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
Fn = Fn-1 + Fn-2
with seed values
F0 = 0 and F1 = 1.
Method 1 ( Use recursion ) :
Python3
# Function for nth Fibonacci numberdef 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 Programprint(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 1FibArray = [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 - 1] else: temp_fib = fibonacci(n - 1) + fibonacci(n - 2) FibArray.append(temp_fib) return temp_fib# Driver Programprint(fibonacci(9))# This code is contributed by Saket Modi |
Output
21
Method 3 ( Space Optimized):
Python
# Function for nth fibonacci# number - Space Optimisation# Taking 1st two fibonacci numbers as 0 and 1def 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 Programprint(fibonacci(9))# This code is contributed by Saket Modi# Then corrected and improved by Himanshu Kanojiya |
Output
34
Please refer complete article on Program for Fibonacci numbers for more details!
.png)