# Geometry cheatsheet for coding interviews

## 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 between two points, using dx^{2} + dy^{2} 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.*

## Recommended practice questions

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

## Recommended courses

### 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 Educative 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!** **Join today for a 10% discount →**

### 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 →**