Big-O Notation

Allows us to measure the scalability (Speed + Memory) of a solution
Big O notation measures the worst case complexity

Asymptotic Notations
O (Upper Bound)
Ω (Lower Bound)
Θ (Tight Bound)

Time Complexity

Constant Time: O(1) - No Loops
Logarithmic Time: O(log(n)) - Searching Algorithms/ Remove half the elements
Linear Time: O(n) - Loop
Log Linear Time: O(nlog(n)) - Sorting Algorithm
Quadric Time: O($n^2$) - Nested Loop
Exponential Time: O($2^n$) - Recursive Function
Factorial Time: O(n!) - Loop for each element

Examples
Subset of Set: O($2^n$)
Permutations of String: O(n!)
Search: O(log(n))
Sorting: O(nlog(n))
Iterating over MxN matrix: O(mn)

Space Complexity

When calculating space complexity we are talking about the extra space required by algorithm (Input size is not considered)

O(1): Primitives
O(n): Strings, Reference Type

Big-O Algorithm Complexity Cheat Sheet (Know Thy Complexities!)