Zeckendorf's Theorem (Non-Neighbouring Fibonacci Representation) - GeeksforGeeks

Zeckendorf's Theorem (Non-Neighbouring Fibonacci Representation) - GeeksforGeeks

Zeckendorf's Theorem (Non-Neighbouring Fibonacci Representation)

Zeckendorf's theorem states that every positive Every positive integer can be written uniquely as a sum of distinct non-neighbouring Fibonacci numbers. Two Fibonacci numbers are neighbours if they one come after other in Fibonacci Sequence (0, 1, 1, 2, 3, 5, ..). For example, 3 and 5 are neighbours, but 2 and 5 are not.

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 10.  

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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 

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