loading...
Cover image for Intro to  Big O Notation πŸ‘€

Intro to Big O Notation πŸ‘€

saigowthamr profile image Sai gowtham Updated on ・2 min read

What is Big O?

In computer science, big O is used to analyze how their running time or the space used by an algorithm.it is invented by Paul Bachmann, Edmund Landau.

Let's discuss some common time complexities with the help of examples.

Constant time O(1)

If an algorithm has a constant time, it means that it always takes the same amount time to produce the output.

Example

function removeLastitem(arr){
  return arr.pop()
}

console.log(removeLastitem([1,2,3,4,5,6]))

In the above example removeLastitem function always takes the same amount of time to remove the last item from the array it doesn't matter if the array has 10 items or 20 items.

Linear time O(n)

if an algorithm has a linear time, it means that the running time of an algorithm grows as the input size grows.

example

function sum(arr) {
    let total = 0;
    for (let i = 0; i < arr.length; i = i + 1) {
        total += arr[i];
    }
    return total;
}

console.log(sum([1, 2, 3, 4])) //10

In the above example,sum function increases its running time according to the size of the array.

Quadratic time O(n2)

The running time of an algorithm is directly proportional to the square of the size of the input.

example :

function addAndLog(arr) {
    for (var i = 0; i < arr.length; i++) {
        for (var j = 0; j < arr.length; j++) {
            console.log(arr[i] + arr[j])
        }//O(n)
        console.log("----")
    }// O(n)
}

In the next tutorial, we will learn about logarithms hope you learned something.

Happy coding ...

Follow me on twitter

Originally published at reactgo.com

Posted on Oct 3 '18 by:

saigowthamr profile

Sai gowtham

@saigowthamr

JavaScript developer, Blogger & Serverless

Discussion

markdown guide
 

The last example doesn't look quadratic to me but linear, because the second loop is executed a fixed number of times. Its complexity would be O(10 * n), which is proportional to O(n)

 
 

O(10 *n) how ?

Can you explain please !

 

The author fixed it, but the code used to be something like:

for (var i = 0; i < arr.length; i++) {
    for (var j = 0; j < 10; j++) {
        console.log(arr[i] + arr[j])
    }
}

The console.log statement is executed arr.length * 10 times. That's a complexity of O(10* n), n being the size of the arr array.

Just to be painfully anal, there is no such thing as O(10*n). Constants disappear in Big-O notation as it is only concerned with growth rates and limiting behavior, not the actual time taken for a certain operation. i.e. your example it is still O(n).

 
 

the last example should have
for (var j = 1; j <= n; j++) {
or
for (var j = 1; j <= i; j++) {
for 2'd loop

to be O(n2). That's critical. Any constants in Big O notation can be dropped

 
 

Best intro I've seen to the Big O!

Well done!

 

Ouch, logarithms one were the content I was looking for when I entered here, I hope you will post it soon.

 
 

It would be nice if you could expand a bit on this topic since there's more to it.

The Big-O Cheat Sheet is nice, especially that poster!!