10688 - The Poor Giant

[Krzysztof Duleba]

zubair - if it's so than I'm sorry for this. I have to admit that I was wrong.

[Per]

I've solved this problem with C++ using DP and my algorithm is of order n^3. My solution took about 5 seconds, but I see a lot of much faster solutions. Can anyone hint me about a faster solution?

I did a DP solution with memoization which is roughly n^2 * k, but it's independent of the number of test cases (since answers can be reused). It took 1.1 secs, would have been a bit too slow for AC in the original contest, but it would probably be fast enough if the computations are done bottom-up instead of with memoization.

The table I used was simply a two-dimensional array indexed by n and k. Tell me if you want a bigger hint than that.

[Maniac]

Thanks, I tried the solution you suggested and got AC in 1.203s with a bottom-up implementation. So I think it isn't much better than the solution with memorization.

Isn't 1 sec a little on the low side for a time limit then? Prefactors really start to make the difference between AC and TLE in this case, which in my humble opinion should always be avoided...

[Krzysztof Duleba]

I used almost the same algorithm as Per and got AC during the contest. My solution was running for 1.082 s, so time limit in the problem statement was inaccurate.

[natalya]

hi,

i'm still curious with sample input #4, n=5, k=0? how to get 22?
thanks.

-natalya-

[breezechan]

first eat #2, then eat #4

#1 : 2
#2 : 2
#3 : 2+4
#4 : 2+4
#5 : 2+4

the sum is 22.

[Emilio]

Hi all!
I think that I don't understand the problem, albuit I understand the four first cases I can't understand the fifth one n=10 k=20 give as result 605.
Can anyone explain me it?
Thanks in advance!

[yiuyuho]

hmm...that's a big case...

It's too hard to explain with human.

[Emilio]

OK. But maybe, could you explain me the problem?
Any hint that you may think that it is important, or whatever to understand the problem, or the method to solve it, ...

[yiuyuho]

Wow, it has been a while (1 year+?) and you're still keep tap on this, that's great!

Well, from my understanding, you have a bunch of apples of weight k+1...k+n.

Now, you want to eat some apples in order and identify the sweet apple (exaclt one of that). Any apple with less weight than the sweet one is bitter and any apple with more weight is sour, as a result, suppose your apples have weight in the range [i,j], if you eat some apple of weight x, i<=x<=j, then you will know (1) the weet apple is x and you found it, (2) apple x is bitter and the actual sweet apple is thus in range [x+1,j], (3) apple x is sour and the actual sweet apple is in range[i,x-1].

The problem with the problem statement is you don't know where the apple is exactly, and that's not what we're after. You want a cost function that is the sum of all the cost considering all possible locations of the sweet apple. So, basically you need to come up with a decision tree of eating apples such that if apple A k+1<=A<=k+n is the sweet apple, that decision tree will give you cost(A), and you want the decision tree such that Sum(cost(x), x=k+1..k+n) is minimized.


Heh, I think this is even more confusing then the problem statement...lol

So, basically in general you have a bunch of apples with weight in the range [i,j], and you eat some apple x. You then need to calculate the cost of eat x given range[i,j], and split the problem into [i,x-1] and [x+1,j].

This is a typical type of DP where you store a range (i,j) of your problem.

Similar problems are: Matrix Chain Multiplication, Minimum Perimeter Triangulation, Bitonic TSP, Cutting Stick (some problem in vol 1), and a lot of others.

Learn this and you can get +50 in problems solved

[Emilio]

Thanks . I understood the problem and I solved it. Although a bit slow, around 5 secs. I used a recursive method with memoization. And to pass the time limit I used a dirty tricky Although I am not proud of that, I have passed it and I have learnt something else about DP. A good problem for that

[yiuyuho]

Is there a way to prevent those spams?

[forthright48]

Seems like the problem statement has not been fixed yet. I was so confused seeing this:

1+3+3+3=13

I kept on checking my code over and over again, until I realized, the equation is just plain wrong. 1+3+3+3 = 10, not 14. Can't believe it took me so long to see the arithmetic error