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Geometry cheatsheet for coding interviews

👋 Hi there, I'm Yangshun, an ex-Meta Staff Engineer, author of this handbook and Blind 75. Follow me on LinkedIn for Software Engineering advice and interview tips!

Introduction​

Geometry is a branch of mathematics that is concerned with properties of space that are related with distance, shape, size, and relative position of figures. Advanced geometry (e.g. 3D geometry) is not taught in most Computer Science courses, so you can expect that you will only be asked on 2D geometry.

In algorithm interviews, geometry is usually not be the focus of the problem (you're not being evaluated on mathematics after all). You typically have to use other algorithms and/or data structures in the problem.

Corner cases​

  • Zero values. This always gets people.

Techniques​

Distance between two points​

When comparing the distance between two points, using dx2 + dy2 is sufficient. It is unnecessary to square root the value. Examples: K Closest Points to Origin

Overlapping circles​

To find out if two circles overlap, check that the distance between the two centers of the circles is less than the sum of their radii.

Overlapping rectangles​

Two rectangles overlap if the following is true:

overlap = rect_a.left < rect_b.right and \
  rect_a.right > rect_b.left and \
  rect_a.top > rect_b.bottom and \
  rect_a.bottom < rect_b.top

Here's a nice visualization. Examples: Rectangle Overlap

Sample questions​

  • You have a plane with lots of rectangles on it, find out how many of them intersect.
  • Which data structure would you use to query the k-nearest points of a set on a 2D plane?
  • Given many points, find k points that are closest to the origin.
  • How would you triangulate a polygon?

Essential questions​

These are essential questions to practice if you're studying for this topic.

These are recommended questions to practice after you have studied for the topic and have practiced the essential questions.

AlgoMonster​

AlgoMonster aims to help you ace the technical interview in the shortest time possible. By Google engineers, AlgoMonster uses a data-driven approach to teach you the most useful key question patterns and has contents to help you quickly revise basic data structures and algorithms. Best of all, AlgoMonster is not subscription-based - pay a one-time fee and get lifetime access. Join today for a 70% discount →

Grokking the Coding Interview: Patterns for Coding Questions​

This course on by Design Gurus expands upon the questions on the recommended practice questions but approaches the practicing from a questions pattern perspective, which is an approach I also agree with for learning and have personally used to get better at coding interviews. The course allows you to practice selected questions in Java, Python, C++, JavaScript and also provides sample solutions in those languages along with step-by-step visualizations. Learn and understand patterns, not memorize answers! Get lifetime access now →

Master the Coding Interview: Data Structures + Algorithms​

This Udemy bestseller is one of the highest-rated interview preparation course (4.6 stars, 21.5k ratings, 135k students) and packs 19 hours worth of contents into it. Like Tech Interview Handbook, it goes beyond coding interviews and covers resume, non-technical interviews, negotiations. It's an all-in-one package! Note that JavaScript is being used for the coding demos. Check it out →

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