Prof. Michael Bender showed us a neat trick when presenting graphs in talks.

Often, we do experiments with Data-Structures and Algorithms, and we want to show that the cost of doing *blah* with the *foo bar* data structure, is $O(n)$ (which means that if we plot the actual cost against the value $n$, we should get a straight line).

Okay. What intuition do you have for something which costs $O(n\log{n})$. I would say its slope is somewhere between a line and a parabola. But how does the audience visually verify this instantly when seeing the graph?

On the y-axis, you do not plot the actual cost, but plot the ratio of the *actual cost to the value that you expected*, and show that the ratio is constant.

This is how we plotted something that we expected to be $O(n\log\^2{n})$:

It was perfectly clear that the ratio is almost constant, and hence our hypothesis was correct.