Fibonacci sequence by python

 

 

Besides there is an interesting post about Fibonaccisequence:

https://www.mathsisfun.com/numbers/fibonacci-sequence.html

 

This artical is aimed to find out best code to compute Fibonacci by python:

 

(1)Complexity of algorithm is O(2ⁿ)

 

 

def fibonacci_1(n):
    
    if n==0:
        return 0
    elif n==1:
        return 1
        
    else:

        return fibonacci_1(n-1)+fibonacci_1(n-2)
        

 

(2)Complexity of algorithm is O(n)

 

def fibonacci_2(n):
    
    result=[0,1]
    
    for i in xrange(2,n+1):
        result.append(result[i-1]+result[i-2])
    
    return result(n)

 

(3)Complexity of algorithm is logn

 

 

def fibonacci_3(n):
    return recuCal(n)[1]

matrix=[0,1,1,1]
def recuCal(n):
    if n == 1:
        return matrix
    elif n == 2:
        return matrixCal(matrix,matrix)
    elif n % 2:
        return matrixCal(matrixCal(recuCal(n/2),recuCal(n/2)),matrix)
    else:
        return matrixCal(recuCal(n/2),recuCal(n/2))

def matrixCal(matrix1,matrix2):
    matrix3 = [0,0,0,0]
    matrix3[0]=matrix1[0]*matrix2[0]+matrix1[1]*matrix2[2]
    matrix3[1]=matrix1[0]*matrix2[1]+matrix1[1]*matrix2[3]
    matrix3[2]=matrix1[2]*matrix2[0]+matrix1[3]*matrix2[2]
    matrix3[3]=matrix1[2]*matrix2[1]+matrix1[3]*matrix2[3]
    return matrix3