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38 lines
1.1 KiB
Python
38 lines
1.1 KiB
Python
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#coding: utf-8
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''' mbinary
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#######################################################################
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# File : fibonacci.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.github.io
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# Github: https://github.com/mbinary
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# Created Time: 2019-02-03 19:10
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# Description: use matrix and fast pow to calculate big numbr fibonacci value.
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#######################################################################
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'''
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def fib(n):
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"""Calculates the nth Fibonacci number"""
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mat,p = (1,1,1,0),n-2
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if n<=0: # for negative fib item, use f(n) = f(n+2)-f(n-1) to calculate
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mat = (0,1,1,-1),2-n
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li = matrix_pow((0,1,1,-1),1-n)
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return li[0]+li[1]
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def matrix_pow(mat,n):
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ans = (1,0,0,1) # element matrix
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while n>0:
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if n%2==1:
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ans = matrix_mul(ans,mat)
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n>>=1
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mat = matrix_mul(mat,mat)
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return ans
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def matrix_mul(a,b):
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'''a,b are four-item tuple, represent matrix [[a[0],a[1]],[a[2],a[3]]]'''
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return a[0]*b[0]+a[1]*b[2], a[0]*b[1]+a[1]*b[3], a[2]*b[0]+a[3]*b[2],a[2]*b[1]+a[3]*b[3]
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if __name__=='__main__':
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for i in range(-5,5):
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print(i,fib(i))
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