Yeah, let’s talk about the code you write
Is it running fast, or lagging through the night?
Don't guess the seconds, don't watch the clock
We use math to put the runtime on lock
Drop the beat, let's analyze
When your data starts to grow, how does your program scale?
Asymptotic runtime tells the ultimate tale
We look at the horizon where the inputs get massive,
forget the small numbers, we can't be passive
Ignore the constants, drop the lower order terms,
we focus on the shape as the algorithm squirms
It’s the trend line mapping out the ultimate peak,
the limiting behavior is the secret that we seek
That's big o, big omega, big theta in the mix,
measuring the steps and the algorithmic tricks
As n goes to infinity, the truth comes out,
asymptotic runtime is what scaling is about
First up is the king, call it constant time,
o(1) efficiency, the cleanest in the rhyme.
An array lookup by index, it never has to wait,
no matter if the input size is 10 or 88
Then comes linear time, o(n) is the name,
looping through a list, every element the same
If the data doubles up, the work will double too,
like searching for a needle til the whole scan is through
Now log it down, o log n on the track,
binary search cutting all the data in the back
Divide and conquer, splitting choices right in half,
super fast scaling makes the engineer laugh
But watch out for quadratic, o n squared is a trap,
nested loops spinning till your cpu snaps
Bubble sort lagging when the database gets wide,
with a million inputs, there's nowhere to hide
So check your efficiency before you deploy,
don't let a slow runtime ki-l your coding joy
Analyze the growth rate, see how it behaves,
that’s how a senior dev saves the day and saves the waves
Asymptotic vision
Infinity and beyond
Peace