Imprima los primeros n números de Fibonacci usando la fórmula directa

Dado un número n, la tarea es imprimir primero n números de Fibonacci .
Prerrequisito: Programa para imprimir primero n Números de Fibonacci | Serie 1

Ejemplos: 

Input : 7
Output :0 1 1 2 3 5 8

Input : 5
Output :0 1 1 2 3

N-ésimo Número de Fibonacci = [(1 + √5) ⁿ – (1 – √5) ⁿ )] / [2 ⁿ * √5]

A continuación se muestra la implementación.  

// C++ code to print fibonacci
// numbers till n using direct formula.
#include<bits/stdc++.h>
using namespace std;
 
// Function to calculate fibonacci
// using recurrence relation formula
void fibonacci(int n){
    long long int fib;
    for ( long long int i = 0; i < n; i++)
    {
        // Using direct formula
        fib = (pow((1 + sqrt(5)), i) -
               pow((1 - sqrt(5)), i)) /
              (pow(2, i) * sqrt(5));
               
        cout << fib << " ";
    }
}
 
// Driver code
int main()
{
    long long int n = 8;   
    fibonacci(n);   
    return 0;
}

// Java code to print fibonacci
// numbers till n using direct formula.
 
class GFG{
 
// Function to calculate fibonacci
// using recurrence relation formula
static void fibonacci(double n){
    double fib;
    for (double i = 0; i < n; i++)
    {
        // Using direct formula
        fib = (Math.pow((1 + Math.sqrt(5)), i) -
            Math.pow((1 - Math.sqrt(5)), i)) /
            (Math.pow(2, i) * Math.sqrt(5));
             
        System.out.print((int)fib+" ");
    }
}
 
// Driver code
public static void main(String[] args)
{
    double n = 8;
    fibonacci(n);
}
}
// This code is contributed by mits

# Python3 code to print fibonacci
# numbers till n using direct formula.
import math
 
# Function to calculate fibonacci
# using recurrence relation formula
def fibonacci(n):
 
    for i in range(n):
        # Using direct formula
        fib = ((pow((1 + math.sqrt(5)), i) -
                pow((1 - math.sqrt(5)), i)) /
               (pow(2, i) * math.sqrt(5)));
                 
        print(int(fib), end = " ");
 
# Driver code
n = 8;
fibonacci(n);
 
# This code is contributed by mits

// C#  code to print fibonacci
// numbers till n using direct formula.\
 
using System;
 
public class GFG{
     
// Function to calculate fibonacci
// using recurrence relation formula
static void fibonacci(double n){
    double fib;
    for (double i = 0; i < n; i++)
    {
        // Using direct formula
        fib = (Math.Pow((1 + Math.Sqrt(5)), i) -
            Math.Pow((1 - Math.Sqrt(5)), i)) /
            (Math.Pow(2, i) * Math.Sqrt(5));
             
        Console.Write((int)fib+" ");
    }
}
 
// Driver code
    static public void Main (){
            double n = 8;
            fibonacci(n);
}
}
// This code is contributed by ajit.

<?php
// PHP code to print fibonacci
// numbers till n using direct formula.
 
// Function to calculate fibonacci
// using recurrence relation formula
function fibonacci($n)
{
    for ($i = 0; $i < $n; $i++)
    {
        // Using direct formula
        $fib = (pow((1 + sqrt(5)), $i) -
                pow((1 - sqrt(5)), $i)) /
               (pow(2, $i) * sqrt(5));
                 
        echo $fib , " ";
    }
}
 
// Driver code
$n = 8;
fibonacci($n);
 
// This code is contributed by jit_t
?>

<script>
 
// Javascript code to print fibonacci
// numbers till n using direct formula.
 
// Function to calculate fibonacci
// using recurrence relation formula
function fibonacci(n)
{
    var fib;
    for(i = 0; i < n; i++)
    {
         
        // Using direct formula
        fib = (Math.pow((1 + Math.sqrt(5)), i) -
               Math.pow((1 - Math.sqrt(5)), i)) /
           (Math.pow(2, i) * Math.sqrt(5));
 
        document.write(parseInt(fib) + " ");
    }
}
 
// Driver code
var n = 8;
 
fibonacci(n);
 
// This code is contributed by gauravrajput1
 
</script>

0 1 1 2 3 5 8 13

Nota: el programa anterior es costoso en comparación con el método 1 , ya que genera cálculos de potencia en coma flotante. Además, es posible que no funcione perfectamente debido a errores de precisión de punto flotante.