Python Program for n-th Fibonacci number

In this article, we will compute the nth Fibonacci number.

A Fibonacci number is defined by the recurrence relation given below −

Fn = Fn-1 + Fn-2

With F₀= 0 and F₁ = 1.

First, few Fibonacci numbers are

0,1,1,2,3,5,8,13,..................

We can compute the Fibonacci numbers using the method of recursion and dynamic programming.

Now let’s see the implementation in the form of Python script

Approach 1: Recursion Method

Example

#recursive approach
def Fibonacci(n):
   if n<0:
      print("Fibbonacci can't be computed")
   # First Fibonacci number
   elif n==1:
      return 0
   # Second Fibonacci number
   elif n==2:
      return 1
   else:
      return Fibonacci(n-1)+Fibonacci(n-2)
# main
n=10
print(Fibonacci(n))

Output

34

The scope of all the variables declared is shown below.

Approach 2: Dynamic Programming Method

Example

#dynamic approach
Fib_Array = [0,1]
def fibonacci(n):
   if n<0:
      print("Fibbonacci can't be computed")
   elif n<=len(Fib_Array):
      return Fib_Array[n-1]
   else:
      temp = fibonacci(n-1)+fibonacci(n-2)
      Fib_Array.append(temp)
      return temp
# Driver Program
n=10
print(fibonacci(n))

Output

34

The scope of all the variables declared is shown below

Conclusion

In this article, we learned about the computation of nth Fibonacci number using recursion and dynamic programming approach.