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
// Java program for Zeckendorf's theorem. It finds representation // of n as sum of non-neighbouring Fibonacci Numbers. class GFG {
public static int nearestSmallerEqFib( int n)
{
// Corner cases
if (n == 0 || n == 1 )
return n;
// Find the greatest Fibonacci Number smaller
// than n.
int f1 = 0 , f2 = 1 , f3 = 1 ;
while (f3 <= n) {
f1 = f2;
f2 = f3;
f3 = f1 + f2;
}
return f2;
}
// Prints Fibonacci Representation of n using
// greedy algorithm
public static void printFibRepresntation( int n)
{
while (n > 0 ) {
// Find the greates Fibonacci Number smaller
// than or equal to n
int f = nearestSmallerEqFib(n);
// Print the found fibonacci number
System.out.print(f + " " );
// Reduce n
n = n - f;
}
}
// Driver method to test
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!
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