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Brilliant

Algorithm Fundamentals

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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 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.
    • Repetition: Performing simple actions repeatedly is at the heart of every interesting algorithm.
  • Storing Information: Arrays are a fundamental way of storing information.
    • Manipulating Numbers: Most algorithms store and manipulate numbers using assignable variables.
    • Arrays: Arrays are critical for understanding algorithms that manipulate collections of information.
    • Searching an Array: Arrays can store lots of information. To find out what's there, you just have to look!
  • Array Algorithms: Master repetition through understanding algorithms that manipulate arrays.
    • 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.
  • 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.
  • Algorithmic Complexity: We will analyze the Gale-Shapley algorithm to show that is correct and always finishes.
    • 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.
    • Variants: Transition from an oversimplified problem to one that's much more like the real world.

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