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I'm looking at the second test case
5 3 4 5 6
And don't understand can it be solved in a day. We have 2 problems with the same difficulty level - 5.
Solving two problems with same difficulty in a day will be against the rules, right ?
5 in '5 3 4 5 6' do not mean difficulty.
It says that the two consecutive problems that you solve in a given day should have a minimum difference of K in their vi ( and not every pair of problems that you solve in a given day)
n=5, k=1; 5 3 4 5 6 is can be solved in a given day because that sequence has atleast a variation of 1 between consecutive numbers that is met.
However, if instead it was n=3, k=1; 5 5 6, then you need minimum 2 days to solve it.
It also mentions that the difficulty of problems within a same day must increase . So you cannot solve 3 4 5 5 6 in that order on a same day, because you are not increasing difficulty from 5 to 5.
Therefore, I have the same doubt, seems like you need 2 days to solve the second example for me too.
I can only assume that: " Problems with similar vi values are similar in nature" means you can solve all fives at the same time, but that might be stretching it