intermediate problem solving and data structures

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Intermediate problem solving and data structures : walls and mirrors

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• Computers & Technology
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Walls and Mirrors: Intermediate Problem Solving and Data Structures : Modula, 2 (Benjamin/Cummings Series in Structured Programming) 2nd Edition

There is a newer edition of this item:.

• ISBN-10 0805389458
• ISBN-13 978-0805389456
• Edition 2nd
• Publisher Benjamin-Cummings Pub Co
• Publication date January 1, 1988
• Language English
• Print length 649 pages
• See all details

Product details

• Publisher ‏ : ‎ Benjamin-Cummings Pub Co; 2nd edition (January 1, 1988)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 649 pages
• ISBN-10 ‏ : ‎ 0805389458
• ISBN-13 ‏ : ‎ 978-0805389456
• Item Weight ‏ : ‎ 1.1 pounds
• #9,862 in Computer Programming Languages
• #25,973 in Programming Languages (Books)
• #83,297 in Professional

About the author

Paul helman.

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Problem Solving

Solving problems is the core of computer science. Programmers must first understand how a human solves a problem, then understand how to translate this "algorithm" into something a computer can do, and finally how to write the specific code to implement the solution. At its core, problem-solving focuses on the study, understanding, and usage of data structures and algorithms. 

This competency area includes usage of hash maps, stacks, queues, heaps, and analyzing run-time complexities and space complexities, among others. 

Key Competencies:

• Data Structures  - Use data structures such as hash maps, stacks, queues, heaps. Manipulate single or double-linked lists, and maintain basic information about subtrees, node distances, etc.
• Algorithms  - Use optimal solutions to solve problems. Analyze run-time complexities and space complexities. Create simple dynamic programming-based algorithms.

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Intermediate Data Structures and Algorithms

• (Jun 6) Problems discussed in class posted
• (Jun 3) Updated slides on weighted graphs (all-pairs example)
• (May 25) Midterm 2 posted
• (May 16) Homework 6 and 7 posted
• (May 16) Problems discussed in class posted
• (May 13) Practice exam for midterm 2
• (May 9) Slides on graphs posted
• (May 9) Homework 5 posted
• (May 2) Homework 4 posted
• (May 1) Dynamic programming slides posted
• (May 1) Midterm 1 posted
• (Apr 25) Problems discussed in class posted
• (Apr 18) Homework 3 posted
• (Apr 18) Greedy slides posted
• (Apr 17) Closest pair animation slides posted
• (Apr 11) Homework 2 posted
• (Apr 9) Slides on divide-and-conquer posted
• (Apr 4) Homework 1 posted
• (Apr 1) Slides on Algorithm Analysis posted
• (Apr 1) Our TAs are Anuja Patil, Lixiao Li and Tanmay Shah: welcome!
• Happy Spring Break

Basic information

• Read the syllabus .
• Stefano Lonardi ( [email protected] )
• Office hours: Tuesdays 11am-12noon.
• Office: CHUNG HALL , room 325.
• Tanmay Shah ( [email protected] )
• Tanmay's office hours: Tuesdays 10am-11am
• Lixiao Li ( [email protected] )
• Lixiao' office hours: Wednesday 10-11 am
• Anuja Patil ( [email protected] )
• Anuja's office hours: Monday 3-4pm
• TA Office hours are held in CHUNG HALL , room 110.
• TR 2:10am-3:30pm, Watkins , room 1000.
• Algorithms , by Sanjoy Dasgupta, Christos Papadimitriou, Umesh Vazirani. McGrawHill 2007.
• Introduction to Algorithms (3rd Edition) by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Cliff Stein, MIT Press.
• Algorithm Design (Foundations, Analysis, and Internet Examples) by Michael T. Goodrich and Roberto Tamassia, Wiley.
• This is a four-unit CS course. As such, you should expect to spend the following approximate amount of time: 3 hours/week in lecture 1 hour/week discussion 6 to 10 hours/week doing individual study (readings, homework, programming assignments, preparation for lectures, etc).
• Please don't underestimate the time you will need to spend on this course. These are real time amounts spent by average successful past students. Computer Science and Engineering are challenging disciplines requiring extensive time to master.

Discussion Board

• Course Overview [PDF]
• Algorithm Analysis [PDF]
• Divide & Conquer [PDF]
• Closest Pair animation [PPT]
• Greedy (part I) [PDF]
• Greedy (part II) [PDF]
• Dynamic Programming [PDF]
• Weighted Graphs [PDF]
• Apr  2 : Overview of the course, Analysis (slides 1-33)
• Apr  4 : Analysis (34-65) [hw1 posted]
• Apr  9 : Analysis (66-end)
• Apr 11 : Divide and Conquer (1-32) [hw1 due][hw2 posted]
• Apr 16 : Divide and Conquer (33-57)
• Apr 18 : Divide and Conquer (58-end), Greedy (1-24) [hw2 due][hw3 posted]
• Apr 23 : Greedy (25-45)
• Apr 25 : Greedy (46-49), Midterm 1 prep [hw3 due]
• Apr 30 : Midterm 1
• May 2 : Greedy (50-end), Dynamic Programming (1-28) [hw4 posted]
• May 7 : Dynamic Programming (29-42)
• May 9 : Midterm 1 review, Dynamic Programming (43-end) [hw4 due][hw5 posted]
• May 14 : Weighted graphs (1-44)
• May 16 : Weighted graphs (45-50), Midterm 2 prep [hw5 due]
• May 21 : Midterm 2
• May 23 : Weighted graphs (51-77) [hw6 posted]
• May 28 : Weighted graphs (78-108)
• May 30 : Midterm 2 review, Weighted graphs (109-119) [hw6 due][hw7 posted]
• Jun 4 : Weighted graphs (120-end)
• Jun 6 : Final prep [hw7 due]
• Jun 13 : Final 8am-11am

Python Code

• Examples from slides

Homework and Solutions

• Homework 1 [PDF] , [LaTeX] (posted April 4th, due April 11th)
• Homework 1 solution [PDF] (posted April 13th)
• Homework 2 [PDF] , [LaTeX] (posted April 11th, due April 18th)
• Homework 2 solution [PDF] (posted April 19th)
• Homework 3 [PDF] , [LaTeX] (posted April 18th, due April 25th)
• Homework 3 solution [PDF] (posted April 28th)
• Homework 4 [PDF] , [LaTeX] (posted May 2nd, due May 9th)
• Homework 4 solution [PDF] (posted May 12th)
• Homework 5 [PDF] , [LaTeX] (posted May 9th, due May 16th)
• Homework 5 solution [PDF] (posted May 17th)
• Homework 6 [PDF] , [LaTeX] (posted May 23th, due May 30th)
• Homework 6 solution [PDF] (posted Jun 3rd)
• Homework 7 [PDF] , [LaTeX] (posted May 30th, due Jun 6th)
• Homework 7 solution [PDF] (posted Jun 6th)

Exams and related material

• Syllabus for Midterm 1
• A mock exam for Midterm 1
• Solution for the mock exam
• Problems discussed in class
• Midterm 1/A
• Midterm 1/B
• Midterm 1/A solution
• Midterm 1/B solution
• Syllabus for Midterm 2
• A mock exam for Midterm 2
• Midterm 2/A
• Midterm 2/B
• Midterm 2/A solution
• Midterm 2/B solution
• Syllabus for final

General course features and policies

Some useful pointers.

• Get LaTeX for your computer
• Dive into Python
• Python Documentation
• Davis's algorithm python examples
• More python examples from David Eppstein

EnjoyMathematics

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?

Enjoy learning, Enjoy coding, Enjoy algorithms!

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Exploring Intermediate JavaScript Concepts: Moving Beyond Basics

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JavaScript is an essential component of modern web development.

With the JavaScript programming language community encompassing around 57.8 percent of software developers as of 2023, it holds the position of the most widely used programming language globally.

As developers become more proficient in the language, it is important to move beyond the basics and explore intermediate JavaScript concepts that can enhance their skills and enable them to tackle more complex projects.

This article delves into various intermediate JavaScript concepts, spanning from functions and objects to asynchronous programming and debugging.

Understanding the importance of intermediate JavaScript

Intermediate JavaScript concepts are a crucial stepping stone for web developers looking to improve their skills and build more sophisticated applications.

While mastering the basics of JavaScript is essential, it is equally important to explore the intermediate concepts that the language offers.

With intermediate JavaScript knowledge, developers can create more dynamic web pages, handle complex data structures, and enhance user interactions.

Developers can unlock new possibilities and broaden their programming horizons by delving into the intricacies of intermediate JavaScript concepts.

The role of intermediate JavaScript concepts in web development

JavaScript plays a vital role in modern web development. It allows developers to add interactivity, dynamic content, and responsiveness to web pages.

With intermediate JavaScript concepts, developers can create user-friendly interfaces, validate user input, manipulate data, and communicate with web servers.

As the backbone of many web applications and frameworks, JavaScript empowers developers to build scalable, interactive, and feature-rich websites.

Therefore, developers need to elevate their JavaScript skills beyond the basics.

Why moving beyond basics is crucial

Moving beyond the basics of JavaScript is crucial for developers aiming to build professional-grade applications.

Basic knowledge might be sufficient for simple scripting tasks, but when it comes to developing complex web applications, intermediate JavaScript concepts are indispensable.

By expanding their skillset and delving into intermediate JavaScript concepts, developers gain the ability to solve more complex problems, write efficient code, and optimise performance.

Moving beyond basics is the pathway to becoming a well-rounded JavaScript developer.

Diving into JavaScript functions

JavaScript functions are the building blocks of the language. They allow developers to encapsulate reusable blocks of code, promo code organisation, and enhance code modularity.

A key concept to explore in this section is higher-order functions. These functions take one or more functions as arguments or return a function as a result.

With higher-order functions, developers can implement powerful functional programming techniques and tackle complex algorithms with ease.

Unpacking higher-order functions

Higher-order functions open up new avenues for developers to write concise and expressive code.

By accepting functions as arguments or returning functions, higher-order functions enable developers to implement advanced functionality such as function composition, function currying, and memoisation.

Understanding how to use and create higher-order functions can greatly improve the code quality and maintainability of JavaScript applications.

Mastering closure in JavaScript

Closure is another fundamental concept to explore when diving into JavaScript functions.

A closure is created when a function retains access to variables from its outer lexical scope, even after the outer function has finished executing.

This powerful mechanism allows developers to create private variables, implement data hiding, and build modular code.

By mastering closure, developers can design more robust and secure JavaScript applications.

Exploring JavaScript objects and prototypes

In JavaScript, objects are a fundamental data structure that enables developers to model real-world entities and organise data.

Understanding object-oriented programming and the role of prototypes is essential for utilising JavaScript’s object capabilities to their full potential.

The power of object-oriented programming

Object-oriented programming (OOP) is a paradigm widely used in JavaScript development. It enables developers to model complex systems and create reusable, modular code.

By utilising classes, inheritance, and encapsulation, developers can build scalable and maintainable applications.

Exploring the principles and techniques of OOP in JavaScript empowers developers to design elegant and extensible solutions.

Understanding prototypes and inheritance

Prototypes and inheritance form the core of object-oriented programming in JavaScript.

Prototypes allow objects to inherit properties and methods from other objects, enabling code reuse and defining class hierarchies.

By understanding prototypal inheritance, developers can create efficient and extensible object-oriented JavaScript code.

This knowledge is crucial for developers looking to maximise code reuse and maintainability.

Decoding asynchronous JavaScript

JavaScript operates in an asynchronous and event-driven environment, making it crucial for developers to understand how to manage asynchronous operations effectively.

This section will delve into the magic of promises and async/await, as well as the event loop and callback queue.

The magic of promises and async/await

Asynchronous operations are a common feature in intermediate JavaScript concepts and applications.

Promises and async/await are powerful techniques that alleviate the complexity of handling asynchronous code.

Promises provide a way to work with asynchronous operations more elegantly and reliably, while async/await syntax simplifies asynchronous code by allowing developers to write it in a synchronous style.

By mastering promises and async/await, developers can build robust and maintainable asynchronous JavaScript code.

Event loop and callback queue explained

The event loop and callback queue are fundamental concepts to understand how JavaScript manages asynchronous code execution.

The event loop ensures that JavaScript remains responsive by continuously checking and executing tasks from the callback queue.

Understanding how the event loop works is crucial for developers to write performant and responsive JavaScript applications.

Mastering JavaScript debugging and testing

Effective debugging and testing are essential skills for every JavaScript developer.

This section will cover essential debugging techniques and introduce JavaScript testing frameworks to ensure code quality and mitigate potential issues.

Essential debugging techniques

Bugs are an inevitable part of the development process. Knowing how to effectively debug JavaScript code can save developers valuable time and frustration.

This section will explore techniques such as console debugging, breakpoints, and logging to uncover and fix issues in JavaScript applications.

Introduction to JavaScript testing frameworks

Testing is crucial for maintaining code quality and preventing regressions. JavaScript testing frameworks provide developers with the tools and infrastructure to automate the testing process.

This section will introduce popular JavaScript testing frameworks, such as Jest and Mocha, and explain how to write unit tests and integration tests for JavaScript applications.

Exploring intermediate JavaScript concepts is essential for developers looking to enhance their skills and move beyond the basics.

By gaining a deeper understanding of JavaScript functions, objects, asynchronous programming, and debugging/testing techniques, developers can elevate their JavaScript expertise and build more sophisticated applications.

As JavaScript continues to evolve, delving into these intermediate JavaScript concepts will keep developers well-equipped to tackle the challenges of modern web development.

If you’re interested in enrolling in an online course designed to fit your schedule, you can download a copy of the Institute of Data’s comprehensive Software Engineering program outline for free.

Alternatively, book a free career consultation with a member of our team to discuss the program further.

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