# Big-O Notation

The Big-O notation is about the performance or time complexity of an algorithm. It describes the worst-case scenario, the execution time required, and the space used by an algorithm. You can get the more explanation here and the cheat sheet here.

## O(1) - Constant Time

It only takes a single step.

z = x + y

## O(log n) - Logarithmic Time

The number of steps decreases in every step by some factor.

x = 1 while x < 10: print(x) x *= 2

## O(n) - Linear Time

The running time increases linearly with the size of the input.

for x in range(10): print(x)

## O(n log n) - Quasilinear Time

The result of performing an O(log n) operation in n times.

for x in range(10): x = 1 while x < 10: print(x) x *= 2

## O(n^{2}) - Quadratic Time

The result of performing an O(n) operation in n times.

for x in range(10): for x in range(10): print(x)

## O(2^{n}) - Exponential Time

This is common in situations when you traverse all the nodes in a binary tree.

def fibonacci(x): if x <= 1: return x return fibonacci(x - 2) + fibonacci(x - 1)

## O(n!) - Factorial Time

This is common in generating permutations.

def factorial(x): for i in range(x): factorial(x - 1)