Algorithms, Part I

Go to Course: https://www.coursera.org/learn/algorithms-part1

Introduction

### Course Review: Algorithms, Part I on Coursera **Overview:** The "Algorithms, Part I" course offered by Coursera is an essential learning resource for anyone who is serious about programming and software development. This course delivers a comprehensive foundation in the world of algorithms and data structures, focusing primarily on Java implementations. Whether you are a novice looking to strengthen your understanding or a seasoned developer aiming to refine your algorithmic skills, this course is designed to elevate your proficiency in algorithm design and analysis. **Course Features:** - **Accessibility:** One of the most appealing aspects of this course is that all features are available for free. This means that anyone can gain access to high-quality educational content without incurring any fees. - **No Certification:** While it does not offer a certificate upon completion, the value remains in the knowledge and practical skills you will acquire, which can be applied in real-world programming scenarios. **Course Content:** The syllabus is well-structured, diving into various critical areas: 1. **Union-Find Data Structure:** Beginning with the dynamic connectivity problem, learners will understand the union-find data type and multiple implementations, applying these concepts to percolation problems. 2. **Analysis of Algorithms:** This module emphasizes the scientific approach to performance analysis, teaching how to measure and hypothesize the efficiency of algorithmic implementations. 3. **Stacks and Queues:** Participants will explore these fundamental data structures, learning practical applications and how to implement them using Java. 4. **Elementary Sorting Algorithms:** The course covers various sorting algorithms, providing insight into their methodologies and applications, including a study of the Graham scan for computing convex hulls. 5. **Advanced Sorting Techniques (Mergesort and Quicksort):** Understanding these complex sorting algorithms allows learners to grasp their inner workings and performance analysis. 6. **Priority Queues & Binary Heaps:** By introducing the priority queue data type and implementing heaps, the course underscores the functionality behind efficient sorting algorithms, such as heapsort. 7. **Balanced Search Trees and Hash Tables:** Participants will learn how to manage and manipulate data efficiently, including binary search trees and hash functions, which are crucial for indexing and retrieval tasks. 8. **Geometric Applications:** Applying algorithms to real-world scenarios helps solidify understanding, particularly in range searching and computational geometry. Each section builds on the previous material, encouraging students to develop a comprehensive understanding of algorithm design. **Learning Experience:** The course utilizes a mix of video lectures, readings, and practical assignments that reinforce the concepts being taught. The clarity of the instructor combined with real-world problem-solving scenarios enhances the learning experience. Students are encouraged to engage in discussions and practice coding to solidify their comprehension. **Recommendation:** I highly recommend "Algorithms, Part I" for anyone interested in deepening their understanding of algorithms and data structures, especially in Java. The course’s focus on fundamental concepts, combined with practical applications, makes it a valuable resource for aspiring software engineers, computer science students, or those looking to enhance their programming skills. By the end of this course, you will not only acquire theoretical knowledge but also gain practical insights that can be directly applied in software development projects. Given that the course is free, it presents an excellent opportunity for learners to enrich their resume without the pressure of paying for a certificate. Dive into this course to transform your approach to programming and problem-solving!

Syllabus

Course Introduction

Welcome to Algorithms, Part I.

We illustrate our basic approach to developing and analyzing algorithms by considering the dynamic connectivity problem. We introduce the union−find data type and consider several implementations (quick find, quick union, weighted quick union, and weighted quick union with path compression). Finally, we apply the union−find data type to the percolation problem from physical chemistry.

The basis of our approach for analyzing the performance of algorithms is the scientific method. We begin by performing computational experiments to measure the running times of our programs. We use these measurements to develop hypotheses about performance. Next, we create mathematical models to explain their behavior. Finally, we consider analyzing the memory usage of our Java programs.

We consider two fundamental data types for storing collections of objects: the stack and the queue. We implement each using either a singly-linked list or a resizing array. We introduce two advanced Java features—generics and iterators—that simplify client code. Finally, we consider various applications of stacks and queues ranging from parsing arithmetic expressions to simulating queueing systems.

We introduce the sorting problem and Java's Comparable interface. We study two elementary sorting methods (selection sort and insertion sort) and a variation of one of them (shellsort). We also consider two algorithms for uniformly shuffling an array. We conclude with an application of sorting to computing the convex hull via the Graham scan algorithm.

We study the mergesort algorithm and show that it guarantees to sort any array of n items with at most n lg n compares. We also consider a nonrecursive, bottom-up version. We prove that any compare-based sorting algorithm must make at least n lg n compares in the worst case. We discuss using different orderings for the objects that we are sorting and the related concept of stability.

We introduce and implement the randomized quicksort algorithm and analyze its performance. We also consider randomized quickselect, a quicksort variant which finds the kth smallest item in linear time. Finally, we consider 3-way quicksort, a variant of quicksort that works especially well in the presence of duplicate keys.

We introduce the priority queue data type and an efficient implementation using the binary heap data structure. This implementation also leads to an efficient sorting algorithm known as heapsort. We conclude with an applications of priority queues where we simulate the motion of n particles subject to the laws of elastic collision.

We define an API for symbol tables (also known as associative arrays, maps, or dictionaries) and describe two elementary implementations using a sorted array (binary search) and an unordered list (sequential search). When the keys are Comparable, we define an extended API that includes the additional methods min, max floor, ceiling, rank, and select. To develop an efficient implementation of this API, we study the binary search tree data structure and analyze its performance.

In this lecture, our goal is to develop a symbol table with guaranteed logarithmic performance for search and insert (and many other operations). We begin with 2−3 trees, which are easy to analyze but hard to implement. Next, we consider red−black binary search trees, which we view as a novel way to implement 2−3 trees as binary search trees. Finally, we introduce B-trees, a generalization of 2−3 trees that are widely used to implement file systems.

We start with 1d and 2d range searching, where the goal is to find all points in a given 1d or 2d interval. To accomplish this, we consider kd-trees, a natural generalization of BSTs when the keys are points in the plane (or higher dimensions). We also consider intersection problems, where the goal is to find all intersections among a set of line segments or rectangles.

We begin by describing the desirable properties of hash function and how to implement them in Java, including a fundamental tenet known as the uniform hashing assumption that underlies the potential success of a hashing application. Then, we consider two strategies for implementing hash tables—separate chaining and linear probing. Both strategies yield constant-time performance for search and insert under the uniform hashing assumption.

We consider various applications of symbol tables including sets, dictionary clients, indexing clients, and sparse vectors.