An unofficial tutorial on 2115C / Failure to GM

Fail to become GM.

Hints are omitted.

\(O(nmh^2)\) is too simple,just use dynamic programming.
\(dp(i,j,k)\) means the probability to reach the goal in the first \(i\) turns,\(\min(h_i)=j\),\(\sum (h_i-j)=k\),and make simple transitions.

As we see,the \(k\) cound be big. And if \(k\leq n\),we get \(O(nmh)\),which is fast enough.

And the \(k\) can only be big in the beginning,and we can enumerate the time when \(h_i\) are equal.

And set another dp,which is used frequently. \(g(i,j)\) means the probability to have \(j\) times when the Sword doesn't shine.It can be done in \(O(nmh)\).

So the work are done.

https://codeforces.com/contest/2115/submission/322464169