3 sequential numbers

Alright geniuses, if you think your programming ability is up to par, lets see you solve this:

Write an algorithm which in O(n) time finds 3 indices i, j, and k such that i < j < k and array[i] < array[j] < array[k].

I don't feel like actually coding it, but I think I've got a solution.

Split the list into a list of increasing lists:
[1,2,3,2,3,4] => [[1,2,3], [2,3,4]]
[1,3,2,4,3,5] => [[1,3], [2,4], [3,5]]
[5,4,3,2,1] => [[5], [4], [3], [2], [1]]

If a list's last value is greater than the previous list's last value, remove all elements from the beginning of the list that are less than or equal to the last element in the previous list.
[[1,2,3], [2,3,4]] => [[1,2,3], [4]]
[[4], [1,2,3]] => [[4], [1,2,3]] (don't do anything because 3 < 4)

Repeat the first step.
If any sublist's length is at least 3, there's your answer.

After writing all that out, I just realized that you want the indices and not the values. Store each element as (i,v) where i is the index and v is the value, and make all comparisons between v.