Need help from some smart math people
Wow. I saw 18 replies and figured it was answered, but it turns out it... Very, very much was not.
OP, that excerpt is essentially introducing the idea of maximizing productivity.
You have a set of tasks ("requests") that occur over a specified interval of time, and two intervals are compatible if the times don't overlap, meaning that only one thing can be happening at a time. So the interval 1:00-4:00 is compatible with the interval 5:00-6:00, but it's not compatible with the interval 2:00-5:00, because that overlaps.
You are given a set of tasks that each have their own time interval, and your goal is to do as many of those tasks as you can without doing more than one of them at once. Like scheduling in as many parties as you can in a weekend -You can't choose when they happen, you can only choose which ones to go to.
Continuing with that analogy, let's say there are 6 parties happening in one day back-to-back, and there's one that's happening for the entire day. That one party overlaps with all the others, so you can either choose to go to that one party or the 6 others -Of which you would choose the 6, because you're trying to get as many in as possible.
I don't usually do those sort of heavily abstracted "let's make this relatable!" examples... It just sort of happened...
Continuing on with the excerpt, it says to sort the set of tasks in order of increasing finish time (it says "nondescending" because multiple tasks can finish at the same time). So a set of intervals like {1-4, 2-3, 5-8, 3-7} would be sorted as {2-3, 1-4, 3-7, 5-8}. Then is says for the element j from that set, p(j) is the latest element before it that doesn't overlap. So p(5-8) would be 1-4, and p(3-7) would be 2-3. p(j) is 0 if there isn't an interval that doesn't overlap.
Then it says you have an optimal solution O, meaning the biggest set of compatible tasks you can make. If the last element in the set, which we'll call n (5-8 from the one above), is in O, then you know that nothing after p(n) (1-4 from above) is in O because the point of the p(n) function is that everything after it overlaps with n, and therefore can't be in the solution with n.
So then let's say you remove everything after p(n) from the problem (giving you {2-3, 1-4}, again from above). Since O was an optimal solution, and you removed both n and everything that could have replaced n, what's left of O is still an optimal solution.
@BetterThanLife
I take great issue with your sentiment. There are many paths in life that don't require higher education, many of them where going through college for it can even be a detriment, but there are still many more where it's desirable or even necessary. Just because you got where you are just fine without the need for education, or because you saw that you could've gotten where you are without it, doesn't mean that everyone else's goals are the same. And, chances are that if you ended up being particularly financially successful without higher education, you were unusually lucky.
The part that really grinds my gears, though: Economics without math... That's... That's one hell of an oxymoron, man.
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