Question

Below you will find a recursive function that computes a Fibonacci sequence (Links to an external site.).  

# Python program to display the Fibonacci sequence up to n-th term using recursive functions

def recur_fibo(n):
"""Recursive function to
print Fibonacci sequence"""
if n <= 1:
return n
else:
return(recur_fibo(n-1) + recur_fibo(n-2))

# Change this value for a different result
nterms = 10

# uncomment to take input from the user
#nterms = int(input("How many terms? "))

# check if the number of terms is valid
if nterms <= 0:
print("Plese enter a positive integer")
else:
print("Fibonacci sequence:")
for i in range(nterms):
print(recur_fibo(i))

Group Discussion

How does the performance of this recursive functions compare to that of an iterative version?

Answer 1

Python Code for the Fibonacci sequence:-

#Recursive method to find the fibonacci sequence
def fibonacci_sequence(list1,n):
if n==0:
return list1
length=len(list1)
list1.append(list1[length-1]+list1[length-2])
return fibonacci_sequence(list1,n-1) #Recursive call
  
# Method to display the fibonacci sequence
def disp(list1):
for i in list1:
print(i,end=" ")
def main():
list1=[]
n=int(input("Enter the value of n: ")) # User input the value of n
print("Fibonacci Sequence: ",end=" ")
if n==1:
list1.append(0)
disp(list1)
elif n==2:
list1.append(0)
list1.append(1)
disp(list1)
else:
list1.append(0)
list1.append(1)
list1=fibonacci_sequence(list1,n-2)
disp(list1)
  
if __name__=='__main__':
main() #Calling main method

The Above Recursive implementation for finding a Fibonacci sequence performance is the same as that of the iterative approach Both approach time Complexity and Space Complexity is O(n).

The only difference is the recursive approach uses recursion tree to produce Fibonacci series