Can anyone tell me how to solve this problem?
http://codeforces.net/contest/177/problem/G2
Thanks in advance!
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Can anyone tell me how to solve this problem?
http://codeforces.net/contest/177/problem/G2
Thanks in advance!
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This is enhanced version of one problem in ICPC WF 2012: https://icpc.kattis.com/problems/fibonacci
Short editorial for WF 2012: http://www.csc.kth.se/~austrin/icpc/finals2012solutions.pdf
I "guess" matrix exponentiation will do the trick for enhanced version (unproven for now, I didn't have time to analyse further).
Let's calculate for each prefix s[1..i] the minimum fibonacci index minind[i] such that s[1..i] is a suffix of fib[i] and s[i + 1..n] is a prefix of fib[i + 1].
Because the relation
can be written equivalently as:
it follows that $min_ind[i]$ is either ∞ or less than n (because fib[i] has all the prefixes of fib[i - 2]). After that, it is essentially a linear reccurence of type
for all $\i \geq n$ (or n + 2 or smth.).
You basically have to compute DP[n] and DP[n + 1] and occurences_less_than_inf, and then do matrix exp. I think that should work :).