Consider the algorithm for the Fibonacci sequence a) Write a recursive algorithm which computes F(n) for and show that its running time complexity is exponential with n Hint the Fibonacci number can be approximated as where is the golden ratio ( 1 61801 ) and denotes rounding to the nearest integer b) Add memoization to the recursive algorithm and show that the running time is 0(n) c) Reimplement the memoized recursive algorithm as a bottom up iterative algorithm (Note an optimality substructure is not in this exercise )

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Question: Consider the algorithm for the Fibonacci sequence. a) Write a recursive algorithm which computes F(n) for and show that its running-time complexity is exponential with

Consider the algorithm for the Fibonacci sequence.

a) Write a recursive algorithm which computes F(n) for Consider the algorithm for the Fibonacci sequence. a) Write a recursive algorithm and show that its running-time complexity is exponential with n. Hint: the Fibonacci number can be approximated as which computes F(n) for and show that its running-time complexity is exponential where is the golden ratio (= the golden ratio (= = 1.61801.. ) and [.] denotes rounding to = 1.61801.. ) and [.] denotes rounding to the nearest integer.

b) Add memoization to the recursive algorithm and show that the running-time is 0(n)..

c) Reimplement the memoized recursive algorithm as a bottom-up iterative algorithm. (Note an optimality substructure is not in this exercise.)

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