Question

Write an algorithm to return the fibonacci number. Show the trace of you algorithm for fib(6).

1. when n <= 2 fib(n) = 1
2. when n > 2 fib(n) = fib(n-1) + fib(n-2)

Answer 1

algorithm:

step1: set f1=1
setp2: set f2=1
step3: for i=1 to n-2
set temp=f1+f2
set f1=f2
   set f2=temp
step4:display f2 for nth fibonacci number
  

fib(6)::::

---->f1=1,f2=1

(1)---> temp=1+1=2

f1=1,f2=2

(2)-->temp=1+2=3 f1=2 f2=3

(3)-->temp=3+2=5 f1=3 f2=5

(4)--->temp=5+3=8 f1=5 f2=8

display f2 means "8"

fibonacii series

1 1 2 3 5 8 13 21 34 ----------

index;1 2 3 4 5 6 7 8

therefore 6th fibonacii is 8