Thursday, April 2, 2020

Fibonacci series starting with any two numbers

def multiply(F, M):
    x = (F[0][0] * M[0][0] + F[0][1] * M[1][0])
    y = (F[0][0] * M[0][1] + F[0][1] * M[1][1])
    z = (F[1][0] * M[0][0] + F[1][1] * M[1][0])
    w = (F[1][0] * M[0][1] + F[1][1] * M[1][1])
    F[0][0] = x
    F[0][1] = y
    F[1][0] = z
    F[1][1] = w
   
def power(F, n):
    if( n == 0 or n == 1):return
    M = [[0, 1],[1, 1]] 
    power(F, n // 2)
    multiply(F, F)
    if (n % 2 != 0):
        multiply(F, M) 


def fib(a,b,n):
     
    F = [[0, 1],[1, 1]]
    if (n == 0): return a
    if (n == 1): return b
    power(F, n - 1)
         
    return F[0][1]*a + F[1] [1]*b