问题
Today there was a question on SO, where the author was given an NP-complete problem during an interview and he obviously hadn't been told that it was one.
What is the purpose of asking such questions? What behavior does the interviewer expect when asking such things? Proof? Useful heuristics? And is it even legitimate to ask one if it's not a well-known NP-complete problem everyone should know about? (there's a plenty of them)
回答1:
Completely legitimate to me. If you are Computer Science professional there are good chances that you can either argument informally why the problem seems to be hard, or (even better) provide a sketch of reduction from a known NP-hard problem.
Many real world problems eventually turn out to be NP-hard, and stackoverflow also has now and then questions about the complexity of a problem which turns out to be a difficult one (NP-hard, for instance). It is an important part of a CS professionals toolbox to be able to recognize and to argue for problems which are known to be difficult to solve.
回答2:
I don't see any problem with asking something like this. Also, programmers should NOT be expected to recognize NP-complete problems by rote. They should, however, be able to identify that their algorithm is potentially slow regardless of whether a given problem is NP-complete.
回答3:
Sure, why not? NP-complete doesn't mean unsolvable, it just means your solution will be slow. You may be looking to see if the candidate will choose the brute-force solution, or try a dynamic programming solution. And this type of question can lead into questions about runtime and other useful theory.
回答4:
There's a category of interview questions that are illegal in some countries, usually pertaining to personal details that are none of the employer's business. That aside, any question is fair game if the interviewer feels it'll help get an idea of the interviewee's capabilities!
If you're hiring for a position that calls for a thinker rather than just a code monkey, it may be useful to throw this kind of problem at the applicant. Who cares if a problem is "well known" to be NP? If the guy is good he'll come to that understanding in analyzing the problem. That may well be the result the interviewer wants to see, or the applicant can go on to do some more pre-analysis and describe how he'd brute-force the problem, or what optimizations he can think to apply to make it more manageable.
回答5:
I don't see a problem with this, but I do somewhat question the usefulness of these sorts of questions in interviews in general.
The benefit of asking questions like this, as an interviewer, is see how the person approaches a problem, and how they think. If you tell them to talk it out, you can find out quite a bit about how they will approach a difficult problem.
That being said, during an interview, most people aren't at their best - so throwing something that's somewhat "tricky" like this is often overkill, IMO.
回答6:
I think it's valid to ask a question you know the interviewee won't know the answer to.
Everyone encounters problems they don't know the answer to. This type of question will give you insight as to what the interviewee's internal process is. If they logically conclude things and start to formulate a correct answer, even if it's not the best dynamic programming algorithm for it, it shows that they can reason well and discover an answer.
Also, since they likely don't know everything about the problem, this sort of question lets you see how comfortable the interviewee is with asking for help or clarification.
I think the best way to answer this type of question is to ask for any clarifications if something is missing or not well known, and then postulate an answer, pointing out why you think it is correct, and why it likely isn't the best solution.
回答7:
It's good to ask a question that is hard to answer, to see how a programmer reasons through a problem.
But it all depends on how the interviewer asks the question, and prompts the programmer towards a solution if they aren't a mathematical genius (i.e. to see how they reason, and how they react to questions like "that's a good start, but what if...") rather than to detect if they are autistic and can provide an optimal solution in 4.3 seconds).
It's worth remembering that interviews are highly stressful affairs in which many people find such questions very difficult to answer well - a much simpler question will usually suffice without putting the interviewee under undue stress/pressure.
If you do it to deliberately try to see how they deal with stress is just stupid - that isn't the sort of stress a programmer has to deal with in their job, so you're not testing anything worthwhile.
回答8:
It's sort of mean to ask nigh-impossible questions without informing the interviewee of it, but in observed problem solving, the question is often asked so that you may demonstrate critical thinking skills, how you approach problem solving, and how you handle pressure or failure.
I've been asked interview questions I couldn't solve, and I don't think I've ever "failed" an interview because of it.
回答9:
Is it fair to ask in an interview how to factorise numbers?
That's not known to be NP-C, but no polynomial-time solution[*] is known, so it is certainly not known to be in P.
I think the answer to both my question, and the original question, is "yes", and for the same reasons. Some problems have no solution which scales well, but do need to be solved anyway for certain inputs. If you need programmers who can handle such problems, there's a good way to let them prove it in interview, and that's to pitch them one and see whether they freak out.
If someone claims a CompSci background, then they should even be able to provide good solutions to certain NP-C problems on demand, such as solving the knapsack problem with dynamic programming. I would consider it pointless asking an applicant for a programming job to take a problem they've never seen before, and actually prove it NP-complete (for example by reducing knapsack to the specified problem). You don't need very many programmers per company who can do that (usually 0), and all you'll likely discover is how long the candidate keeps at it before attempting to change the subject and do something more valuable with the interview time...
[*] polynomial in the size of the input in bits, that is. You often see people discussing algorithmic complexity of integer problems like factorisation in terms of the size of the number represented by the input, e.g. "sqrt(N) trial divisions". But that's not how NP and NP-C are defined.
回答10:
No, it's rude and a sign that the interviewer just likes being in a position of power. Haha, peon! I know the answer, and you don't! And boy, do I love to make you squirm trying to come up with it!
About the only way it could be even slightly valid as a useful interview question is if it were a well-known question or one that was somehow obviously NP-complete, and asked in a way that encouraged discussion of feasibility.
回答11:
There is nothing wrong with giving an NP-complete problem as a programming challenge during an interview. I only see something wrong with expecting to find a polynomial-time solution to the problem during the interview.
An interviewer should want to see how a candidate deals with a variety of situations -- including situations that the candidate can't find an easy solution to. "Impossible" questions show how the candidate reacts when there's no simple solution. Does the candidate just give up? How many different attempts does the candidate search? How far-reaching are the solutions tried? When does the candidate ask for help -- and how? Does the candidate complain that the problem "isn't fair"?
In short, such an interview question isn't about solving P=NP... it's a psychological answer.
回答12:
If such a question was given before an interview(to be answered at an interview) I would say it's ok.. but to just solve such a difficult problem as that on the spot is definitely not going to be done well by any programmer, and if the programmer does do it well that just means they can act on the spot(which isn't always the best thing for programming as designing things needs to take time and check every possible flaw) or that they have seen a similar problem before.
Edit: Or possibly discussion about the problem would be good, like say laying down a plan of action whether or not you completely solve it.. and discussing how feasible and if there is a fast(but difficult) way to do it and such. I would not say that the interviewee should have to write down over 50 lines of C code in an interview to solve it though
回答13:
That is evil!
If the interviewer asks an NP-complete question in an interviewer the only response they can reasonably expect is that the interviewee respond with a proof that the problem is NP-complete. In a low-stress environment like a university homework question, this usually takes a bright student 2-3 or more hours to prove. The proof itself can take several pages to write out completely, perhaps several hours of work itself. In a high-stress environment like an interview you can expect that the interviewee may not even recognize that this is np-complete.
The only reasonable alternative is that the interviewee produce an approximation algorithm; however, in this case the interviewer should make it explicitly clear that they are fine with approximations.
Even so, most approximations only come with an order of 2 of the correct answer.
I guess there is 1 more alternative: the interviewee suggests that a search-type algorithm maybe the most suitable (take for example the integer-domain optimization problem which is NP-complete, most approximation algorithms use a branch and bound search spin on the simplex algorithm to produce decent results.)
回答14:
I prefer asking them to prove that P != NP or P == NP. Someday a candidate will answer it, I'll steal their answer and be famous!
On a more serious note, though, I think it's completely fair. Most NP complete problems are easy to solve, they just run very slowly. Unless the job requires them to know a lot about complexity theory, though, all they need to demonstrate is that they understand the solution will be slow. Bonus points if they know it's non-polynomial time, gold star if they know it's NP complete.
来源：https://stackoverflow.com/questions/1724673/is-it-correct-to-ask-to-solve-an-np-complete-problem-on-a-job-interview