Python Program for Fibonacci numbers

The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

    F_n = F_n-1 + F_n-2

with seed values

   F₀ = 0 and F₁ = 1.

Method 1 ( Use recursion ) :

# Function for nth Fibonacci number 
  
def Fibonacci(n): 
    if n<0: 
        print("Incorrect input") 
    # First Fibonacci number is 0 
    elif n==1: 
        return 0
    # Second Fibonacci number is 1 
    elif n==2: 
        return 1
    else: 
        return Fibonacci(n-1)+Fibonacci(n-2) 
  
# Driver Program 
  
print(Fibonacci(9)) 
  
#This code is contributed by Saket Modi 

Output:

Method 2 ( Use Dynamic Programming ) :

# Function for nth fibonacci number - Dynamic Programing 
# Taking 1st two fibonacci nubers as 0 and 1 
  
FibArray = [0,1] 
  
def fibonacci(n): 
    if n<0: 
        print("Incorrect input") 
    elif n<=len(FibArray): 
        return FibArray[n-1] 
    else: 
        temp_fib = fibonacci(n-1)+fibonacci(n-2) 
        FibArray.append(temp_fib) 
        return temp_fib 
  
# Driver Program 
  
print(fibonacci(9)) 
  
#This code is contributed by Saket Modi 

Output:

Method 3 ( Space Optimized):

# Function for nth fibonacci number - Space Optimisataion 
# Taking 1st two fibonacci numbers as 0 and 1 
  
def fibonacci(n): 
    a = 0
    b = 1
    if n < 0: 
        print("Incorrect input") 
    elif n == 0: 
        return a 
    elif n == 1: 
        return b 
    else: 
        for i in range(2,n): 
            c = a + b 
            a = b 
            b = c 
        return b 
  
# Driver Program 
  
print(fibonacci(9)) 
  
#This code is contributed by Saket Modi 

Output:

Please refer complete article on Program for Fibonacci numbers for more details!

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