if k = n — 1, all of the differences must be different and one of them is d = n — 1, which means 1 and n must come together. till now we have [1 n]

to get d = n — 2, either 1 and n — 1 would have to come together, or n and 2

so, [n — 1, 1, n] or [1, n, 2] are correct.

I know that adding each element greedily to [1, n] at the back i.e. [1, n, 2, ].... does work[or to the front]

[1, n, 2, n — 1, 3, n — 2]

But, how does one think through it during the contest? Is it grabbing pen and paper and trying brute force like

approach to find solution? That would take a hell lot of time (at least for me). But this was an specific case, [k = n

• 1] and using this case, general solution is obtained. So, is looking for some special cases a problem solving

strategy?

I cannot infer how people reach such a simple and sweet solution for such a seemingly complex problem.

Any suggestions would be helpful.