Would you mind if you can share your code here?
You mentioned you use the Y numbers to generate the expected cost. I am not 
sure if that's possible to be done in O(N) without looking at your 
implementation.

Also the analysis does *not *suggest that O(N^2) is the *best *solution.
It just give you *a *solution that is easy to implement and still fit the 
time constraint.

在2021年4月6日星期二 UTC-7 下午1:28:32<Sergii Olshanetskyi> 写道:

> The analysis for the problem suggest O(N^2) as the best solution.
> However, it can be solved in O(N). 
>
> The idea is to break the expected array into two parts of size X and Y: 
> 1) X are the numbers can be put at first position without any permutations 
> [ 1 2 3 4 ..... ]
> 2) Y are the number that have to be at specific positions to get the 
> needed complexity
> [ 12 3 4.... 9  11 10 8]
>
> It is possible to create the most costly solution for N digits, by putting 
> each number at the worst position. For instance, the most costly solution 
> for N = 5 would be: 2 4 5 3 1.
>
> My approach is to use Y numbers to generate the expected cost, and numbers 
> X are just printed as they are.
>
> My submission worked. I also tested in locally on N = 10^6.
>
> I am curious why didn't the Google Code Jam team mentioned O(N) solution 
> in the analysis section?..
>

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