Considerations and Tutorial of TopCoder SRM 532

Hi everybody;

Today's SRM was quite exciting, the problem set was tricky but nice, an easy 250, and not too difficult but with some tricky test cases 500 and a harder than usual 1000 which until now I didn't thought in any possible "in-time" solution, I guess it's because I'm really bad in dynamic programming.

I'll write a brief tutorial about this round problems which I was able to solve, in the contest time, I just solved the 250 one, who was quite easy, but in less than 5 minutes in practice room, I solved the 600 problem without issues.

250:

Reading the statement carefully, it's easy to notice that the approach is:
Find the Maximum and Minimum values of the array, theses values are the minimum possible bound for the set; then check all the values between this whole set who's not in the array;

My solution in the actual contest is ridiculous expensive but here is an O(N * log(N)) solution:

In the 600 the idea is quite simple get all the 'non-rusty' chain links, and then, get the most profitable prefix and suffix. It can be done straightforwardly, but the trick starts with possible chains as '9.9' where the link can be both the best prefix and suffix, as we have only two end points "prefix and suffix" we can brute force this two possibilities which I called 'prefixBeforeSuffix' and 'suffixBeforePrefix', which ended up in a O(6*(N*3)) solution, running smoothly under Topcoder time limits.