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
# Python program for Zeckendorf's theorem. It finds representation # of n as sum of non-neighbouring Fibonacci Numbers. # Returns the greatest Fibonacci Number smaller than # or equal to n. def nearestSmallerEqFib(n):
# Corner cases
if (n = = 0 or n = = 1 ):
return n
# Finds the greatest Fibonacci Number smaller
# than n.
f1, f2, f3 = 0 , 1 , 1
while (f3 < = n):
f1 = f2;
f2 = f3;
f3 = f1 + f2;
return f2;
# Prints Fibonacci Representation of n using # greedy algorithm def printFibRepresntation(n):
while (n> 0 ):
# Find the greates Fibonacci Number smaller
# than or equal to n
f = nearestSmallerEqFib(n);
# Print the found fibonacci number
print (f,end = " " )
# Reduce n
n = n - f
# Driver code test above functions 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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