Open in App
Not now

# Python Program for Fibonacci numbers

• Difficulty Level : Easy
• Last Updated : 30 Jan, 2023

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

Fn = Fn-1 + Fn-2

with seed values

F0 = 0 and F1 = 1.

Method 1 ( Use recursion ) :

## Python3

 # Function for nth Fibonacci number def Fibonacci(n):         # Check if input is 0 then it will     # print incorrect input     if n < 0:         print("Incorrect input")       # Check if n is 0     # then it will return 0     elif n == 0:         return 0       # Check if n is 1,2     # it will return 1     elif n == 1 or n == 2:         return 1       else:         return Fibonacci(n-1) + Fibonacci(n-2)   # Driver Program print(Fibonacci(9))   # This code is contributed by Saket Modi # then corrected and improved by Himanshu Kanojiya

Output

34

Method 2 ( Use Dynamic Programming ) :

## Python3

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

Output

34

Method 3 ( Space Optimized):

## Python

 # Function for nth fibonacci # number - Space Optimisation # Taking 1st two fibonacci numbers as 0 and 1   def fibonacci(n):     a = 0     b = 1           # Check is n is less     # than 0     if n < 0:         print("Incorrect input")               # Check is n is equal     # to 0     elif n == 0:         return 0             # Check if n is equal to 1     elif n == 1:         return b     else:         for i in range(1, n):             c = a + b             a = b             b = c         return b   # Driver Program print(fibonacci(9))   # This code is contributed by Saket Modi # Then corrected and improved by Himanshu Kanojiya

Output

34

Method 4 (Cache):

## Python3

 from functools import lru_cache   # Function for nth Fibonacci number   # lru_cache will store the result # so we don't have to find # fibonacci for same num again     @lru_cache(None) def fibonacci(num: int) -> int:       # check if num is less than 0     # it will return none     if num < 0:         print("Incorrect input")         return       # check if num between 1, 0     # it will return num     elif num < 2:         return num       # return the fibonacci of num - 1 & num - 2     return fibonacci(num - 1) + fibonacci(num - 2)     # Driver Program print(fibonacci(9))   # This code is contributed by Sayedul Haque Sarker

Output

34

Method 5(Using Backtracking):

## Python3

 def fibonacci(n, memo={}):     if n <= 0:         return 0     elif n == 1:         return 1     elif n in memo:         return memo[n]     else:         memo[n] = fibonacci(n-1) + fibonacci(n-2)         return memo[n]   # Driver Program print(fibonacci(9))

Output

34

Time complexity: O(n)
Auxiliary Space: O(n)

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

My Personal Notes arrow_drop_up
Related Articles