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Algorithm Fundamentals

via Brilliant

Overview

An algorithm is a step-by-step process to achieve some outcome. When algorithms involve a large amount of input data, complex manipulation, or both, we need to construct clever algorithms that a computer can work through quickly.

By the end of this course, you’ll know methods to measure and compare performance, and you’ll have mastered the fundamental problems in algorithms.

Syllabus

  • Building Blocks: The nuts and bolts of how computer scientists communicate algorithmic ideas.
    • Pseudocode: Start your study of algorithms by learning about this key aspect of how computer scientists communicate.
    • Conditional Algorithms: All interesting algorithms perform tests, and react in different ways based on the results of those tests.
    • Manipulating Numbers: Most algorithms store and manipulate numbers using assignable variables.
    • Repetition: Performing simple actions repeatedly is at the heart of every interesting algorithm.
    • Arrays: Arrays are critical for understanding algorithms that manipulate collections of information.
  • Array Algorithms: Master repetition through understanding algorithms that manipulate arrays.
    • Searching an Array: Arrays can store lots of information. To find out what's there, you just have to look!
    • Binary Search: Looking in the middle of a sorted array requires a bit of cleverness, but it can save you a lot of work.
    • Sorting an Array: Sorting an array with selection sort unlocks the power of binary search.
    • Insertion Sort: There's more than one way to sort an array. Insertion sort is another classic algorithm for sorting.
  • The Speed of Algorithms: Part of the study of algorithms is learning to predict how fast or slow they run.
    • Timing Programs with a Stopwatch: In science, sometimes the best thing to do is run an experiment!
    • Counting Operations: Find out why computer scientists talk about "cost" instead of "time."
    • Best, Worst and Average Case: Algorithms don't always have predictable costs. To prepare for the worst or hope for the best, you need to know what those are!
    • Comparing Algorithms: Big O notation is a simple notation that helps computer scientists compare algorithms and implementations.
    • Understanding Big O: The flexibility of Big O can make it a bit tricky. But it's the trickiness that makes it so useful!
    • The Mathematics of Big O: Dive into the details to really understand why Big O notation works the way it does.
  • Stable Matching: You now have the tools to understand and reason about important algorithms, including algorithms that can change the course of people's lives.
    • The Stable Matching Problem: Discover a simple problem faced by every teaching hospital and medical student every year.
    • Using Greediness: An individual applicant can make the best decision with a greedy algorithm.
    • Deferred Acceptance Algorithm: The Gale-Shapley algorithm uses individual greedy decisions to produce a global matching.
    • Correctness: An algorithm for producing a stable matching is only good if it outputs a stable matching!
    • Termination: A good algorithm can't just promise that it will do the right thing if it finishes. A good algorithm actually has to deliver.
    • Running Time: The tools you've learned for describing the speed of algorithms apply to the Gale-Shapley deferred acceptance algorithm.
    • Variants: Transition from an oversimplified problem to one that's much more like the real world.
    • Who Benefits?: In order to really understand an algorithm, you need to think about more than just the mathematics.

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