Python Program for Zeckendorf\’s Theorem (Non-Neighbouring Fibonacci Representation)
Last Updated :
20 Jan, 2022
Given a number, find a representation of number as sum of non-consecutive Fibonacci numbers.
Examples:
Input: n = 10
Output: 8 2
8 and 2 are two non-consecutive Fibonacci Numbers
and sum of them is 10.
Input: n = 30
Output: 21 8 1
21, 8 and 1 are non-consecutive Fibonacci Numbers
and sum of them is 30.
The idea is to use Greedy Algorithm.
1) Let n be input number
2) While n >= 0
a) Find the greatest Fibonacci Number smaller than n.
Let this number be 'f'. Print 'f'
b) n = n - f
Python3
def nearestSmallerEqFib(n):
if (n = = 0 or n = = 1 ):
return n
f1, f2, f3 = 0 , 1 , 1
while (f3 < = n):
f1 = f2;
f2 = f3;
f3 = f1 + f2;
return f2;
def printFibRepresntation(n):
while (n> 0 ):
f = nearestSmallerEqFib(n);
print (f,end = " " )
n = n - f
n = 30
print ( "Non-neighbouring Fibonacci Representation of" , n, "is" )
printFibRepresntation(n)
|
Output:
Non-neighbouring Fibonacci Representation of 30 is
21 8 1
Please refer complete article on Zeckendorf’s Theorem (Non-Neighbouring Fibonacci Representation) for more details!
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