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.

Corner cases

Division by 0
Multiplication by 1
Negative numbers
Floats

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	2⁰ + 2¹ + 2² + 2³ + ... 2ⁿ = 2ⁿ⁺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)

Essential questions

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

Source and license

This page is copied from the Tech Interview Handbook by Yangshun Tay (source commit e1d28e8), used under the MIT License — Copyright (c) 2017-Present Yangshun Tay. The license text is kept locally at /licenses/tech-interview-handbook.txt.