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The most optimal way here would be to use Dynamic Programming because the subproblems overlap.
- Learner June 20, 2013F(n) = F(n-1) + F(n-2)
and in next set of iteration:
F(n-1) = F(n-2) + F(n-3).
So, as you can see, there are unnecessary recompuation of same subproblem, which can be avoided by using Dynamic Programming and storing intermediate results in a table. THe normal fibonacci program won't be of much interest since it incurs heavy complexity (exponential factor).