Big O notation

Invented by Paul Bachmann, Edmund Landau (et al.), big O notation is used in computer science to describe the amount of time and space used by an algorithm. In other words, it describes the efficiency of algorithms.

Big O notation follows the syntax:

O(f(n))

…where f(n) is some function of growth. Given n input items, the maximum number of operations required to complete the algorithm is f(n).

Algorithm speed isn’t measured in seconds, but in growth of the number of operations.^[1]

A few common big O designations

(slowest to fastest):

Factorial time/space (Very inefficient. Traveling salesperson problem.)
```
O(n!)
```
Exponential time/space (Selection sort)
```
O(n^2)
```
Logarithmic-linear time/space (Quicksort)
```
O(n log n)
```
Linear time/space (Simple search)
```
O(n)
```
Logarithmic time/space (Binary search)
```
O(log n)
```
Constant time/space (Reading an array at a known index)
```
O(1)
```

Note: in big O notation, log is always log2.