6 ms·
Asymptotically, the question with more coconuts is more interesting. I haven't verified this for sure (there are some assumptions), but: With the "naive" asymp
by eranki 14y ago
Asymptotically, the question with more coconuts is more interesting. I haven't verified this for sure (there are some assumptions), but:
With the "naive" asymptotically correct solution (go up a constant number k of floors, then linearly search the remainder), two coconuts gives us a worst case cost of:
n/k + k
minimize for k, we get a cost of
2n^(1/2)
With 3 coconuts, we have
n/k + 2k^(1/2)
minimize for k, we get
3n^(1/3)
What happens when we get log(n) coconuts?
log(n)n^(1/log(n))
= O(log(n))
Sweet! So at least we can see that it converges to binary search as we add coconuts.