https://www.codechef.com/problems/CHN16H
My observations:
f(2s, 2x) = f(s, x) if
f(2s, 2x) = 3f(s - 1, x) if
f(2s + 1, 2x + 1) = 3f(s, x) if
f(2s + 1, 2x + 1) = f(s - 1, x) if
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https://www.codechef.com/problems/CHN16H
My observations:
f(2s, 2x) = f(s, x) if
f(2s, 2x) = 3f(s - 1, x) if
f(2s + 1, 2x + 1) = 3f(s, x) if
f(2s + 1, 2x + 1) = f(s - 1, x) if
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I did not see the question. Going by your recurrence. This recurrence can be calculated in poly logarithmic time if you do it naively.
It is easy to compute f(a,b) for some a, b in logarithmic time but the problem is to compute sum f(ia, ib) for all i <= n. a,b <= 30, n <= 10^12.