PS: oh and of course all those 'It’s quite easy to show that the...' and similar 'by this point it should be obvious'. No, it is not... I guess I will never understand or use those algorithms even though I'd like to.
But please don't confuse "straightforward" with "obvious". Sometimes I deliberately gloss over mechanical details because I think they're a distraction from the main point. I'm NOT claiming that you should immediately know how to fill in the details; I'm claiming that filling in the details is boring.
If it's obvious to the reader, they know it whether or not you tell them it's obvious. If it's not obvious to them, then they will try to figure it out. Telling this person "it's obvious" only serves to make them feel bad about not getting it right away.
An example: http://jeffe.cs.illinois.edu/teaching/algorithms/book/Algori... Page 15
> It’s quite easy to show that the singing time is Θ(n2); in particular,the singer mentions the name of a gift ∑ni=1i=n(n+1)/2times (counting thepartridge in the pear tree).
I'm pretty sure that I still remember how to read the formula and I even know what does Θ(n2) means, but it's still unclear for me how do we get n^2 and this formula from the "NDaysOfChristmas(gifts[2..n]):" example.
the proof is easy and left as an exercise
The main takeaway I got from Polya's How to Solve it is that properly conceptualizing the problem in your head before attempting to solve it is key.