OK OK, I say some "InfoViz", but then, the big question would stay the same : HOW ?
According to the human-computer interaction course I have got, Humans don't react like machine, they should have "Mental Models" to manipulate information and resolve problems. We don't have one Human mental model but we are sure about some reactions.
According to (Philip Johnson-Laird, 1983), humans need examples to how a mathematical functions work (hmmm, we don't speak about math nerds here...), so when we see a formula, we need to play it on some examples in order to construct our mental model.
So, to understand an algorithm, we should see it running on a sample data step by step, and then we should select the best data to not fall in a trivial example and this is another problem...
But, why we don't add a step in between ?
We have the algorithm coded in some language in one side, and the algorithm running in the other side.
Maybe adding the visualization of the algorithm itself can help the reader constructing quickly his mental model and reducing the time needed to see the algorithm running on data.
Some people tried to visualize algorithms by translating loops directly using schematics like these :