You will be exploring the Fibonacci sequence through programming. Complete the following tasks:
The recursive formula F(n) that can be used to define the
Fibonacci sequence.
F(n) = F(n-1) + F(n-2) when n >= 2
F(n) = 0 when n=0
F(n) = 1 when n=1
Pseudocode
Fibonacci(n):
if(n == 0) return 0;
if(n == 1) return 1;
return Fibonacci(n-1) + Fibonacci(n-2)
calculation F(8)
F(8) = F(7) + F(6)
F(8) = F(6) + F(5) + F(5) + F(4) = F(6) + 2*F(5) + F(4)
F(8) = F(5) + F(4) + 2*F(5) + F(4) = 3*F(5) + 2*F(4)
F(8) = 3*(F(4) + F(3)) + 2*(F(3) + F(2))
F(8) = 3*(F(3) + F(2) + F(3)) + 2*(F(2) + F(1) + F(2))
F(8) = 3*(2*F(3) + F(2)) + 2*(2*F(2) + F(1))
F(8) = 3*(2*(F(2) + F(1)) + F(2)) + 2*(2*(F(1) + F(0)) +
F(1))
F(8) = 3*(3*F(2) + 2*F(1)) + 2*(3*F(1) + 2*F(0))
F(8) = 3*(3*(F(1) + F(0)) + 2*F(1)) + 2*(3*F(1) + 2*F(0))
F(8) = (15*F(1) + 9*F(0)) + (6*F(1) + 4*F(0))
F(8) = 15*1 + 9*0 + 6*1 + 4*0
F(8) = 15 + 6 = 21
Number of times F(1) executed for each F(5) execution = 5 times
We can observe that this implementation does a lot of repeated work. For calculating F(5) , F(1) executed 5 times.
You will be exploring the Fibonacci sequence through programming. Complete the following tasks: Research and take...
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