Create nth_fibonacci_using_goldenratio.cpp

math/nth_fibonacci_using_goldenratio.cpp

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+//
+// CPP program to find n-th Fibonacci number 
+// More documentation about the algorithm
+//
+// The All ▲lgorithms Project
+//
+// https://allalgorithms.com/
+// https://github.com/allalgorithms/cpp
+//
+// Contributed by: Mohbius
+// Github: @mohbius
+//
+#include <iostream>
+#include <cstdlib> 
+#include <cmath>
+using namespace std; 
+
+// Approximate value of golden ratio 
+double PHI = 1.6180339; 
+
+// Fibonacci numbers upto n = 5 
+int f[6] = { 0, 1, 1, 2, 3, 5 }; 
+
+// Function to find nth 
+// Fibonacci number 
+int fib (int n) 
+{ 
+    // Fibonacci numbers for n < 6 
+    if (n < 6) 
+        return f[n]; 
+
+    // Else start counting from  
+    // 5th term 
+    int t = 5, fn = 5; 
+
+    while (t < n) { 
+         fn = round(fn * PHI); 
+         t++; 
+    } 
+
+    return fn;    
+} 
+
+int main() 
+{ 
+    std::cout << fib(9) << std::endl; // 34
+    std::cout << fib(8) << std::endl; // 21
+    std::cout << fib(7) << std::endl; // 13
+    return 0; 
+}