C++ Program for Zeckendorf's Theorem?

Here we will see how to check whether the given sum is found by adding some nonneighbouring Fibonacci numbers or not, if so, what are the numbers? For example if the give sum value is 10, this is sum of 8 and 2. Both 8 and 2 are Fibonacci terms and they are not adjacent. Let us see the algorithm to get the idea.

Algorithm

nonNeighbourFibo(sum)

Begin
   while sum > 0, do
      fibo := greatest Fibonacci term but not greater than sum
      print fibo
      sum := sum - fibo
   done
End

Example

#include<iostream>
using namespace std;
int fibonacci(int n) {
   if (n == 0 || n == 1)
      return n;
   // get the greatest Fibonacci Number smaller than n.
   int prev = 0, curr = 1, next = 1;
   while (next <= n) {
      prev = curr;
      curr = next;
      next = prev + curr;
   }
   return curr;
}
void nonNeighbourFibo(int sum) {
   while (sum > 0) {
      int fibo = fibonacci(sum);
      cout << fibo << " ";
      sum = sum - fibo;
   }
}
int main() {
   int sum = 120;
   cout << "Sum is same as Non-adjacent Fibonacci terms: ";
   nonNeighbourFibo(sum);
}

Output

Sum is same as Non-adjacent Fibonacci terms: 89 21 8 2

Arnab Chakraborty

Published on 31-Jul-2019 12:40:35

• Related Questions & Answers
• Kirchoff's Theorem
• Extended Midy's theorem in C++
• Fermat's Last Theorem in C++
• Fermat's little theorem in C++
• C++ Program to Implement Fermat’s Little Theorem
• C++ Program to Implement the Vizing’s Theorem
• C / C++ Program for Dijkstra's shortest path algorithm
• Lagrange’s four square theorem in C++
• Construct RE for given finite automata with Arden’s theorem
• C++ Program to Implement Euler Theorem
• Bayes Theorem for Conditional Probability in C/C++
• An application on Bertrandís ballot theorem in C/C++
• Explain Arden’s Theorem in TOC.
• What is Kleene’s Theorem in TOC?
• Thevenin’s Theorem and Thevenin Equivalent Circuit