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http://codeforces.com/problemset/problem/698/C
Hi codeforces, though read the tutorial, I still don't understand it. Please anyone explain how to solve it in detail?why we can look backwards? What is the idea?
Btw, what math should I know to understand it?(i can know the dp,bitmask)
Thank you:D
consider the choosing sequence from beginning, a1, a2, a3, .. an, now let set S containing the k elements in the cache.
let's see what S actually contains. Since S contains most recently chosen k elements, we can look backward from an and the first k different elements form S.
so event "S contains b1, b2,.. bk"
equals to
event "the last k different elements in the choosing sequence consist of b1, b2, .. bk".
And since prob(a1, a2, .., an) = prob(an, a(n-1),.., a1)
so its probability also equal to
the event "the first k different elements in the choosing sequence consist of b1,b2,..bk"
and this can be calculated easily using dp.
I feel grateful to tinytiny and Tornad0