斐波那契数列的Python程序

斐波那契数是以下整数序列中的数字。
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ......
在数学术语中，斐波那契数列 Fn 由递归关系定义

Fn = Fn-1 + Fn-2

带有种子值

F0 = 0 and F1 = 1.

方法1（使用递归）：

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

输出

34

方法2（使用动态规划）：

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 - 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

输出

21

方法3（空间优化）：

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

输出

34

有关详细信息，请参阅有关斐波那契数列程序的完整文章！