Interestingly enough the problem can be solved with simple simulation. Just simulate the process, choosing random directions and random initial positions while you are within the time limit and you will get accepted.
I really doubt this is the correct solution, so I was wondering what is the real one?

There is very simple O(m) solution - just use your algorithm for solution of previous problem.

I've got WA#9.
My algo is:
first I generate the possible answers in both directions (strating from 1 and n) with algorithm from the previous problem, and with KMP I'm searching the input array for match, also I added special cases for 2 (1 1 and 2 2) and for 3 (2 2).

Edited by author 20.10.2010 04:44

To Alexander Georgiev:
now your solution gets wa51. do you happy? :)

Edited by author 20.10.2010 16:37

To KALO:
Try this test
5 10
1 2 3 4 5 1 2 3 4 5

Yep.
It is interesting - how many brute force solutions fail after new tests :)

Sort of =) NOW I have to write a real solution :)

If N is odd = then sequence are
1..N 1..N
2..N-1 N-1
else the sequence is 2..N-1 N-1.. 2
I'm right?

Edited by author 20.10.2010 17:04

I don't understand you. As I know, jury's solution don't use misterious knowledges about any sequences. =)

O(m) solution doesn't use them as well =)
No, I was talking about general logic of my algorithm. Of course, it is incorrect to search for some predefined sequence in the answer. For example, for m=5 general algorithm gives
sequence like 1 2 3 4 5 1 2 3 4 (or something like that), but possible answer is 2 2 4 4 4 4 3 2.

if m = 5, 2 2 4 4 4 4 3 2 can't be the answer
imagine original is on 4th pedestal

you touch 2 orig move 4 -> 3
you touch 2 orig move 3 -> 2
you touch 4 orig move 2 -> 3
you touch 4 orig move 3 -> 2
you touch 4 orig move 2 -> 3
you touch 4 orig move 3 -> 2
you touch 3 orig move 2 -> 3
you touch 2 orig move 3 -> 4

you didn't catch the orig!

if the sequence has 2 * k numbers suquencially you can
take only 2 if 2 * k - 1 you can take 1 (I think)

example  2 2 2 2 3 3 3 5 6 --> 2 2 3 5 6

Edited by author 20.10.2010 22:39

Idea:
Game of two person
and bacward analysis from the end
Example:
3 3
1 2 3
3: 1,2-win; 3- fail
2:1,3-win(1->2,3->2) 2- fail
1:2-win(2->1)1,3-fail
so win:2->1->2


Edited by author 25.10.2010 14:41

I understand ur algo but I think it's O(n*m). Isn't It? Won't it get TL

Yes. But pattern of failed states exits and it's maitaining costts O(1) on eaxh of n steps.

what if n = 10^5 and m = 10^5
sequence is like this 4 6 4 6 4 6 4 6 4 6 . . .
I think at this test the length of failed pattern is 1 all the time and time is O(n, m) again. Or I didn't understand your previous massage rightly?