# Math cheatsheet for coding interviews

## Introduction

Math is a foundational aspect of Computer Science and every programmer and computer scientist needs to have basic mathematical knowledge. Thankfully, for the purpose of coding interviews, there usually won't be that much math involved, but some basic math techniques is helpful to know as you may be asked to implement mathematical operations.

## Things to look out for during interviews

- If code involves division or modulo, remember to check for division or modulo by 0 case.
- Check for and handle overflow/underflow if you are using a typed language like Java and C++. At the very least, mention that overflow/underflow is possible and ask whether you need to handle it.
- Consider negative numbers and floating point numbers. This may sound obvious, but under interview pressure, many obvious cases go unnoticed.

## Common formulas

Formula | |
---|---|

Check if a number is even | `num % 2 == 0` |

Sum of 1 to N | 1 + 2 + ... + (N - 1) + N = (N+1) * N/2 |

Sum of Geometric Progression | 2^{0} + 2^{1} + 2^{2} + 2^{3} + ... 2^{n} = 2^{n+1} - 1 |

Permutations of N | N! / (N-K)! |

Combinations of N | N! / (K! * (N-K)!) |

## Techniques

### Multiples of a number

When a question involves "whether a number is a multiple of X", the modulo operator would be useful.

### Comparing floats

When dealing with floating point numbers, take note of rounding mistakes. Consider using epsilon comparisons instead of equality checks. E.g. `abs(x - y) <= 1e-6`

instead of `x == y`

.

### Fast operators

If the question asks you to implement an operator such as power, square root or division and want it to be faster than O(n), some sort of doubling (fast exponentiation) or halving (binary search) is usually the approach to go. Examples: Pow(x, n), Sqrt(x)

## Corner cases

- Division by 0
- Multiplication by 1
- Negative numbers
- Floats

## 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 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 →**