Consider the following recurrence relation:
f(1) = 1; f(2) = 2; f(3) = 3; f(4) = 2; f (5) = 4;
f(n) = 2* f (n- 1) + f(n- 5) for all n > 5.
a. Compute f(n) for the following values of n: 6, 7, 10, 12.
b. If you were careful, rather than computing5) from scratch (the way a recursive Java method would compute it), you would have computed f(6), then f(7), then f(8), and so on up to f(15), recording the values as you computed them. This ordering would have saved you the effort of ever computing the same value more than once. (Recall the nonrecursive version of the rabbit method discussed at the end of this chapter.)
Note that during the computation, you never need to remember all the previously computed values—only the last five. By taking advantage of these observations, write a Java method that computes f(n) for arbitrary values of n.
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