# 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(n2) - 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(2n) - 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)
```