Lest's geek out about Big-O notation.

What is Big O notation ?

Big O notation is a way to formalize fuzzy counting, it allows us to talk formally about how the runtime of an algorithm grows as it's input grows.

Big O helps you determine which of two functions that do the same thing is better, either in terms of time complexity or space complexity.

Time Complexity refers to the amount of time it takes for a function to run as the number of inputs grow while Space Complexity refers to the amount of space a functions output takes as the number of input grows.

In this article we will focus on time complexity.

let's do it practically.

I will create two functions that both calculate the sum of a number from 1 (up to and including) some number n.

//snippet 1

function addNum(n) {
  let total = 0;

  for (i = 0; i <= n; i++) {
    total += i;
  }

  return total;
}

//snippet 2

function addNum(n) {
  return (n * (n + 1)) / 2;
}

let's figure out the Big O of Snippet 1.

Tip: In Big O we focus on counting the simple number of operations the computer has to perform each time you run a function.

so how many operations does the computer perform in snippet 1 ?

let's count.

//snippet 1

function addNum(n) {
  let total = 0;

  for (i = 0; i <= n; i++) {
    total += i;
  }

  return total;
}

//O(1)

here, we have five operations inside the loop and two operations outside the loop.

This will give us a value like (5n + 2).

This only shows that the number of n operations grow directly proportional to number of inputs.

This makes the growth linear(meaning the number of operations increase as the value of n increases).

the Big O of n is: O(n).

Moving on to snippet 2.

//snippet 2

function addNum(n) {
  return (n * (n + 1)) / 2;
}

Snippet 2 perfoms 3 operations regardless of the size of n.

So, we can conclude that the big O of snippet 2 is a constant since it is not affected by the growth of n.

The big O of n will be: O(1).

How does this help me on day to day programming ?

it's important that while programming you take sometime off to reflect on your functions and ask yourself what their big O is.

This will help you optimize your apps performance.

Happy Coding!