The writing for the statements of the three problems has some severe errors at the level of eighth grade English and Algebra I. No one very good at solving those problems should spend their time on problems so poorly written.
E.g., for the first, really serious, substantive error, in the first problem, the largest possible size or absolute value of each of the "N numbers" was not specified. Without any such specification, it is not possible to write solid code to solve the problem.
The problems look like rotten bait on rusty hooks. I'm not biting.
The third problem does have some cute contact with convexity that can be exploited to give a relatively fast algorithm.
Will I write out the code? I will not! The problems suggest that writing the code is the main challenge, that if I could write the code then I would, and if I don't write the code then I can't and am shown to be unable and should be embarrassed. This suggestion is nonsense and an incompetent insult, and I'm not falling for that insult.
My work in computing and computer science has passed reviews with competence far, far, FAR above that of what the problems show for Interview Street. Net, Interview Street is promising that its really bad house painters are the ones to pick someone to paint the ceiling of the Sistine Chapel which is insulting nonsense.
Besides, more important than the code would be the documentation that explained why the code is correct, but the problems are not seeking such explanations. So, the problems are a bad example of how to work in computing and a 'bummer'.
Today I'm writing code to get a use of Windows Communications Foundation (WCF) working for the asynchronous 'remote procedure call' communications I need for the server farm for the Web site for my project.
Yes, the third problem has some math, but my startup has at its core much more math, much more advanced, powerful, and valuable, and some nicely original. Besides, I have all such math for my startup in code ready for production so that at this point I just need to get code using WCF to connect together the asynchronous parts of my server farm and write a few more, simple Web pages to have code ready to go live. That is, WCF will so help me go live assuming, still open to question, that WCF is the 'right stuff' for my project; else I'll just write a TCP/IP sockets application. So, I have no time for puzzles with convexity with no business connection.
Besides, who at Interview Street would actually understand the convexity exploitation? From the writing of the math in the questions, likely no one would! That is, people who write math as badly as in the problem statements have little chance of understanding the convexity math of the third problem. That is, the writing of the math indicates solidly that the writers know far too little math to understand the role of convexity in the third problem.
Instead, it looks like Interview Street got the third problem from a textbook on, maybe, facility location and, then, made a mess of copying over the problem.
So, the third problem is in facility location: Maybe I should call up one of my old facility location profs, J. Cohon, now President at CMU, or just get out my class notes! Or, with convexity, maybe I should get out my old notes on optimization. Besides, what employer would appreciate the role of convexity? Likely none.
So, writing the code is a fool's errand. Life is awash in fools' errands to be avoided.
No, to solve the third problem well, the main issue is actually not writing the code but exploiting the convexity; that I have noted this is likely a better 'solution' than most of what will be submitted.
Indeed, any good solution will have to address the math of the convexity carefully and otherwise be just a lot of gibberish with no reason to believe in its value. Net, the third problem is not in computer science but in applied math; once again, computing, out'a gas, is looking to applied math for 'content' and is making a mess.
My background is in applied math, especially for business problems. Given the math, the computing is routine! The coding ain't the main challenge, guys!
Interview Street is illustrating a serious, fundamental problem with current computing: It doesn't know the difference between applied math and software. In particular, a good solution should not be in C, etc. but in TeX and is not 'code' but theorems and proof. Sorry 'bout that!