sum.

With a goal of reaching the largest sum, at each step, the greedy algorithm will choose what appears to be the optimal immediate choice, so it will choose 12 instead of 3 at the second step and will not reach the best solution, which contains 99.

Dynamic Programming

Dynamic Programming (DP) is an algorithmic technique for solving optimization problems by breaking them into simpler sub-problems and storing each sub-solution so that the corresponding sub-problem can be solved only once. Dynamic Programming is a good methodology for optimization problems that seek the maximal or minimal solution with restrictions as it searches through all possible sub-problems and never recomputes the conclusion to any sub-problem.

It’s an algorithmic strategy for breaking down an optimization problem into smaller sub-problems and leveraging the fact that the best solution for the overall problem is defined by the best solution for its sub-problems. For example in case of Fibonacci Series in which each number is the sum of the two preceding numbers. Suppose the first two numbers of the series are 0, 1. If it is asked to find the nth number of the series, we can do that as follows:

Dynamic Programming Example

Here, to solve the overall problem i.e., Fib(n) , we have to break it down into two smaller sub-problems i.e., Fib(n-1) and Fib(n-2). Hence, we can use Dynamic Programming to solve above mentioned problem, which is elaborated in more detail in the following figure:

Fibonacci Series using Dynamic Programming

## Branch and Bound Algorithm

For combinatory, discrete, and general mathematical optimization problems, branch and bound algorithms are applied to determine the optimal solution. A branch and bound algorithm searches the set of all possible solutions before recommending the best one. This algorithm enumerates possible candidate solutions in a stepwise manner by exploring all possible set of solutions.

Branch and Bound Algorithm Example

First of all we build a rooted decision tree where the root node represents the entire search space. Each child node is a part of the solution set and is a partial solution. Based on the optimal solution, we set an upper and lower bound for a given problem before constructing the rooted decision tree and we need to make a decision about which node to include in the solution set at each level. It is very important to find upper and lower bound and to find upper bound any local optimization method can be used. It can also be found by picking any point in the search space and convex relaxation. Whereas, duality can be used for finding lower bound.

## Randomized Algorithm

Randomized Algorithm refers to an algorithm that uses random numbers to determine what to do next at any point in its logic. In a standard algorithm, it is usually used to reduce either the running time, or time complexity, or the memory used, or space complexity. The algorithm works by creating a random number, r, from a set of numbers and making decisions based on its value. This algorithm could assist in making a decision in a situation of doubt by flipping a coin or drawing a card from a deck.

Randomized Algorithm Flowchart

When utilizing a randomized method, keep the following two considerations in mind:

- It takes source of random numbers and makes random choices during execution along with the input.
- Behavior of an algorithm varies even on fixed inputs.

## Backtracking Algorithms

Backtracking means that if the current solution isn’t working, you should go back and attempt another option. It is a method for resolving issues recursively by attempting to construct a solution incrementally, one piece at a time, discarding any solutions that do not satisfy the problem’s constraints at any point in time. This approach is used to resolve problems having multiple solutions. For example if we want to find all the possible ways of arranging 2 boys and 1 girl on 3 benches with a constraint that Girl should not be on the middle bench. So there will be 3! = 6 possibilities to solve this problem. We will try all possible ways recursively to get the required solution. Those possibilities are as follows:

Backtracking Example Possibilities

Following diagram shows the possible solutions for the above mentioned problem:

Solutions of Backtracking

## Related Posts

## Master Method in DAA

## Asymptotic Analysis in DAA

## Radix Sort in Data Structure

## Singly Linked List in Data Structure

## Recursion Tree Method

## Analyzing Algorithm Control Structure in DAA

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## DAA Tutorial: Design and Analysis of Algorithms

## DAA Tutorial Summary

This Design and Analysis of Algorithms Tutorial is designed for beginners with little or no coding experience. It covers algorithm Design and Analysis process concepts.

## What is an Algorithm?

An Algorithm is a set of well-defined instructions designed to perform a specific set of tasks. Algorithms are used in Computer science to perform calculations, automatic reasoning, data processing, computations, and problem-solving. Designing an algorithm is important before writing the program code as the algorithm explains the logic even before the code is developed.

## DAA Syllabus

Introduction, advanced stuff, why study design and analysis of algorithm.

Design and Analysis of Algorithm help to design the algorithms for solving different types of problems in Computer Science. It also helps to design and analyze the logic on how the program will work before developing the actual code for a program.

## Prerequisites for learning DAA Tutorial

For learning this DAA tutorial, you should know the basic programming and mathematics concepts and data structure concepts. The basic knowledge of algorithms will also help you learn and understand the DAA concepts easily and quickly.

## What will you learn in this Design and Analysis of Algorithms Tutorial?

In this Design and Analysis of Algorithms tutorial, you will learn the basic concepts about DAA like the introduction to Algorithm, Greedy algorithm, linked list, and arrays in a data structure. You will also learn advanced concepts like Trees in a data structure, search algorithms, sorting algorithms, hash tables, and interview questions related to Algorithms.

## DAA (Design and Analysis of Algorithms)

Dcrust syllabus.

CSE 206C Design and Analysis of Algorithms

CATEGORY : ENGINEERING SCIENCE COURSE

Course Objectives:

- To analyze worst-case running times of algorithms based on asymptotic analysis and justify the correctness of algorithms.
- To apply the algorithms and design techniques to solve problems.
- To explain the major graph algorithms and their analyses and to employ graphs to model engineering problems.
- To understand the concepts of tractable and intractable problems and the classes P, NP and NP-complete problems.

Introduction: Characteristics of algorithm. Analysis of algorithm: Asymptotic analysis of complexity bounds – best, average and worst-case behavior; Performance measurements of Algorithm, Time and space trade-offs, Analysis of recursive algorithms through recurrence relations: Substitution method, Recursion tree method and Masters’ theorem.

Click on any topic to read about the topic.

Fundamental Algorithmic Strategies: Brute-Force, Greedy, Dynamic Programming, Branch- and-Bound and Backtracking methodologies for the design of algorithms; Illustrations of these techniques for Problem-Solving, Bin Packing, Knap Sack TSP. Heuristics-characteristics and their application domains.

Graph and Tree Algorithms: Traversal algorithms: Depth First Search (DFS) and Breadth First Search (BFS); Shortest path algorithms, Transitive closure, Minimum Spanning Tree, Topological sorting, Network Flow Algorithm.

Tractable and Intractable Problems: Computability of Algorithms, Computability classes – P, NP, NP-complete and NP-hard. Cook’s theorem, Standard NP-complete problems and Reduction techniques.

Advanced Topics: Approximation algorithms, Randomized algorithms, Class of problems beyond NP – P SPACE

TEXT BOOKS:

- Introduction to Algorithms, 4TH Edition, Thomas H Cormen, MIT Press/McGraw-Hill.Fundamentals of Algorithms – E. Horowitz et al.

REFERENCE BOOKS:

- Algorithm Design, 1ST Edition, Jon Kleinberg and ÉvaTardos, Pearson.
- Algorithm Design: Foundations, Analysis, and Internet Examples, Second Edition, Michael T Goodrich and Roberto Tamassia, Wiley.
- Algorithms — A Creative Approach, 3 RD Edition, UdiManber, Addison-Wesley, Reading, MA.

Course Outcomes: After successful completion of the course students will be able to:

- Analyze worst-case running times of algorithms based on asymptotic analysis and justify the correctness of algorithms.
- Apply the algorithms and design techniques to solve problems;
- Explain the major graph algorithms and their analyses. Employ graphs to model engineering problems,
- Understand the concepts of tractable and intractable problems and the classes P, NP and NP-complete problems.

## Related Posts

Aca (advanced computer architecture), ai (artificial intelligence and expert system), aj (advanced java), aj lab (advanced java lab), cd (compiler design), cd lab (compiler design lab), cfcl (cyber forensics and cyber laws), cg (computer graphics), cn (computer networks), coa (computer organisation and architecture, cs (cyber security), daa lab (design and analysis of algorithms lab), dbms (database management systems), dbms lab (database management system lab ), dsa (data structure and algorithms), dsa lab (data structures and algorithms lab), flat (formal languages & automata theory), itw (it workshop) / matlab, mm (multimedia technology), oop (object oriented programming).

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## Steps of Problem Solving in Data Structures and Algorithms

Every solution starts with a strategy, and an algorithm is a strategy for solving a coding problem. So, we must learn to design an efficient algorithm and translate this 'algorithm' into the correct code to get the job done.

But there are many coding problems available in data structures and algorithms, and most of the time, these problems are new to us. So as programmers, we need to develop ourselves as confident problem-solvers who are not intimidated by the difficulty of the given problem.

Our long-term goal should be simple: Learn to design correct and efficient code within a given time. As we practice more and more, we will gain experience in problem-solving, and our work will become easier. Here are some essential skills that we should practice for every DSA problem:

- Developing an approach to understanding the problem
- Thinking of a correct basic solution
- Designing step-by-step pseudocode solutions
- Analyzing the efficiency of a solution
- Optimizing the solution further
- Transforming pseudocode into correct code

Now, the critical question would be: Is there a well-defined, guided strategy to approach and solve a coding problem? If yes, then what are the critical steps? Let's think and explore!

## Step 1: Understanding the problem

Solving a problem requires a clear understanding of the problem. Unfortunately, sometimes we read only the first few lines and assume the rest of the problem or ignore this step because we have seen something similar in the past. We should view these as unfair practices and develop a clear approach to understanding problems.

During problem-solving, every small detail can help us design an efficient solution. Sometimes, a small change in the question can alter the solution approach. Taking extra time to understand the problem will give us more confidence later on. The fact is, we never want to realize halfway through that we misunderstood the problem.

It doesn't matter if we have encountered a question before or not; we should read the question several times. So, take a paper and write down everything while going through the problem. Exploring some examples will also help us clarify how many cases our algorithm can handle and the possible input-output patterns. We should also explore scenarios for large input, edge cases, and invalid input.

Sometimes, it is common for problem descriptions to suffer from these types of deficiencies:

- The problem description may rely on undefined assumptions
- The problem description may be ambiguous or incomplete
- The problem description may have various contradictions.

These deficiencies may be due to the abstract explanation of the problem description in our natural languages. So, it is our responsibility to identify such deficiencies and work with the interviewer or problem provider to clarify them. We should start by seeking answers to the following questions:

- What are the inputs and outputs?
- What type of data is available?
- What is the size or scale of the input?
- How is the data stored? What is the data structure?
- Are there any special conditions or orders in the data?
- What rules exist for working with the data?

## Step 2: Thinking of a correct basic solution

The best approach would be to think of a correct solution that comes immediately to our mind. It does not matter even if it is an inefficient approach. Having a correct and inefficient answer is much better than an incorrect solution or significant delay in finding the solution. This could help us in so many ways:

- Help us to build good confidence or motivation at the start.
- Provide an excellent point to start a conversation with the interviewer.
- Sometimes, it provides a hint to improve efficiency by reducing some loops, removing some intermediate steps, or performing some operations efficiently.

Here are some examples of brute force patterns: three nested loops, two nested loops, solution using extra memory, solution using sorting, double traversal in the binary tree, considering all sub-arrays or substrings, exhaustive search, etc.

After thinking and communicating the brute force idea, the interviewer may ask for its time and space complexity. We need to work on paper, analyze each critical operation, and write it in the form of Big-O notation. Clear conceptual idea of time and space complexity analysis is essential at this stage.

## Step 3: Designing efficient solution with pseudocode

This is a stage to use the best experience of DSA problem-solving and apply various problem-solving strategies . One practical truth is: moving from a basic algorithm to the most efficient algorithm is a little difficult in a single step. Each time, we need to optimize the previous algorithm and stop when there is no further optimization possible. Revisiting the problem description and looking for some additional information can help a lot in further optimization. For example:

- If the input array is sorted or nearly sorted, we can apply optimized algorithms such as a single loop, two-pointer approach, or binary search.
- If we need to find a subarray of size k, we can use the sliding window technique, which involves maintaining a window of size k over the array and sliding it over the elements to find the desired subarray.
- When searching is a critical operation, we can use optimized search algorithms or data structures like binary search, BST, or hash table.
- For optimization problems, we can consider divide and conquer, dynamic programming, or greedy algorithm approaches.
- If we need to find a solution with a given constraint, we can use backtracking.
- When working with string data, direct address tables, hash tables, or trie data structures can be useful.
- To frequently access and process max or min elements, we can use a priority queue or heap data structure.
- For dictionary operations such as insert, search, and delete, we can use hash tables or BST.
- If we need to perform both dictionary and priority queue operations, a BST may be useful.
- For range query operations such as range max, range min, or range sum, we can use data structures like segment trees or Fenwick trees.
- To process binary tree data level by level, BFS or level-order traversal can be used.

The idea would be simple: we should learn the use case of efficient problem-solving patterns on various data structures. Continuously thinking, analyzing, and looking for a better solution is the core idea.

Here are some best examples of problems where several levels of optimisations are feasible. Practicing such types of coding questions helps a lot in building confidence.

Find equilibrium index of an array

- Using nested loops: Time = O(n²), Memory = O(1)
- Using prefix sum array: Time = O(n), Memory = O(n)
- Using single scan: Time = O(n), Memory = O(1)

Trapping rain water

- Using Dynamic Programming: Time = O(n), Memory = O(n)
- Using Stack: Time = O(n), Memory = O(n)
- Using two pointers: Time = O(n), Memory = O(1)

Check for pair with a given sum

- Using sorting and binary search: Time = O(nlogn), Memory = O(1)
- Using sorting and Two Pointers: Time = O(nlogn), Memory = O(1)
- Using a Hash Table: Time = O(n), Memory = O(n)

Find the majority element in an array

- Using two nested loops: Time = O(n²), Memory = O(1)
- Using Sorting: Time = O(nlogn), Memory = O(1)
- Using the divide and conquer: Time = O(nlogn), Memory = O(logn)
- Using Bit Manipulation: Time = O(n), Memory = O(1)
- Using Randomisation: Time = O(nlogn), Memory = O(1) Note: If value of n is very large.
- Boyer-Moore Voting Algorithm: Time = O(n), Memory = O(1)

Maximum Subarray Sum

- Using three nested loops: Time = O(n^3), Memory = O(1)
- Using two nested loops: Time = O(n^2), Memory = O(1)
- Using divide and conquer: Time = O(nlogn), Memory = O(logn)
- Using dynamic programming: Time = O(n), Memory = O(n)
- Kadane algorithm: Time = O(n), Memory = O(1)

Before you jump into the end-to-end code implementation, it’s good practice to write pseudocode on paper. It would be helpful in defining code structure and critical operations. Some programmers skip this step, but writing the final code becomes easier when we have well-designed pseudocode.

## Step 4: Transforming pseudocode into a clean, correct, and optimized code

Finally, we need to replace each line of pseudocode with actual code in our favorite programming languages like C++, Java, Python, C#, JavaScript, etc. Never forget to test actual code with sample test data and check if the actual output is equal to the expected output. When writing code in your interviews, discuss sample data or test cases with the interviewer.

Simplifying and optimizing the code may require a few iterations of observation. We need to ask these questions once we are done writing the code:

- Does this code run for every possible input, including the edge cases?
- Can we optimize the code further? Can we remove some variables or loop or some extra space?
- Are we repeating some steps a lot? Can we define it separately using another function?
- Is the code readable or written with a good coding style?

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- Practice Backtracking
- Interview Problems on Backtracking
- MCQs on Backtracking
- Tutorial on Backtracking
- Backtracking vs Recursion
- Backtracking vs Branch & Bound
- Print Permutations
- Subset Sum Problem
- N-Queen Problem
- Knight's Tour
- Sudoku Solver
- Rat in Maze
- Hamiltonian Cycle
- Graph Coloring

## Backtracking Algorithm

- Introduction to Backtracking - Data Structure and Algorithm Tutorials
- Difference between Backtracking and Branch-N-Bound technique
- What is the difference between Backtracking and Recursion?

## Standard problems on backtracking

- The Knight's tour problem
- Rat in a Maze
- N Queen Problem
- Subset Sum Problem using Backtracking
- M-Coloring Problem
- Algorithm to Solve Sudoku | Sudoku Solver
- Magnet Puzzle
- Remove Invalid Parentheses
- A backtracking approach to generate n bit Gray Codes
- Permutations of given String

## Easy Problems on Backtracking

- Print all subsets of a given Set or Array
- Check if a given string is sum-string
- Count all possible Paths between two Vertices
- Find all distinct subsets of a given set using BitMasking Approach
- Find if there is a path of more than k length from a source
- Print all paths from a given source to a destination
- Print all possible strings that can be made by placing spaces

## Medium prblems on Backtracking

- 8 queen problem
- Combinational Sum
- Warnsdorff's algorithm for Knight’s tour problem
- Find paths from corner cell to middle cell in maze
- Find Maximum number possible by doing at-most K swaps
- Rat in a Maze with multiple steps or jump allowed
- N Queen in O(n) space

## Hard problems on Backtracking

- Power Set in Lexicographic order
- Word Break Problem using Backtracking
- Partition of a set into K subsets with equal sum
- Longest Possible Route in a Matrix with Hurdles
- Find shortest safe route in a path with landmines
- Printing all solutions in N-Queen Problem
- Print all longest common sub-sequences in lexicographical order
- Top 20 Backtracking Algorithm Interview Questions

Backtracking algorithms are like problem-solving strategies that help explore different options to find the best solution. They work by trying out different paths and if one doesn’t work, they backtrack and try another until they find the right one. It’s like solving a puzzle by testing different pieces until they fit together perfectly.

- Backtracking

Table of Content

## What is Backtracking Algorithm?

How does a backtracking algorithm work, example of backtracking algorithm, when to use a backtracking algorithm, applications of backtracking algorithm.

- Basic of Backtracking Algorithm
- Standard Problems on Backtracking Algorithm
- Easy Problems on Backtracking Algorithm
- Medium Problems on Backtracking Algorithm
- Hard Problems on Backtracking Algorithm

Backtracking is a problem-solving algorithmic technique that involves finding a solution incrementally by trying different options and undoing them if they lead to a dead end .

It is commonly used in situations where you need to explore multiple possibilities to solve a problem, like searching for a path in a maze or solving puzzles like Sudoku . When a dead end is reached, the algorithm backtracks to the previous decision point and explores a different path until a solution is found or all possibilities have been exhausted.

A backtracking algorithm works by recursively exploring all possible solutions to a problem. It starts by choosing an initial solution, and then it explores all possible extensions of that solution. If an extension leads to a solution, the algorithm returns that solution. If an extension does not lead to a solution, the algorithm backtracks to the previous solution and tries a different extension.

The following is a general outline of how a backtracking algorithm works:

- Choose an initial solution.
- Explore all possible extensions of the current solution.
- If an extension leads to a solution, return that solution.
- If an extension does not lead to a solution, backtrack to the previous solution and try a different extension.
- Repeat steps 2-4 until all possible solutions have been explored.

Example: Finding the shortest path through a maze

Input: A maze represented as a 2D array, where 0 represents an open space and 1 represents a wall.

- Start at the starting point.
- For each of the four possible directions (up, down, left, right), try moving in that direction.
- If moving in that direction leads to the ending point, return the path taken.
- If moving in that direction does not lead to the ending point, backtrack to the previous position and try a different direction.
- Repeat steps 2-4 until the ending point is reached or all possible paths have been explored.

Backtracking algorithms are best used to solve problems that have the following characteristics:

- There are multiple possible solutions to the problem.
- The problem can be broken down into smaller subproblems.
- The subproblems can be solved independently.

Backtracking algorithms are used in a wide variety of applications, including:

- Solving puzzles (e.g., Sudoku, crossword puzzles)
- Finding the shortest path through a maze
- Scheduling problems
- Resource allocation problems
- Network optimization problems

## Basic of Backtracking Algorithm:

- Introduction to Backtracking – Data Structure and Algorithm Tutorials

## Standard Problems on Backtracking Algorithm:

- The Knight’s tour problem
- N Queen Problem | Backtracking-3
- Subset Sum problem
- m Coloring Problem
- Sudoku | Backtracking-7
- Write a program to print all permutations of a given string

## Easy Problems on Backtracking Algorithm:

- Backtracking to find all subsets
- Count all possible paths between two vertices
- Find all distinct subsets of a given set

## Medium Problems on Backtracking Algorithm:

- Warnsdorff’s algorithm for Knight’s tour problem

## Hard Problems on Backtracking Algorithm:

- Print all palindromic partitions of a string

Quick Links :

- Learn Data Structure and Algorithms | DSA Tutorial
- ‘Practice Problems’ on Backtracking
- ‘Quiz’ on Backtracking
- ‘Videos’ on Backtracking

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## Improve your Coding Skills with Practice

## What kind of Experience do you want to share?

- Open access
- Published: 11 May 2024

## Nursing students’ stressors and coping strategies during their first clinical training: a qualitative study in the United Arab Emirates

- Jacqueline Maria Dias 1 ,
- Muhammad Arsyad Subu 1 ,
- Nabeel Al-Yateem 1 ,
- Fatma Refaat Ahmed 1 ,
- Syed Azizur Rahman 1 , 2 ,
- Mini Sara Abraham 1 ,
- Sareh Mirza Forootan 1 ,
- Farzaneh Ahmad Sarkhosh 1 &
- Fatemeh Javanbakh 1

BMC Nursing volume 23 , Article number: 322 ( 2024 ) Cite this article

142 Accesses

Metrics details

Understanding the stressors and coping strategies of nursing students in their first clinical training is important for improving student performance, helping students develop a professional identity and problem-solving skills, and improving the clinical teaching aspects of the curriculum in nursing programmes. While previous research have examined nurses’ sources of stress and coping styles in the Arab region, there is limited understanding of these stressors and coping strategies of nursing students within the UAE context thereby, highlighting the novelty and significance of the study.

A qualitative study was conducted using semi-structured interviews. Overall 30 students who were undergoing their first clinical placement in Year 2 at the University of Sharjah between May and June 2022 were recruited. All interviews were recorded and transcribed verbatim and analyzed for themes.

During their first clinical training, nursing students are exposed to stress from different sources, including the clinical environment, unfriendly clinical tutors, feelings of disconnection, multiple expectations of clinical staff and patients, and gaps between the curriculum of theory classes and labatories skills and students’ clinical experiences. We extracted three main themes that described students’ stress and use of coping strategies during clinical training: (1) managing expectations; (2) theory-practice gap; and (3) learning to cope. Learning to cope, included two subthemes: positive coping strategies and negative coping strategies.

## Conclusions

This qualitative study sheds light from the students viewpoint about the intricate interplay between managing expectations, theory practice gap and learning to cope. Therefore, it is imperative for nursing faculty, clinical agencies and curriculum planners to ensure maximum learning in the clinical by recognizing the significance of the stressors encountered and help students develop positive coping strategies to manage the clinical stressors encountered. Further research is required look at the perspective of clinical stressors from clinical tutors who supervise students during their first clinical practicum.

Peer Review reports

Nursing education programmes aim to provide students with high-quality clinical learning experiences to ensure that nurses can provide safe, direct care to patients [ 1 ]. The nursing baccalaureate programme at the University of Sharjah is a four year program with 137 credits. The programmes has both theoretical and clinical components withs nine clinical courses spread over the four years The first clinical practicum which forms the basis of the study takes place in year 2 semester 2.

Clinical practice experience is an indispensable component of nursing education and links what students learn in the classroom and in skills laboratories to real-life clinical settings [ 2 , 3 , 4 ]. However, a gap exists between theory and practice as the curriculum in the classroom differs from nursing students’ experiences in the clinical nursing practicum [ 5 ]. Clinical nursing training places (or practicums, as they are commonly referred to), provide students with the necessary experiences to ensure that they become proficient in the delivery of patient care [ 6 ]. The clinical practicum takes place in an environment that combines numerous structural, psychological, emotional and organizational elements that influence student learning [ 7 ] and may affect the development of professional nursing competencies, such as compassion, communication and professional identity [ 8 ]. While clinical training is a major component of nursing education curricula, stress related to clinical training is common among students [ 9 ]. Furthermore, the nursing literature indicates that the first exposure to clinical learning is one of the most stressful experiences during undergraduate studies [ 8 , 10 ]. Thus, the clinical component of nursing education is considered more stressful than the theoretical component. Students often view clinical learning, where most learning takes place, as an unsupportive environment [ 11 ]. In addition, they note strained relationships between themselves and clinical preceptors and perceive that the negative attitudes of clinical staff produce stress [ 12 ].

The effects of stress on nursing students often involve a sense of uncertainty, uneasiness, or anxiety. The literature is replete with evidence that nursing students experience a variety of stressors during their clinical practicum, beginning with the first clinical rotation. Nursing is a complex profession that requires continuous interaction with a variety of individuals in a high-stress environment. Stress during clinical learning can have multiple negative consequences, including low academic achievement, elevated levels of burnout, and diminished personal well-being [ 13 , 14 ]. In addition, both theoretical and practical research has demonstrated that increased, continual exposure to stress leads to cognitive deficits, inability to concentrate, lack of memory or recall, misinterpretation of speech, and decreased learning capacity [ 15 ]. Furthermore, stress has been identified as a cause of attrition among nursing students [ 16 ].

Most sources of stress have been categorized as academic, clinical or personal. Each person copes with stress differently [ 17 ], and utilizes deliberate, planned, and psychological efforts to manage stressful demands [ 18 ]. Coping mechanisms are commonly termed adaptation strategies or coping skills. Labrague et al. [ 19 ] noted that students used critical coping strategies to handle stress and suggested that problem solving was the most common coping or adaptation mechanism used by nursing students. Nursing students’ coping strategies affect their physical and psychological well-being and the quality of nursing care they offer. Therefore, identifying the coping strategies that students use to manage stressors is important for early intervention [ 20 ].

Studies on nursing students’ coping strategies have been conducted in various countries. For example, Israeli nursing students were found to adopt a range of coping mechanisms, including talking to friends, engaging in sports, avoiding stress and sadness/misery, and consuming alcohol [ 21 ]. Other studies have examined stress levels among medical students in the Arab region. Chaabane et al. [ 15 ], conducted a systematic review of sudies in Arab countries, including Saudi Arabia, Egypt, Jordan, Iraq, Pakistan, Oman, Palestine and Bahrain, and reported that stress during clinical practicums was prevalent, although it could not be determined whether this was limited to the initial clinical course or occurred throughout clinical training. Stressors highlighted during the clinical period in the systematic review included assignments and workload during clinical practice, a feeling that the requirements of clinical practice exceeded students’ physical and emotional endurance and that their involvement in patient care was limited due to lack of experience. Furthermore, stress can have a direct effect on clinical performance, leading to mental disorders. Tung et al. [ 22 ], reported that the prevalence of depression among nursing students in Arab countries is 28%, which is almost six times greater than the rest of the world [ 22 ]. On the other hand, Saifan et al. [ 5 ], explored the theory-practice gap in the United Arab Emirates and found that clinical stressors could be decreased by preparing students better for clinical education with qualified clinical faculty and supportive preceptors.

The purpose of this study was to identify the stressors experienced by undergraduate nursing students in the United Arab Emirates during their first clinical training and the basic adaptation approaches or coping strategies they used. Recognizing or understanding different coping processes can inform the implementation of corrective measures when students experience clinical stress. The findings of this study may provide valuable information for nursing programmes, nurse educators, and clinical administrators to establish adaptive strategies to reduce stress among students going clinical practicums, particularly stressors from their first clinical training in different healthcare settings.

A qualitative approach was adopted to understand clinical stressors and coping strategies from the perspective of nurses’ lived experience. Qualitative content analysis was employed to obtain rich and detailed information from our qualitative data. Qualitative approaches seek to understand the phenomenon under study from the perspectives of individuals with lived experience [ 23 ]. Qualitative content analysis is an interpretive technique that examines the similarities and differences between and within different areas of text while focusing on the subject [ 24 ]. It is used to examine communication patterns in a repeatable and systematic way [ 25 ] and yields rich and detailed information on the topic under investigation [ 23 ]. It is a method of systematically coding and categorizing information and comprises a process of comprehending, interpreting, and conceptualizing the key meanings from qualitative data [ 26 ].

## Setting and participants

This study was conducted after the clinical rotations ended in April 2022, between May and June in the nursing programme at the College of Health Sciences, University of Sharjah, in the United Arab Emirates. The study population comprised undergraduate nursing students who were undergoing their first clinical training and were recruited using purposive sampling. The inclusion criteria for this study were second-year nursing students in the first semester of clinical training who could speak English, were willing to participate in this research, and had no previous clinical work experience. The final sample consisted of 30 students.

## Research instrument

The research instrument was a semi structured interview guide. The interview questions were based on an in-depth review of related literature. An intensive search included key words in Google Scholar, PubMed like the terms “nursing clinical stressors”, “nursing students”, and “coping mechanisms”. Once the questions were created, they were validated by two other faculty members who had relevant experience in mental health. A pilot test was conducted with five students and based on their feedback the following research questions, which were addressed in the study.

How would you describe your clinical experiences during your first clinical rotations?

In what ways did you find the first clinical rotation to be stressful?

What factors hindered your clinical training?

How did you cope with the stressors you encountered in clinical training?

Which strategies helped you cope with the clinical stressors you encountered?

## Data collection

Semi-structured interviews were chosen as the method for data collection. Semi structured interviews are a well-established approach for gathering data in qualitative research and allow participants to discuss their views, experiences, attitudes, and beliefs in a positive environment [ 27 ]. This approach allows for flexibility in questioning thereby ensuring that key topics related to clinical learning stressors and coping strategies would be explored. Participants were given the opportunity to express their views, experiences, attitudes, and beliefs in a positive environment, encouraging open communication. These semi structured interviews were conducted by one member of the research team (MAS) who had a mental health background, and another member of the research team who attended the interviews as an observer (JMD). Neither of these researchers were involved in teaching the students during their clinical practicum, which helped to minimize bias. The interviews took place at the University of Sharjah, specifically in building M23, providing a familiar and comfortable environment for the participant. Before the interviews were all students who agreed to participate were provided with an explanation of the study’s purpose. The time and location of each interview were arranged. Before the interviews were conducted, all students who provided consent to participate received an explanation of the purpose of the study, and the time and place of each interview were arranged to accommodate the participants’ schedules and preferences. The interviews were conducted after the clinical rotation had ended in April, and after the final grades had been submitted to the coordinator. The timings of the interviews included the month of May and June which ensured that participants have completed their practicum experience and could reflect on the stressors more comprehensively. The interviews were audio-recorded with the participants’ consent, and each interview lasted 25–40 min. The data were collected until saturation was reached for 30 students. Memos and field notes were also recorded as part of the data collection process. These additional data allowed for triangulation to improve the credibility of the interpretations of the data [ 28 ]. Memos included the interviewers’ thoughts and interpretations about the interviews, the research process (including questions and gaps), and the analytic progress used for the research. Field notes were used to record the interviewers’ observations and reflections on the data. These additional data collection methods were important to guide the researchers in the interpretation of the data on the participants’ feelings, perspectives, experiences, attitudes, and beliefs. Finally, member checking was performed to ensure conformability.

## Data analysis

The study used the content analysis method proposed by Graneheim and Lundman [ 24 ]. According to Graneheim and Lundman [ 24 ], content analysis is an interpretive technique that examines the similarities and differences between distinct parts of a text. This method allows researchers to determine exact theoretical and operational definitions of words, phrases, and symbols by elucidating their constituent properties [ 29 ]. First, we read the interview transcripts several times to reach an overall understanding of the data. All verbatim transcripts were read several times and discussed among all authors. We merged and used line-by-line coding of words, sentences, and paragraphs relevant to each other in terms of both the content and context of stressors and coping mechanisms. Next, we used data reduction to assess the relationships among themes using tables and diagrams to indicate conceptual patterns. Content related to stress encountered by students was extracted from the transcripts. In a separate document, we integrated and categorized all words and sentences that were related to each other in terms of both content and context. We analyzed all codes and units of meaning and compared them for similarities and differences in the context of this study. Furthermore, the emerging findings were discussed with other members of the researcher team. The final abstractions of meaningful subthemes into themes were discussed and agreed upon by the entire research team. This process resulted in the extraction of three main themes in addition to two subthemes related to stress and coping strategies.

## Ethical considerations

The University of Sharjah Research Ethics Committee provided approval to conduct this study (Reference Number: REC 19-12-03-01-S). Before each interview, the goal and study procedures were explained to each participant, and written informed consent was obtained. The participants were informed that participation in the study was voluntary and that they could withdraw from the study at any time. In the event they wanted to withdraw from the study, all information related to the participant would be removed. No participant withdrew from the study. Furthermore, they were informed that their clinical practicum grade would not be affected by their participation in this study. We chose interview locations in Building M23that were private and quiet to ensure that the participants felt at ease and confident in verbalizing their opinions. No participant was paid directly for involvement in this study. In addition, participants were assured that their data would remain anonymous and confidential. Confidentiality means that the information provided by participants was kept private with restrictions on how and when data can be shared with others. The participants were informed that their information would not be duplicated or disseminated without their permission. Anonymity refers to the act of keeping people anonymous with respect to their participation in a research endeavor. No personal identifiers were used in this study, and each participant was assigned a random alpha-numeric code (e.g., P1 for participant 1). All digitally recorded interviews were downloaded to a secure computer protected by the principal investigator with a password. The researchers were the only people with access to the interview material (recordings and transcripts). All sensitive information and materials were kept secure in the principal researcher’s office at the University of Sharjah. The data will be maintained for five years after the study is completed, after which the material will be destroyed (the transcripts will be shredded, and the tapes will be demagnetized).

In total, 30 nursing students who were enrolled in the nursing programme at the Department of Nursing, College of Health Sciences, University of Sharjah, and who were undergoing their first clinical practicum participated in the study. Demographically, 80% ( n = 24) were females and 20% ( n = 6) were male participants. The majority (83%) of study participants ranged in age from 18 to 22 years. 20% ( n = 6) were UAE nationals, 53% ( n = 16) were from Gulf Cooperation Council countries, while 20% ( n = 6) hailed from Africa and 7% ( n = 2) were of South Asian descent. 67% of the respondents lived with their families while 33% lived in the hostel. (Table 1 )

Following the content analysis, we identified three main themes: (1) managing expectations, (2) theory-practice gap and 3)learning to cope. Learning to cope had two subthemes: positive coping strategies and negative coping strategies. An account of each theme is presented along with supporting excerpts for the identified themes. The identified themes provide valuable insight into the stressors encountered by students during their first clinical practicum. These themes will lead to targeted interventions and supportive mechanisms that can be built into the clinical training curriculum to support students during clinical practice.

## Theme 1: managing expectations

In our examination of the stressors experienced by nursing students during their first clinical practicum and the coping strategies they employed, we identified the first theme as managing expectations.

The students encountered expectations from various parties, such as clinical staff, patients and patients’ relatives which they had to navigate. They attempted to fulfil their expectations as they progressed through training, which presented a source of stress. The students noted that the hospital staff and patients expected them to know how to perform a variety of tasks upon request, which made the students feel stressed and out of place if they did not know how to perform these tasks. Some participants noted that other nurses in the clinical unit did not allow them to participate in nursing procedures, which was considered an enormous impediment to clinical learning, as noted in the excerpt below:

“…Sometimes the nurses… They will not allow us to do some procedures or things during clinical. And sometimes the patients themselves don’t allow us to do procedures” (P5).

Some of the students noted that they felt they did not belong and felt like foreigners in the clinical unit. Excerpts from the students are presented in the following quotes;

“The clinical environment is so stressful. I don’t feel like I belong. There is too little time to build a rapport with hospital staff or the patient” (P22).

“… you ask the hospital staff for some guidance or the location of equipment, and they tell us to ask our clinical tutor …but she is not around … what should I do? It appears like we do not belong, and the sooner the shift is over, the better” (P18).

“The staff are unfriendly and expect too much from us students… I feel like I don’t belong, or I am wasting their (the hospital staff’s) time. I want to ask questions, but they have loads to do” (P26).

Other students were concerned about potential failure when working with patients during clinical training, which impacted their confidence. They were particularly afraid of failure when performing any clinical procedures.

“At the beginning, I was afraid to do procedures. I thought that maybe the patient would be hurt and that I would not be successful in doing it. I have low self-confidence in doing procedures” (P13).

The call bell rings, and I am told to answer Room No. XXX. The patient wants help to go to the toilet, but she has two IV lines. I don’t know how to transport the patient… should I take her on the wheelchair? My eyes glance around the room for a wheelchair. I am so confused …I tell the patient I will inform the sister at the nursing station. The relative in the room glares at me angrily … “you better hurry up”…Oh, I feel like I don’t belong, as I am not able to help the patient… how will I face the same patient again?” (P12).

Another major stressor mentioned in the narratives was related to communication and interactions with patients who spoke another language, so it was difficult to communicate.

“There was a challenge with my communication with the patients. Sometimes I have communication barriers because they (the patients) are of other nationalities. I had an experience with a patient [who was] Indian, and he couldn’t speak my language. I did not understand his language” (P9).

Thus, a variety of expectations from patients, relatives, hospital staff, and preceptors acted as sources of stress for students during their clinical training.

## Theme 2: theory-practice gap

Theory-practice gaps have been identified in previous studies. In our study, there was complete dissonance between theory and actual clinical practice. The clinical procedures or practices nursing students were expected to perform differed from the theory they had covered in their university classes and skills lab. This was described as a theory–practice gap and often resulted in stress and confusion.

“For example …the procedures in the hospital are different. They are different from what we learned or from theory on campus. Or… the preceptors have different techniques than what we learned on campus. So, I was stress[ed] and confused about it” (P11).

Furthermore, some students reported that they did not feel that they received adequate briefing before going to clinical training. A related source of stress was overload because of the volume of clinical coursework and assignments in addition to clinical expectations. Additionally, the students reported that a lack of time and time management were major sources of stress in their first clinical training and impacted their ability to complete the required paperwork and assignments:

“…There is not enough time…also, time management at the hospital…for example, we start at seven a.m., and the handover takes 1 hour to finish. They (the nurses at the hospital) are very slow…They start with bed making and morning care like at 9.45 a.m. Then, we must fill [out] our assessment tool and the NCP (nursing care plan) at 10 a.m. So, 15 only minutes before going to our break. We (the students) cannot manage this time. This condition makes me and my friends very stressed out. -I cannot do my paperwork or assignments; no time, right?” (P10).

“Stressful. There is a lot of work to do in clinical. My experiences are not really good with this course. We have a lot of things to do, so many assignments and clinical procedures to complete” (P16).

The participants noted that the amount of required coursework and number of assignments also presented a challenge during their first clinical training and especially affected their opportunity to learn.

“I need to read the file, know about my patient’s condition and pathophysiology and the rationale for the medications the patient is receiving…These are big stressors for my learning. I think about assignments often. Like, we are just focusing on so many assignments and papers. We need to submit assessments and care plans for clinical cases. We focus our time to complete and finish the papers rather than doing the real clinical procedures, so we lose [the] chance to learn” (P25).

Another participant commented in a similar vein that there was not enough time to perform tasks related to clinical requirements during clinical placement.

“…there is a challenge because we do not have enough time. Always no time for us to submit papers, to complete assessment tools, and some nurses, they don’t help us. I think we need more time to get more experiences and do more procedures, reduce the paperwork that we have to submit. These are challenges …” (P14).

There were expectations that the students should be able to carry out their nursing duties without becoming ill or adversely affected. In addition, many students reported that the clinical environment was completely different from the skills laboratory at the college. Exposure to the clinical setting added to the theory-practice gap, and in some instances, the students fell ill.

One student made the following comment:

“I was assisting a doctor with a dressing, and the sight and smell from the oozing wound was too much for me. I was nauseated. As soon as the dressing was done, I ran to the bathroom and threw up. I asked myself… how will I survive the next 3 years of nursing?” (P14).

## Theme 3: learning to cope

The study participants indicated that they used coping mechanisms (both positive and negative) to adapt to and manage the stressors in their first clinical practicum. Important strategies that were reportedly used to cope with stress were time management, good preparation for clinical practice, and positive thinking as well as engaging in physical activity and self-motivation.

“Time management. Yes, it is important. I was encouraging myself. I used time management and prepared myself before going to the clinical site. Also, eating good food like cereal…it helps me very much in the clinic” (P28).

“Oh yeah, for sure positive thinking. In the hospital, I always think positively. Then, after coming home, I get [to] rest and think about positive things that I can do. So, I will think something good [about] these things, and then I will be relieved of stress” (P21).

Other strategies commonly reported by the participants were managing their breathing (e.g., taking deep breaths, breathing slowly), taking breaks to relax, and talking with friends about the problems they encountered.

“I prefer to take deep breaths and breathe slowly and to have a cup of coffee and to talk to my friends about the case or the clinical preceptor and what made me sad so I will feel more relaxed” (P16).

“Maybe I will take my break so I feel relaxed and feel better. After clinical training, I go directly home and take a long shower, going over the day. I will not think about anything bad that happened that day. I just try to think about good things so that I forget the stress” (P27).

“Yes, my first clinical training was not easy. It was difficult and made me stressed out…. I felt that it was a very difficult time for me. I thought about leaving nursing” (P7).

I was not able to offer my prayers. For me, this was distressing because as a Muslim, I pray regularly. Now, my prayer time is pushed to the end of the shift” (P11).

“When I feel stress, I talk to my friends about the case and what made me stressed. Then I will feel more relaxed” (P26).

Self-support or self-motivation through positive self-talk was also used by the students to cope with stress.

“Yes, it is difficult in the first clinical training. When I am stress[ed], I go to the bathroom and stand in the front of the mirror; I talk to myself, and I say, “You can do it,” “you are a great student.” I motivate myself: “You can do it”… Then, I just take breaths slowly several times. This is better than shouting or crying because it makes me tired” (P11).

Other participants used physical activity to manage their stress.

“How do I cope with my stress? Actually, when I get stressed, I will go for a walk on campus” (P4).

“At home, I will go to my room and close the door and start doing my exercises. After that, I feel the negative energy goes out, then I start to calm down… and begin my clinical assignments” (P21).

Both positive and negative coping strategies were utilized by the students. Some participants described using negative coping strategies when they encountered stress during their clinical practice. These negative coping strategies included becoming irritable and angry, eating too much food, drinking too much coffee, and smoking cigarettes.

“…Negative adaptation? Maybe coping. If I am stressed, I get so angry easily. I am irritable all day also…It is negative energy, right? Then, at home, I am also angry. After that, it is good to be alone to think about my problems” (P12).

“Yeah, if I…feel stress or depressed, I will eat a lot of food. Yeah, ineffective, like I will be eating a lot, drinking coffee. Like I said, effective, like I will prepare myself and do breathing, ineffective, I will eat a lot of snacks in between my free time. This is the bad side” (P16).

“…During the first clinical practice? Yes, it was a difficult experience for us…not only me. When stressed, during a break at the hospital, I will drink two or three cups of coffee… Also, I smoke cigarettes… A lot. I can drink six cups [of coffee] a day when I am stressed. After drinking coffee, I feel more relaxed, I finish everything (food) in the refrigerator or whatever I have in the pantry, like chocolates, chips, etc” (P23).

These supporting excerpts for each theme and the analysis offers valuable insights into the specific stressors faced by nursing students during their first clinical practicum. These insights will form the basis for the development of targeted interventions and supportive mechanisms within the clinical training curriculum to better support students’ adjustment and well-being during clinical practice.

Our study identified the stressors students encounter in their first clinical practicum and the coping strategies, both positive and negative, that they employed. Although this study emphasizes the importance of clinical training to prepare nursing students to practice as nurses, it also demonstrates the correlation between stressors and coping strategies.The content analysis of the first theme, managing expectations, paves the way for clinical agencies to realize that the students of today will be the nurses of tomorrow. It is important to provide a welcoming environment where students can develop their identities and learn effectively. Additionally, clinical staff should foster an environment of individualized learning while also assisting students in gaining confidence and competence in their repertoire of nursing skills, including critical thinking, problem solving and communication skills [ 8 , 15 , 19 , 30 ]. Another challenge encountered by the students in our study was that they were prevented from participating in clinical procedures by some nurses or patients. This finding is consistent with previous studies reporting that key challenges for students in clinical learning include a lack of clinical support and poor attitudes among clinical staff and instructors [ 31 ]. Clinical staff with positive attitudes have a positive impact on students’ learning in clinical settings [ 32 ]. The presence, supervision, and guidance of clinical instructors and the assistance of clinical staff are essential motivating components in the clinical learning process and offer positive reinforcement [ 30 , 33 , 34 ]. Conversely, an unsupportive learning environment combined with unwelcoming clinical staff and a lack of sense of belonging negatively impact students’ clinical learning [ 35 ].

The sources of stress identified in this study were consistent with common sources of stress in clinical training reported in previous studies, including the attitudes of some staff, students’ status in their clinical placement and educational factors. Nursing students’ inexperience in the clinical setting and lack of social and emotional experience also resulted in stress and psychological difficulties [ 36 ]. Bhurtun et al. [ 33 ] noted that nursing staff are a major source of stress for students because the students feel like they are constantly being watched and evaluated.

We also found that students were concerned about potential failure when working with patients during their clinical training. Their fear of failure when performing clinical procedures may be attributable to low self-confidence. Previous studies have noted that students were concerned about injuring patients, being blamed or chastised, and failing examinations [ 37 , 38 ]. This was described as feeling “powerless” in a previous study [ 7 , 12 ]. In addition, patients’ attitudes towards “rejecting” nursing students or patients’ refusal of their help were sources of stress among the students in our study and affected their self-confidence. Self-confidence and a sense of belonging are important for nurses’ personal and professional identity, and low self-confidence is a problem for nursing students in clinical learning [ 8 , 39 , 40 ]. Our findings are consistent with a previous study that reported that a lack of self-confidence was a primary source of worry and anxiety for nursing students and affected their communication and intention to leave nursing [ 41 ].

In the second theme, our study suggests that students encounter a theory-practice gap in clinical settings, which creates confusion and presents an additional stressors. Theoretical and clinical training are complementary elements of nursing education [ 40 ], and this combination enables students to gain the knowledge, skills, and attitudes necessary to provide nursing care. This is consistent with the findings of a previous study that reported that inconsistencies between theoretical knowledge and practical experience presented a primary obstacle to the learning process in the clinical context [ 42 ], causing students to lose confidence and become anxious [ 43 ]. Additionally, the second theme, the theory-practice gap, authenticates Safian et al.’s [ 5 ] study of the theory-practice gap that exists United Arab Emirates among nursing students as well as the need for more supportive clinical faculty and the extension of clinical hours. The need for better time availability and time management to complete clinical tasks were also reported by the students in the study. Students indicated that they had insufficient time to complete clinical activities because of the volume of coursework and assignments. Our findings support those of Chaabane et al. [ 15 ]. A study conducted in Saudi Arabia [ 44 ] found that assignments and workload were among the greatest sources of stress for students in clinical settings. Effective time management skills have been linked to academic achievement, stress reduction, increased creativity [ 45 ], and student satisfaction [ 46 ]. Our findings are also consistent with previous studies that reported that a common source of stress among first-year students was the increased classroom workload [ 19 , 47 ]. As clinical assignments and workloads are major stressors for nursing students, it is important to promote activities to help them manage these assignments [ 48 ].

Another major challenge reported by the participants was related to communicating and interacting with other nurses and patients. The UAE nursing workforce and population are largely expatriate and diverse and have different cultural and linguistic backgrounds. Therefore, student nurses encounter difficulty in communication [ 49 ]. This cultural diversity that students encounter in communication with patients during clinical training needs to be addressed by curriculum planners through the offering of language courses and courses on cultural diversity [ 50 ].

Regarding the third and final theme, nursing students in clinical training are unable to avoid stressors and must learn to cope with or adapt to them. Previous research has reported a link between stressors and the coping mechanisms used by nursing students [ 51 , 52 , 53 ]. In particular, the inability to manage stress influences nurses’ performance, physical and mental health, attitude, and role satisfaction [ 54 ]. One such study suggested that nursing students commonly use problem-focused (dealing with the problem), emotion-focused (regulating emotion), and dysfunctional (e.g., venting emotions) stress coping mechanisms to alleviate stress during clinical training [ 15 ]. Labrague et al. [ 51 ] highlighted that nursing students use both active and passive coping techniques to manage stress. The pattern of clinical stress has been observed in several countries worldwide. The current study found that first-year students experienced stress during their first clinical training [ 35 , 41 , 55 ]. The stressors they encountered impacted their overall health and disrupted their clinical learning. Chaabane et al. [ 15 ] reported moderate and high stress levels among nursing students in Bahrain, Egypt, Iraq, Jordan, Oman, Pakistan, Palestine, Saudi Arabia, and Sudan. Another study from Bahrain reported that all nursing students experienced moderate to severe stress in their first clinical placement [ 56 ]. Similarly, nursing students in Spain experienced a moderate level of stress, and this stress was significantly correlated with anxiety [ 30 ]. Therefore, it is imperative that pastoral systems at the university address students’ stress and mental health so that it does not affect their clinical performance. Faculty need to utilize evidence-based interventions to support students so that anxiety-producing situations and attrition are minimized.

In our study, students reported a variety of positive and negative coping mechanisms and strategies they used when they experienced stress during their clinical practice. Positive coping strategies included time management, positive thinking, self-support/motivation, breathing, taking breaks, talking with friends, and physical activity. These findings are consistent with those of a previous study in which healthy coping mechanisms used by students included effective time management, social support, positive reappraisal, and participation in leisure activities [ 57 ]. Our study found that relaxing and talking with friends were stress management strategies commonly used by students. Communication with friends to cope with stress may be considered social support. A previous study also reported that people seek social support to cope with stress [ 58 ]. Some students in our study used physical activity to cope with stress, consistent with the findings of previous research. Stretching exercises can be used to counteract the poor posture and positioning associated with stress and to assist in reducing physical tension. Promoting such exercise among nursing students may assist them in coping with stress in their clinical training [ 59 ].

Our study also showed that when students felt stressed, some adopted negative coping strategies, such as showing anger/irritability, engaging in unhealthy eating habits (e.g., consumption of too much food or coffee), or smoking cigarettes. Previous studies have reported that high levels of perceived stress affect eating habits [ 60 ] and are linked to poor diet quality, increased snacking, and low fruit intake [ 61 ]. Stress in clinical settings has also been linked to sleep problems, substance misuse, and high-risk behaviors’ and plays a major role in student’s decision to continue in their programme.

## Implications of the study

The implications of the study results can be grouped at multiple levels including; clinical, educational, and organizational level. A comprehensive approach to addressing the stressors encountered by nursing students during their clinical practicum can be overcome by offering some practical strategies to address the stressors faced by nursing students during their clinical practicum. By integrating study findings into curriculum planning, mentorship programs, and organizational support structures, a supportive and nurturing environment that enhances students’ learning, resilience, and overall success can be envisioned.

## Clinical level

Introducing simulation in the skills lab with standardized patients and the use of moulage to demonstrate wounds, ostomies, and purulent dressings enhances students’ practical skills and prepares them for real-world clinical scenarios. Organizing orientation days at clinical facilities helps familiarize students with the clinical environment, identify potential stressors, and introduce interventions to enhance professionalism, social skills, and coping abilities Furthermore, creating a WhatsApp group facilitates communication and collaboration among hospital staff, clinical tutors, nursing faculty, and students, enabling immediate support and problem-solving for clinical situations as they arise, Moreover, involving chief nursing officers of clinical facilities in the Nursing Advisory Group at the Department of Nursing promotes collaboration between academia and clinical practice, ensuring alignment between educational objectives and the needs of the clinical setting [ 62 ].

## Educational level

Sharing study findings at conferences (we presented the results of this study at Sigma Theta Tau International in July 2023 in Abu Dhabi, UAE) and journal clubs disseminates knowledge and best practices among educators and clinicians, promoting awareness and implementation of measures to improve students’ learning experiences. Additionally we hold mentorship training sessions annually in January and so we shared with the clinical mentors and preceptors the findings of this study so that they proactively they are equipped with strategies to support students’ coping with stressors during clinical placements.

## Organizational level

At the organizational we relooked at the available student support structures, including counseling, faculty advising, and career advice, throughout the nursing program emphasizing the importance of holistic support for students’ well-being and academic success as well as retention in the nursing program. Also, offering language courses as electives recognizes the value of communication skills in nursing practice and provides opportunities for personal and professional development.

For first-year nursing students, clinical stressors are inevitable and must be given proper attention. Recognizing nursing students’ perspectives on the challenges and stressors experienced in clinical training is the first step in overcoming these challenges. In nursing schools, providing an optimal clinical environment as well as increasing supervision and evaluation of students’ practices should be emphasized. Our findings demonstrate that first-year nursing students are exposed to a variety of different stressors. Identifying the stressors, pressures, and obstacles that first-year students encounter in the clinical setting can assist nursing educators in resolving these issues and can contribute to students’ professional development and survival to allow them to remain in the profession. To overcome stressors, students frequently employ problem-solving approaches or coping mechanisms. The majority of nursing students report stress at different levels and use a variety of positive and negative coping techniques to manage stress.

The present results may not be generalizable to other nursing institutions because this study used a purposive sample along with a qualitative approach and was limited to one university in the Middle East. Furthermore, the students self-reported their stress and its causes, which may have introduced reporting bias. The students may also have over or underreported stress or coping mechanisms because of fear of repercussions or personal reasons, even though the confidentiality of their data was ensured. Further studies are needed to evaluate student stressors and coping now that measures have been introduced to support students. Time will tell if these strategies are being used effectively by both students and clinical personnel or if they need to be readdressed. Finally, we need to explore the perceptions of clinical faculty towards supervising students in their first clinical practicum so that clinical stressors can be handled effectively.

## Data availability

The data sets are available with the corresponding author upon reasonable request.

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## Acknowledgements

The authors are grateful to all second year nursing students who voluntarily participated in the study.

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Jacqueline Maria Dias, Muhammad Arsyad Subu, Nabeel Al-Yateem, Fatma Refaat Ahmed, Syed Azizur Rahman, Mini Sara Abraham, Sareh Mirza Forootan, Farzaneh Ahmad Sarkhosh & Fatemeh Javanbakh

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## Contributions

JMD conceptualized the idea and designed the methodology, formal analysis, writing original draft and project supervision and mentoring. MAS prepared the methodology and conducted the qualitative interviews and analyzed the methodology and writing of original draft and project supervision. NY, FRA, SAR, MSA writing review and revising the draft. SMF, FAS, FJ worked with MAS on the formal analysis and prepared the first draft.All authors reviewed the final manuscipt of the article.

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Dias, J.M., Subu, M.A., Al-Yateem, N. et al. Nursing students’ stressors and coping strategies during their first clinical training: a qualitative study in the United Arab Emirates. BMC Nurs 23 , 322 (2024). https://doi.org/10.1186/s12912-024-01962-5

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## DAA Tutorial

Asymptotic analysis, analysis of sorting, divide and conquer, lower bound theory, sorting in linear time, binary search trees, red black tree, dynamic programming, greedy algorithm, backtracking, shortest path, all-pairs shortest paths, maximum flow, sorting networks, complexity theory, approximation algo, string matching.

Interview Questions

In the above matrix, columns represent the weight, i.e., 8. The rows represent the profits and weights of items. Here we have not taken the weight 8 directly, problem is divided into sub-problems, i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8. The solution of the sub-problems would be saved in the cells and answer to the problem would be stored in the final cell. First, we write the weights in the ascending order and profits according to their weights shown as below:

w i = {3, 4, 5, 6}

p i = {2, 3, 4, 1}

The first row and the first column would be 0 as there is no item for w=0

When i=1, W=1

w 1 = 3; Since we have only one item in the set having weight 3, but the capacity of the knapsack is 1. We cannot fill the item of 3kg in the knapsack of capacity 1 kg so add 0 at M[1][1] shown as below:

When i = 1, W = 2

w 1 = 3; Since we have only one item in the set having weight 3, but the capacity of the knapsack is 2. We cannot fill the item of 3kg in the knapsack of capacity 2 kg so add 0 at M[1][2] shown as below:

When i=1, W=3

w 1 = 3; Since we have only one item in the set having weight equal to 3, and weight of the knapsack is also 3; therefore, we can fill the knapsack with an item of weight equal to 3. We put profit corresponding to the weight 3, i.e., 2 at M[1][3] shown as below:

When i=1, W = 4

W1 = 3; Since we have only one item in the set having weight equal to 3, and weight of the knapsack is 4; therefore, we can fill the knapsack with an item of weight equal to 3. We put profit corresponding to the weight 3, i.e., 2 at M[1][4] shown as below:

When i=1, W = 5

W1 = 3; Since we have only one item in the set having weight equal to 3, and weight of the knapsack is 5; therefore, we can fill the knapsack with an item of weight equal to 3. We put profit corresponding to the weight 3, i.e., 2 at M[1][5] shown as below:

When i =1, W=6

W1 = 3; Since we have only one item in the set having weight equal to 3, and weight of the knapsack is 6; therefore, we can fill the knapsack with an item of weight equal to 3. We put profit corresponding to the weight 3, i.e., 2 at M[1][6] shown as below:

When i=1, W = 7

W1 = 3; Since we have only one item in the set having weight equal to 3, and weight of the knapsack is 7; therefore, we can fill the knapsack with an item of weight equal to 3. We put profit corresponding to the weight 3, i.e., 2 at M[1][7] shown as below:

When i =1, W =8

W1 = 3; Since we have only one item in the set having weight equal to 3, and weight of the knapsack is 8; therefore, we can fill the knapsack with an item of weight equal to 3. We put profit corresponding to the weight 3, i.e., 2 at M[1][8] shown as below:

Now the value of 'i' gets incremented, and becomes 2.

When i =2, W = 1

The weight corresponding to the value 2 is 4, i.e., w 2 = 4. Since we have only one item in the set having weight equal to 4, and the weight of the knapsack is 1. We cannot put the item of weight 4 in a knapsack, so we add 0 at M[2][1] shown as below:

When i =2, W = 2

The weight corresponding to the value 2 is 4, i.e., w 2 = 4. Since we have only one item in the set having weight equal to 4, and the weight of the knapsack is 2. We cannot put the item of weight 4 in a knapsack, so we add 0 at M[2][2] shown as below:

When i =2, W = 3

The weight corresponding to the value 2 is 4, i.e., w 2 = 4. Since we have two items in the set having weights 3 and 4, and the weight of the knapsack is 3. We can put the item of weight 3 in a knapsack, so we add 2 at M[2][3] shown as below:

When i =2, W = 4

The weight corresponding to the value 2 is 4, i.e., w 2 = 4. Since we have two items in the set having weights 3 and 4, and the weight of the knapsack is 4. We can put item of weight 4 in a knapsack as the profit corresponding to weight 4 is more than the item having weight 3, so we add 3 at M[2][4] shown as below:

When i = 2, W = 5

The weight corresponding to the value 2 is 4, i.e., w 2 = 4. Since we have two items in the set having weights 3 and 4, and the weight of the knapsack is 5. We can put item of weight 4 in a knapsack and the profit corresponding to weight is 3, so we add 3 at M[2][5] shown as below:

When i = 2, W = 6

The weight corresponding to the value 2 is 4, i.e., w 2 = 4. Since we have two items in the set having weights 3 and 4, and the weight of the knapsack is 6. We can put item of weight 4 in a knapsack and the profit corresponding to weight is 3, so we add 3 at M[2][6] shown as below:

When i = 2, W = 7

The weight corresponding to the value 2 is 4, i.e., w 2 = 4. Since we have two items in the set having weights 3 and 4, and the weight of the knapsack is 7. We can put item of weight 4 and 3 in a knapsack and the profits corresponding to weights are 2 and 3; therefore, the total profit is 5, so we add 5 at M[2][7] shown as below:

When i = 2, W = 8

Now the value of 'i' gets incremented, and becomes 3.

When i = 3, W = 1

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set having weights 3, 4, and 5, and the weight of the knapsack is 1. We cannot put neither of the items in a knapsack, so we add 0 at M[3][1] shown as below:

When i = 3, W = 2

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set having weight 3, 4, and 5, and the weight of the knapsack is 1. We cannot put neither of the items in a knapsack, so we add 0 at M[3][2] shown as below:

When i = 3, W = 3

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set of weight 3, 4, and 5 respectively and weight of the knapsack is 3. The item with a weight 3 can be put in the knapsack and the profit corresponding to the item is 2, so we add 2 at M[3][3] shown as below:

When i = 3, W = 4

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set of weight 3, 4, and 5 respectively, and weight of the knapsack is 4. We can keep the item of either weight 3 or 4; the profit (3) corresponding to the weight 4 is more than the profit corresponding to the weight 3 so we add 3 at M[3][4] shown as below:

When i = 3, W = 5

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set of weight 3, 4, and 5 respectively, and weight of the knapsack is 5. We can keep the item of either weight 3, 4 or 5; the profit (3) corresponding to the weight 4 is more than the profits corresponding to the weight 3 and 5 so we add 3 at M[3][5] shown as below:

When i =3, W = 6

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set of weight 3, 4, and 5 respectively, and weight of the knapsack is 6. We can keep the item of either weight 3, 4 or 5; the profit (3) corresponding to the weight 4 is more than the profits corresponding to the weight 3 and 5 so we add 3 at M[3][6] shown as below:

When i =3, W = 7

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set of weight 3, 4, and 5 respectively, and weight of the knapsack is 7. In this case, we can keep both the items of weight 3 and 4, the sum of the profit would be equal to (2 + 3), i.e., 5, so we add 5 at M[3][7] shown as below:

When i = 3, W = 8

The weight corresponding to the value 3 is 5, i.e., w 3 = 5. Since we have three items in the set of weight 3, 4, and 5 respectively, and the weight of the knapsack is 8. In this case, we can keep both the items of weight 3 and 4, the sum of the profit would be equal to (2 + 3), i.e., 5, so we add 5 at M[3][8] shown as below:

Now the value of 'i' gets incremented and becomes 4.

When i = 4, W = 1

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 1. The weight of all the items is more than the weight of the knapsack, so we cannot add any item in the knapsack; Therefore, we add 0 at M[4][1] shown as below:

When i = 4, W = 2

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 2. The weight of all the items is more than the weight of the knapsack, so we cannot add any item in the knapsack; Therefore, we add 0 at M[4][2] shown as below:

When i = 4, W = 3

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 3. The item with a weight 3 can be put in the knapsack and the profit corresponding to the weight 4 is 2, so we will add 2 at M[4][3] shown as below:

When i = 4, W = 4

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 4. The item with a weight 4 can be put in the knapsack and the profit corresponding to the weight 4 is 3, so we will add 3 at M[4][4] shown as below:

When i = 4, W = 5

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 5. The item with a weight 4 can be put in the knapsack and the profit corresponding to the weight 4 is 3, so we will add 3 at M[4][5] shown as below:

When i = 4, W = 6

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 6. In this case, we can put the items in the knapsack either of weight 3, 4, 5 or 6 but the profit, i.e., 4 corresponding to the weight 6 is highest among all the items; therefore, we add 4 at M[4][6] shown as below:

When i = 4, W = 7

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 7. Here, if we add two items of weights 3 and 4 then it will produce the maximum profit, i.e., (2 + 3) equals to 5, so we add 5 at M[4][7] shown as below:

When i = 4, W = 8

The weight corresponding to the value 4 is 6, i.e., w 4 = 6. Since we have four items in the set of weights 3, 4, 5, and 6 respectively, and the weight of the knapsack is 8. Here, if we add two items of weights 3 and 4 then it will produce the maximum profit, i.e., (2 + 3) equals to 5, so we add 5 at M[4][8] shown as below:

As we can observe in the above table that 5 is the maximum profit among all the entries. The pointer points to the last row and the last column having 5 value. Now we will compare 5 value with the previous row; if the previous row, i.e., i = 3 contains the same value 5 then the pointer will shift upwards. Since the previous row contains the value 5 so the pointer will be shifted upwards as shown in the below table:

Again, we will compare the value 5 from the above row, i.e., i = 2. Since the above row contains the value 5 so the pointer will again be shifted upwards as shown in the below table:

Again, we will compare the value 5 from the above row, i.e., i = 1. Since the above row does not contain the same value so we will consider the row i=1, and the weight corresponding to the row is 4. Therefore, we have selected the weight 4 and we have rejected the weights 5 and 6 shown below:

x = { 1, 0, 0}

The profit corresponding to the weight is 3. Therefore, the remaining profit is (5 - 3) equals to 2. Now we will compare this value 2 with the row i = 2. Since the row (i = 1) contains the value 2; therefore, the pointer shifted upwards shown below:

Again we compare the value 2 with a above row, i.e., i = 1. Since the row i =0 does not contain the value 2, so row i = 1 will be selected and the weight corresponding to the i = 1 is 3 shown below:

X = {1, 1, 0, 0}

The profit corresponding to the weight is 2. Therefore, the remaining profit is 0. We compare 0 value with the above row. Since the above row contains a 0 value but the profit corresponding to this row is 0. In this problem, two weights are selected, i.e., 3 and 4 to maximize the profit.

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Design and Analysis of Algorithms. Design and Analysis of Algorithms is a fundamental aspect of computer science that involves creating efficient solutions to computational problems and evaluating their performance. DSA focuses on designing algorithms that effectively address specific challenges and analyzing their efficiency in terms of time ...

Learn the general method of backtracking in DAA and how to apply it to solve complex problems. Understand the concept, algorithm, and examples of backtracking. ... Backtracking is a problem-solving strategy that involves recursively exploring all possible solutions to a problem. It is a form of brute force approach that systematically generates ...

Algorithm Design Techniques. 1. Divide and Conquer Approach: It is a top-down approach. The algorithms which follow the divide & conquer techniques involve three steps: Divide the original problem into a set of subproblems. Solve every subproblem individually, recursively. Combine the solution of the subproblems (top level) into a solution of ...

The divide-and-conquer strategy DAA 2019 2. Divide and Conquer Algorithms - 3 / 52 The divide-and-conquer strategy solves a problem by: 1. Breaking it into subproblems (smaller instances of the same problem) 2. Recursively solving these subproblems [Base case: If the subproblems are small enough, just solve them by brute force.] 3.

Problem Solving: Different problems require different algorithms, and by having a classification, it can help identify the best algorithm for a particular problem. Performance Comparison: By classifying algorithms, it is possible to compare their performance in terms of time and space complexity, making it easier to choose the best algorithm for a particular use case.

Design and Analysis of Algorithms Tutorial - An Algorithm is a sequence of steps to solve a problem. It acts like a set of instructions on how a program should be executed. Thus, there is no fixed structure of an algorithm. Design and Analysis of Algorithms covers the concepts of designing an algorithm as to solve various problems in computer.

As the name says divide and conquer, it follows following steps: Step 1: Divide the problem into several subproblems. Step 2: Conquer or solve each sub-problem. Step 3: Combine each sub-problem to get the required result. Divide and Conquer solve each subproblem recursively, so each subproblem will be the smaller original problem.

Divide and Conquer Approach. This strategy is about dividing a problem into more than one subproblems, solving each of them, and then, if necessary, combining their solutions to get a solution to the original problem. We solve many fundamental problems efficiently in computer science by using this strategy. Example problems: Merge Sort , Quick ...

Analysis of algorithm is the process of analyzing the problem-solving capability of the algorithm in terms of the time and size required (the size of memory for storage while implementation). However, the main concern of analysis of algorithms is the required time or performance.

DAA 2020-22 7. Greedy Algorithms - 2 / 35 Greedy algorithms are typically used to solve optimisation problems. The solution is constructed step by step. At each step, the algorithm makes the choice that offers the greatest immediate beneﬁt (also called the greedy choice). A choice made at one step is not reconsidered at subsequent steps.

An Algorithm is a set of well-defined instructions designed to perform a specific set of tasks. Algorithms are used in Computer science to perform calculations, automatic reasoning, data processing, computations, and problem-solving. Designing an algorithm is important before writing the program code as the algorithm explains the logic even ...

Analysis of algorithm is the process of analyzing the problem-solving capability of the algorithm in terms of the time and size required (the size of memory for storage while implementation ...

DAA Algorithm with daa tutorial, introduction, Algorithm, Asymptotic Analysis, Control Structure, Recurrence, Master Method, Recursion Tree Method, Sorting Algorithm, Bubble Sort, Selection Sort, Insertion Sort, Binary Search, Merge Sort, Counting Sort, etc. ... The greedy method is a problem-solving strategy in the design and analysis of ...

Fundamental Algorithmic Strategies: Brute-Force, Greedy, Dynamic Programming, Branch- and-Bound and Backtracking methodologies for the design of algorithms; Illustrations of these techniques for Problem-Solving, Bin Packing, Knap Sack TSP. Heuristics-characteristics and their application domains.

The first strategy you might try when solving a routine problem is called an algorithm. Algorithms are step-by-step strategies or processes for how to solve a problem or achieve a goal. Another solution that many people use to solve problems is called heuristics. Heuristics are general strategies used to make quick, short-cut

Divide and Conquer is an algorithmic pattern. In algorithmic methods, the design is to take a dispute on a huge input, break the input into minor pieces, decide the problem on each of the small pieces, and then merge the piecewise solutions into a global solution. This mechanism of solving the problem is called the Divide & Conquer Strategy.

Step 3: Designing efficient solution with pseudocode. This is a stage to use the best experience of DSA problem-solving and apply various problem-solving strategies. One practical truth is: moving from a basic algorithm to the most efficient algorithm is a little difficult in a single step. Each time, we need to optimize the previous algorithm ...

DAA, short for Design and Analysis of Algorithms, is a fundamental concept in computer science that deals with the study of efficient algorithms for solving problems. It encompasses various techniques and strategies used to design algorithms and assess their efficiency in terms of time and space complexity. DAA plays a crucial role in developing efficient […]

Backtracking is a problem-solving algorithmic technique that involves finding a solution incrementally by trying different options and undoing them if they lead to a dead end. It is commonly used in situations where you need to explore multiple possibilities to solve a problem, like searching for a path in a maze or solving puzzles like Sudoku .

6. Approximate algorithms are a strategy for overcoming NP-completeness in optimisation problems. The optimal answer is not always ensured by this method. The approximation algorithm aims to reach ...

DAA Tutorial. Our DAA Tutorial is designed for beginners and professionals both. Our DAA Tutorial includes all topics of algorithm, asymptotic analysis, algorithm control structure, recurrence, master method, recursion tree method, simple sorting algorithm, bubble sort, selection sort, insertion sort, divide and conquer, binary search, merge sort, counting sort, lower bound theory etc.

In general, effective problem-solving strategies include the following steps: Define the problem. Come up with alternative solutions. Decide on a solution. Implement the solution. Problem-solving ...

Understanding the stressors and coping strategies of nursing students in their first clinical training is important for improving student performance, helping students develop a professional identity and problem-solving skills, and improving the clinical teaching aspects of the curriculum in nursing programmes. While previous research have examined nurses' sources of stress and coping styles ...

Create a Results Strategy and an Implementation Plan. The Results Strategy is a working road map and a problem-solving tool that guides the allocation of time and resources.

The 0/1 knapsack problem means that the items are either completely or no items are filled in a knapsack. For example, we have two items having weights 2kg and 3kg, respectively. If we pick the 2kg item then we cannot pick 1kg item from the 2kg item (item is not divisible); we have to pick the 2kg item completely.