Lot of students get confused while understanding the concept of time-complexity, but in this article we will explain it with a very simple example:

Imagine a classroom of 100 students in which you gave your pen to one person. Now, you want that pen. Here are some ways to find the pen and what the O order is.

**O(n ^{2}):** You go and ask the first person of the class, if he has the pen. Also, you ask this person about other 99 people in the classroom if they have that pen & So on,

This is what we call O(n

^{2}).

**O(n):** Going and asking each student individually is O(N).

**O(log n):** Now I divide the class in two groups, then ask: “Is it on the left side, or the right side of the classroom?” Then I take that group and divide it into two and ask again, and so on. Repeat the process till you are left with one student who has your pen. This is what you mean by O(log n).

I might need to do the O(n^{2}) search if only one student knows on which student the pen is hidden. I’d use the O(n) if one student had the pen and only they knew it. I’d use the O(log n) search if all the students knew, but would only tell me if I guessed the right side.

Hope it will help 🙂 !!

Source : Reddit

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