Fibonacci sequence is given by the recursive relation: F(0) = 1 and F(1) = 1 F(n) = F(n-1) + F(n-2) Ultimately, as discussed in lecture 6, Slide 23, it can be shown that: F(n) =1/√5 ((1+√5)/2)n - 1/√5((1-√5)/2)n The number (1+√5)/2 = 1.618 is called the Golden Ratio Clearly F(n) = O(2n). Write a recursive program like the one described in Lecture 5, Slide 32. Then, perform a numeric asymtotic analysis and try to determine a more precise asymptotic estimate of time needed to calculate F(n) (e.g., use a time function). Esentially, try to estimate/infer the tight bound, (f(n)). More details on Big O and in Lecture 5b. Upload both the program (upload your exact cpp, java, py file - source files) and a pdf file analyzing the output of your program.
Fibonacci sequence is given by the recursive relation:
F(0) = 1 and F(1) = 1
F(n) = F(n-1) + F(n-2)
Ultimately, as discussed in lecture 6, Slide 23, it can be shown that: F(n) =1/√5 ((1+√5)/2)n - 1/√5((1-√5)/2)n
The number (1+√5)/2 = 1.618 is called the Golden Ratio
Clearly F(n) = O(2n).
Write a recursive
Then, perform a numeric asymtotic analysis and try to determine a more precise asymptotic estimate of time needed to calculate F(n) (e.g., use a time function).
Esentially, try to estimate/infer the tight bound, (f(n)). More details on Big O and in Lecture 5b.
Upload both the program (upload your exact cpp, java, py file - source files) and a pdf file analyzing the output of your program.
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