Fibonacci Cube Graph
You are given input as order of graph n (highest number of edges connected to a node), you have to find the number of vertices in a Fibonacci cube graph of order n.
Examples :
Input : n = 3 Output : 5 Explanation : Fib(n + 2) = Fib(5) = 5 Input : n = 2 Output : 3
A Fibonacci Cube Graph is similar to hypercube graph, but with a fibonacci number of vertices. In fibonacci cube graph only 1 vertex has degree n rest all has degree less than n.
Fibonacci cube graph of order n has F(n + 2) vertices, where F(n) is a n-th fibonacci number,
Fibonacii series : 1, 1, 2, 3, 5, 8, 13, 21, 34……………….
For input n as order of graph, find the corresponding fibonacci number at the position n + 2.
where F(n) = F(n – 1) + F(n – 2)
Approach : Find the (n + 2)-th fibonacci number.
Below is the implementation of above approach :
C++
// CPP code to find vertices in a fibonacci // cube graph of order n #include<iostream> using namespace std; // function to find fibonacci number int fib(int n) { if (n <= 1) return n; return fib(n - 1) + fib(n - 2); } // function for finding number of vertices // in fibonacci cube graph int findVertices (int n) { // return fibonacci number for f(n + 2) return fib(n + 2); } // driver program int main() { // n is the order of the graph int n = 3; cout << findVertices(n); return 0; } |
chevron_right
filter_none
Java
// java code to find vertices in a fibonacci // cube graph of order n public class GFG { // function to find fibonacci number static int fib(int n) { if (n <= 1) return n; return fib(n - 1) + fib(n - 2); } // function for finding number of vertices // in fibonacci cube graph static int findVertices (int n) { // return fibonacci number for f(n + 2) return fib(n + 2); } public static void main(String args[]) { // n is the order of the graph int n = 3; System.out.println(findVertices(n)); } } // This code is contributed by Sam007 |
chevron_right
filter_none
Python3
# Python3 code to find vertices in
# a fibonacci cube graph of order n
# Function to find fibonacci number
def fib(n):
if n <= 1: return n return fib(n - 1) + fib(n - 2) # Function for finding number of # vertices in fibonacci cube graph def findVertices(n): # return fibonacci number # for f(n + 2) return fib(n + 2) # Driver Code if __name__ == "__main__": # n is the order of the graph n = 3 print(findVertices(n)) # This code is contributed # by Rituraj Jain [tabby title="C#"]
// C# code to find vertices in a fibonacci // cube graph of order n using System; class GFG { // function to find fibonacci number static int fib(int n) { if (n <= 1) return n; return fib(n - 1) + fib(n - 2); } // function for finding number of // vertices in fibonacci cube graph static int findVertices (int n) { // return fibonacci number for // f(n + 2) return fib(n + 2); } // Driver code static void Main() { // n is the order of the graph int n = 3; Console.Write(findVertices(n)); } } // This code is contributed by Sam007 |
chevron_right
filter_none
PHP
<?php // PHP code to find vertices in a // fibonacci cube graph of order n // function to find fibonacci number function fib($n) { if ($n <= 1) return $n; return fib($n - 1) + fib($n - 2); } // function for finding number of // vertices in fibonacci cube graph function findVertices ($n) { // return fibonacci number // for f(n + 2) return fib($n + 2); } // Driver Code // n is the order of the graph $n = 3; echo findVertices($n); // This code is contributed by Sam007 ?> |
chevron_right
filter_none
Output :
5
Note that the above code can be optimized to work in O(Log n) using efficient implementations discussed in Program for Fibonacci numbers
Recommended Posts:
- Convert the undirected graph into directed graph such that there is no path of length greater than 1
- Graph implementation using STL for competitive programming | Set 2 (Weighted graph)
- Detect cycle in the graph using degrees of nodes of graph
- Check if a M-th fibonacci number divides N-th fibonacci number
- Fibonacci Word
- Even Fibonacci Numbers Sum
- Nth Even Fibonacci Number
- GCD and Fibonacci Numbers
- Non Fibonacci Numbers
- Fibonacci Power
- Fibonacci problem (Value of Fib(N)*Fib(N) - Fib(N-1) * Fib(N+1))
- Sum of Fibonacci Numbers
- Fibonacci Coding
- K- Fibonacci series
- Fibonacci Search
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
- Check if the given Binary Expressions are valid
- Count the nodes of the given tree whose weight has X as a factor
- Count the nodes in the given tree whose weight is even parity
- Build original array from the given sub-sequences
- Count the nodes of the tree which make a pangram when concatenated with the sub-tree nodes
