Good advice but they're basically all the same thing: think. It's way too easy to get into a habit of hacking away at something without actually give it a moment's thought.
Reminds me very much of the Feynman story "He fixes radios by thinking!"
It is actually not that simple. I mean if it was, we wouldn't have countless reams of paper devoted to how to learn and comprehend better. Everyone comprehends things differently and sometime different perspectives help.
I thought the article was pretty decent as one man's perspective on how to learn algorithms. The whole talk through an algorithm reminds me of my real analysis class where the only way to comprehend and understand highly abstract proofs and constructs was to talk through them as if they were telling a story (which incidentally they are, except that it is a story that has been highly refined and evolved over 200 years which makes it appear very sophisticated.)
This is all good advice. When I taught algorithms, the difference in performance between students who stepped through the algorithms by hand on small examples and students who just memorized pseudocode was tremendous.
One thing that can make "talking and writing" even more useful is to do it on a whiteboard in front of someone. Then, not only are you practicing the algorithm, you're also practicing whiteboard coding, which is useful for interviews and a lot of day-to-day technical communication.
Reminds me very much of the Feynman story "He fixes radios by thinking!"