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; } |
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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 |
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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 |
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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 ?> |
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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
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