Algorithms, Part I
Princeton University via Coursera
- Provider Coursera
- Cost Free Online Course (Audit)
- Session Upcoming
- Language English
- Effort 6-12 hours a week
- Duration 6 weeks long
- Learn more about MOOCs
Taken this course? Share your experience with other students. Write review
Class Central Custom Lists
Build and share your own catalog of courses with Class Central's custom lists.
Overview
Class Central Tips
All the features of this course are available for free. It does not offer a certificate upon completion.
Syllabus
-Welcome to Algorithms, Part I.
Union−Find
-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.
Analysis of Algorithms
-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.
Stacks and Queues
-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.
Elementary Sorts
-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.
Mergesort
-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.
Quicksort
-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.
Priority Queues
-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.
Elementary Symbol Tables
-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.
Balanced Search Trees
-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.
Geometric Applications of BSTs
-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.
Hash Tables
-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.
Symbol Table Applications
-We consider various applications of symbol tables including sets, dictionary clients, indexing clients, and sparse vectors.
Taught by
Tags
Help Center
Most commonly asked questions about Coursera
Reviews for Coursera's Algorithms, Part I Based on 60 reviews
- 5 stars 73%
- 4 stars 15%
- 3 stars 5%
- 2 star 2%
- 1 stars 5%
Did you take this course? Share your experience with other students.
Write a review- 1
this review helpful
Another point: the course involves automated grading/feedback on the programming assignments. This feedback is incredibly detailed, giving information about error checking, performance testing, and even good coding style. As a new developer, I found this immensely helpful.
this review helpful
The exercises tend to have a few challenging questions but a couple of questions which force you to simulate a computer and run the algorithms. Personally, I dislike these type of questions. On the other hand, the programming assignments are fun and force students to think out of the box. Also, the grading system is very detailed and gives a lot of useful feedback.
In general, this course is an great fit for anyone who wishes to learn about algorithms and is new to the field.
this review helpful
The best part of the course is of course problem sets with rigorous tests. There are a lot of additional exercises in their book if you're interested in programming of algorithms - many of them are from job interviews.
this review helpful
this review helpful
it's useful to learn the different performance of different implementations of an algorithm. there's no much theoretical explanation in this course, and so it's a short for those who want real understanding of some tricky algorithms, such as quick-selection.
the assignments are also practical, not directly related to the algorithms taught, but about how to use them. from my point of view, it's not worth spending hours on …
this review helpful
this review helpful
this review helpful
this review helpful
this review helpful
this review helpful
The lectures are clear and concise, the simulations explain clearly the algorithms in study.
The homeworks are challenging and interesting. Each assignment took me about 5 hours on average. It is a good refresh on Java as well. Looking forward for the next part of the course.
Sergey.
The great course lectures are doing well and the best I have seen. Programming homework is also good, even if they are Java, I do not know at the beginning of the course. The problem set is good, but some work can improve the interface. Everything is on time
this review helpful
- 1