Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case scenario and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.

**-Big Os**

**O(1)**Constant- no loops

**O(log N)**Logarithmic- usually searching algorithms have log n if they are sorted (Binary Search)

**O(n)**Linear- for loops, while loops through n items

**O(n log(n))**Log Liniear- usually sorting operations

**O(n^2)**Quadratic- every element in a collection needs to be compared to ever other element. Two nested loops

**O(2^n)**Exponential- recursive algorithms that solves a problem of size N

**O(n!)**Factorial- you are adding a loop for every element

**Iterating through half a collection is still O(n)**

**Two separate collections: O(a * b)**

**-What can cause time in a function?-**

Operations (+, -, *, /)

Comparisons (<, >, ==)

Looping (for, while)

Outside Function call (function())

Operations (+, -, *, /)

Comparisons (<, >, ==)

Looping (for, while)

Outside Function call (function())

-Rule Book

Rule 1: Always worst Case

Rule 2: Remove Constants

Rule 3: Different inputs should have different variables. O(a+b). A and B arrays nested would be
O(a*b)

+ for steps in order

* for nested steps

Rule 4: Drop Non-dominant terms

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