Improve algorithmic thinking [closed]

Question

Solve problems on a daily basis. Watch traffic lights and ask yourself, "How can these be synced to optimize the flow of traffic? Or to optimize the flow of pedestrians? What is the best solution for both?". Look at elevators and ask yourself "Why should these elevators use different rules than the elevators in that other building I visited yesterday? How is it actually implemented? How can it be improved?".

Try to see a problem everywhere, even if it is solved already. Reflect on the solution. Ask yourself why your own superior solution probably isn't as good as the one you can see - what are you missing?

And so on. Every day. All of the time.

The idea is that almost everything can be viewed as an algorithm (a goal that has some kind of meaning to somebody, and a method with which to achieve it). Try to have that in mind next time you watch a gameshow on TV, or when you read the news coverage of the latest bank robbery. Ask yourself "What is the goal?", "Whose goal is it?" and "What is the method?".

It can easily be mistaken for critical thinking but is more about questioning your own solutions, rather than the solutions you try to understand and improve.

First of all, and most important: practice. Think of solutions to everything everytime. It doesn't have to be on your computer, programming. All algorithms will do great. Like this: when you used to trade cards, how did you compare your deck and your friend's to determine the best way for both of you to trade? How can you define how many trades can you do to do the maximum and yet don't get any repeated card?

Use problem databases and online judges like this site, http://uva.onlinejudge.org/index.php, that has hundreds of problems concerning general algorithms. And you don't need to be an expert programmer at all to solve any of them. What you need is a good ability with logic and math. There, you can find problems from the simplest ones to the most challenging. Most of them come from Programming Marathons.

You can, then, implement them in C, C++, Java or Pascal and submit them to the online judge. If you have a good algorithm, it will be accepted. Else, the judge will say your algorithm gave the wrong answer to the problem, or it took too long to solve.

Reading about algorithms helps, but don't waste too much time on it... Reading won't help as much as trying to solve the problems by yourself. Maybe you can read the problem, try to figure out a solution for yourself, compare with the solution proposed by the source and see what you missed. Don't try to memorize them. If you have the concept well learned, you can implement it anywhere. Understanding is the hardest part for most of them.

Polya's "How To Solve It" is a great book for thinking about how to solve mathematical problems and do proofs, and I'd recommend it for anyone who does problem solving.

But! It doesn't really address the excitement that happens when the real world provides input to your system, via channel noise, user wackiness, other programs grabbing resources, etc. For that it is worth looking at algorithms that get applied to real-world input (obligatory and deserved nod to Knuth's collection), and systems which are fairly robust in the face of same (TCP, kernel internals). Part of coming up with good algorithmic solutions is to know what already exists.

And alongside reading all that, of course practice practice practice.

You should check out Mathematics and Plausible Reasoning by G. Polya. It is a rare math book, which actually deals with the thought process involved in making mathematical discoveries. I think it is the same thought process that is involved in coming up with algorithms.