Problem solving/ Algorithm Skill is a knack or can be developed with practice? [closed]

Question

Every time I start a hard problem and if can not figure out the exact solution or can not get started, I get into this never ending discussion with myself, as below:

• That problem solving/mathematics/algorithms skills are gifted (not that you can learn by practicing, by practice, you only master the kind of problems that you already have solved before)

• only those who went to good schools can do it, as they learned it early.

What are your thoughts, can one achieve awesomeness in problem solving/algorithms just by hard work or you need to have that extra-gene in you?

Answer 1

I spent a big part of my life wondering whether talent was something you developed or something you were born with. Then it occurred to me that the answer was irrelevant, at least if you want to achieve things yourself. Even if you have talent, it will only help you if you act as if talent only comes from practice, because you will work that much harder.

With regards to algorithms, as well as any other really difficult skill, it takes practice to get good. Whether or not you have to have some amount of talent too, I don't know. I do know for a fact, however, that people have made huge improvements in competitions like TopCoder by practicing. I myself have learned a lot from that.

If you set up a systematic training program, you will be way ahead of the pack, even if it is not perfect. I have written a few hundred programs on TopCoder by now and it has affected my thinking in a profound way. I have learned a lot of things that could only ever be learned by doing them wrong and then fixing my mistake. A friend of mine has written several thousand programs on TopCoder and he is way better than I am, even though his stats were worse when he started out than mine were. That is no coincidence.

EDIT:

I just came across this answer at math.stackexchange. I think it is one of the best explanations of how to learn algorithms I have read, even though he writes about chess and math.

Answer 2

1) Don't try to solve the problem in its most general abstraction.
2) Choose the right time when your mind is working at maximum.

I got the first point as an advice from a math instructor. It works! try to do different examples and scenarios of the problem. This helps greatly in identifying the edge cases which are the hardest to understand in most problems.

My favorite time for solving this kind of problems is the dawn(4-6 AM). Have a good sleep the night before, and wakeup ready to solve the problem. Silence is your friend.

I do believe that some people have extra intelligence than others, but it is not the most important factor. It is how you utilize this intelligence to solve the problem.