Question

Hi I am trying to understand this algorithm and I and trying to walk through it to see what values will result but not much luck in doing so. I think I don’t know if I am getting this right or not. This is the algorithm

Algorithm Fast-Fibonacci(n)
Let fib[0] and fib[1] be 1.
for each i from 2 to n, do:
  Let fib[i] be fib[i - 2] + fib[i - 1].
end of loop
return fib[n].

say Fast-Fib(5)
fib[0] = 0
Fib[1] = 1
fib[2] = {2-2] + [2-1] = 1
fib[3] = [3-2] + [3-1] = 3
fib[4] = 4-2] + [4-1] = 5

then the loop quits right?
resulting in
01135 as the answer

Answer 1

You are accessing the elements of fib, so for Fast-Fib(5) you get:

fib[0] = 1
fib[1] = 1
fib[2] = fib[2-2] + fib[2-1] = fib[0] + fib[1] = 1+1 = 2 // i==2
fib[3] = fib[3-2] + fib[3-1] = fib[1] + fib[2] = 1+2 = 3 // i==3
fib[4] = fib[4-2] + fib[4-1] = fib[2] + fib[3] = 2+3 = 5 // i==4
fib[5] = fib[5-2] + fib[5-1] = fib[3] + fib[4] = 3+5 = 8 // i==5

returning fib[5] (i.e. 5)

Note: I updated the values according to the questions initial conditions (fib[0]=fib[1]=1); often fib[0]=0; fib[1]=1