I've decided to watch these lectures, but I don't know which ones are more important (common) for competitive programming.
What do you suggest?
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I suggest to watch it here.
As for which ones are important, I honestly have no idea.
Most of these topics covered are really really hard.
Why do you suggest to watch to it there? They're basically the same.
L01 as an example.
You'll see Prof. Erik's notes on the right, and the cool thing is that the notes actually sync with the video (It automatically switch from page to page based on where you're watching).
Another thing is that it provides scribe notes which I find useful for later review.
The link you gave is a course from Spring 2012. A classmate of mine discovered a mistake in one of the lectures which was corrected in Spring 2014. Therefore, I think in terms of correctness, Spring 2014 might be more reliable.