• used to describe efficiency of algorithm → has precision where O refers to order of the function or algorithm in question
  • order meaning orders of magnitude/rate of increase in each run_time for an input size

$B_o = O(n)$ where n is the input → this is only for linear operations, and so if you declared 20 variables, your input n = 20 and thus $B_o = O(20)$

• algebraic function is always expression of input n, with exeption of O(1) = O(n**0)

  

• EXAMPLE: Outlines the different steps you take in your program

  1. collect input and store in variable + you create a new variable for total output → O(2)
  2. you iterate through each item in an input (ie. list) and then get the product of the input with 5 and add that to the output (2 operations) → O(2n)
  3. print(output)

• Therefore, $B_o = O(2n+2)$

• Now let's say that while you also did the product, you took each item in the input and calculated the quotient which was nested inside of the product loop, hence a for loop inside of another for-loop → in that case, the time-space complexity is represented by $B_o = O([2n]^2+2)$

• if you notice, the +2 doesn't really matter here because it doesn't change the final value, and so you can approximate the value to just n^2 instead of (2n)^2 + 2