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

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?

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.

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.

I took magic lessons in a group setting when I was twelve years old. The magician's name was Joe Carota. He did a magic trick one time and I blurted out, "How did you do that?" He said something that day that has stuck with me ever since.

Joe's response, "Michael, if you really want to know how that trick is done you must figure out how you would do it yourself."

Well of course that's not what I wanted to hear but it did get my mind focused on problem solving. This was problem solving from my perspective. If my first attempt at solving the problem took seventeen steps and was really klunky, the good news was I solved the problem.

Then by looking at the solution I had developed and further looking for ways to refine that solution I would learn how to streamline the end result. Later on in my computer programming life I found out that this process was called "Stepwise Refinement".

It worked back in 1971 and it still works today.

For me, i think it's a bit talent, but much more important is experience and practice. If you know many problems and the best solutions to them, you can come up more easily with a solution to a new problem.

Example from my own past: There was some programming contest (good for training, btw) and I did not find a good solution. The winner solved the problem mainly by using a KD-Tree. To come up with this, you first of all need to know what, in this case, a KD-Tree is, and where it's useful. Today, this is clear to me and if i'd encounter a similar problem again, i'd be able to solve it really quickly.

> Hardwork beats talent if talent doesn't work hard. This above statement defines what the true potential of persistence is.Any skill in this world can be developed by practice.This process is analogous to nailing a nail in the wall.It not only requires correct magnitude but also appropriate direction.

To answer the question, first we need to find the ingredients for the capability to solve an issue.

1. There is a so-called natural talent. This is the talent you are born with. This predetermines your potential. People born with more gray matter will tend to perform better than people with whom nature was less generous with. This means that a person having better talent has a higher probability to perform better than a person not as talented if they had the same parameters (education, personality, resistance to stress, willpower). If one observes that he or she tends to consume a great time to absorb new information until he or she is able to apply it, then the wisest decision for the person is to leave programming and prevent a life full of frustration. Naturally, one cannot expect as a beginner to be able to instantly understand the most complex phenomenon, but if a beginner is too slow to understand beginner concepts, then programming is not his or her cup of tea.

2. Developed talent. One has a natural talent, but that is, in itself not enough to solve problems. I have never seen newborns writing code. One has to get some education. The earlier, the better. Also, the quality of school is of high importance. We should never deny the fact that a person who did not have the chance to learn programming at a good school early, then he or she has a handicap in the race for success. However, if someone misses good schools early, then the handicap can be covered with hard work. For instance, my wife had an education in another field, but after finishing the university, she did not find proper jobs. So I started to educate her. After a month she learned how to learn and was able to solve almost any problems presented to her, but she was not yet effective. She gradually became to start learning in auto-didacting manner. After a year she was already a professional coder. She does not have a paper from a school that she can code, but she is doing a fantastic job. So, she missed early education, but was later able to neutralize the handicap. Developed talent can be described as the set of information learned and known, along with the right attitude, the scientific approach to new types of challenges.

3. Practice: Practice is good to increase the level of developed talent, yet, it SHOULD not be the sole source of developing talent. Along with practice, the theoretical horizons must be regularly expanded.

4. Working strategy: One can be extremely talented, can have a lot of knowledge. If he or she does not have a right working strategy, then he or she has a handicap. Whenever a new task is given, the right questions should be asked:

• what was the closest task to this one? Can I reuse my solution to an extent?
• what should I learn to be able to solve this problem?
• how can I write clear and efficient code to solve the problem?

So the answer is: while it is good to have excellent education as early as possible, it is not necessary. Do not forget, that life is the best school and you can recuperate the lost opportunity later if you have talent, willpower and source of information. Practice is not only showing you the right steps to solve a problem, it also widens your horizons. For instance, if one understands number systems, then he or she will be able to understand a variety of things later, like colors in CSS, PSD, or number overflows. If one learns how to code in Java, then he or she will understand C# very quickly. So, practice is giving you knowledge about the solution to a given problem type, but also, gives new theoretical knowledge which will be useful in various areas. The core skill one has to develop is the ability to learn quickly.

There have been many examples of people having extraordinary talent with minimum success. You see such examples in sports,politics,business and also in general around you. So, I feel after a certain limit, talent is a meaningless virtue. Its mostly the hard word that rewards you with greater success. If you follow cricket, here is a link with good example. I feel same principle applies to algorithm and problem solving. An year back I use to pick up algorithmic problems to solve and used to find myself completely lost. An year invested in reading algorithmic books, solving its exercises and also practicing some more programming problems, I am confident that now I can solve most problems ( I still have a long way to go in making myself efficient in it). But the point is smart work is enough to develop this knack of solving problems.

Talent is cheap and useless without hardwork. Talent can only take you to some extent, but with hardwork and practice anybody can reach great heights

• Josh Waitzkin, 8-time National Chess Champion, a 13-Time National and 2-time World Champion
  
  He himself says this in his voice over in http://www.amazon.co.uk/Chessmaster-Grandmaster-Edition-PC-DVD/dp/B001F50TAK">Chessmaster Grandmaster Edition