Java Program for Zeckendorf\’s Theorem (Non-Neighbouring Fibonacci Representation)
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
class GFG {
public static int nearestSmallerEqFib( int n)
{
if (n == 0 || n == 1 )
return n;
int f1 = 0 , f2 = 1 , f3 = 1 ;
while (f3 <= n) {
f1 = f2;
f2 = f3;
f3 = f1 + f2;
}
return f2;
}
public static void printFibRepresntation( int n)
{
while (n > 0 ) {
int f = nearestSmallerEqFib(n);
System.out.print(f + " " );
n = n - f;
}
}
public static void main(String[] args)
{
int n = 30 ;
System.out.println( "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!
Last Updated :
06 Dec, 2018
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