Encuentre la media armónica usando la media aritmética y la media geométrica

Dados dos números, primero calcule la media aritmética y la media geométrica de estos dos números. Usando la media aritmética y la media geométrica así calculadas, encuentre la media armónica entre los dos números.

Ejemplos: 

Input : a = 2
        b = 4
Output : 2.666

Input : a = 5
        b = 15
Output : 7.500

Media aritmética: La media aritmética ‘AM’ entre dos números ayb es un número tal que AM-a = b-AM. Así, si nos dan estos dos números, la media aritmética AM = 1/2(a+b)
Media geométrica: La media geométrica ‘GM’ entre dos números ayb es un número tal que GM/a = b/GM. Así, si nos dan estos dos números, la media geométrica GM = sqrt(a*b)
Media armónica: La media armónica ‘HM’ entre dos números a y b es un número tal que 1/HM – 1/a = 1/ b – 1/HM. Entonces, si nos dan estos dos números, la media armónica HM = 2ab/a+b
Ahora, también sabemos que 

// C++ implementation of computation  of
// arithmetic mean, geometric mean
// and harmonic mean
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate arithmetic
// mean, geometric mean and harmonic mean
double compute(int a, int b)
{
 
    double AM, GM, HM;
 
    AM = (a + b) / 2;
    GM = sqrt(a * b);
    HM = (GM * GM) / AM;
    return HM;
}
 
// Driver function
int main()
{
 
    int a = 5, b = 15;
    double HM = compute(a, b);
    cout << "Harmonic Mean between " << a
          << " and " << b << " is " << HM ;
    return 0;
}

// Java implementation of computation  of
// arithmetic mean, geometric mean
// and harmonic mean
import java.io.*;
 
class GeeksforGeeks {
     
    // Function to calculate arithmetic
    // mean, geometric mean and harmonic mean
    static double compute(int a, int b)
    {
 
        double AM, GM, HM;
 
        AM = (a + b) / 2;
        GM = Math.sqrt(a * b);
        HM = (GM * GM) / AM;
        return HM;
    }
     
    // Driver function
    public static void main(String args[])
    {
        int a = 5, b = 15;
        double HM = compute(a, b);
        String str = "";
        str = str + HM;
        System.out.print("Harmonic Mean between " 
                         + a + " and " + b + " is " 
                         + str.substring(0, 5));
    }
}

# Python 3 implementation of computation
# of arithmetic mean, geometric mean
# and harmonic mean
 
import math
 
# Function to calculate arithmetic
# mean, geometric mean and harmonic mean
def compute( a, b) :
    AM = (a + b) / 2
    GM = math.sqrt(a * b)
    HM = (GM * GM) / AM
    return HM
 
# Driver function
a = 5
b = 15
HM = compute(a, b)
print("Harmonic Mean between " , a,
      " and ", b , " is " , HM )
 
 
# This code is contributed by Nikita Tiwari.

// C# implementation of computation  of
// arithmetic mean, geometric mean
// and harmonic mean
using System;
 
class GeeksforGeeks {
     
    // Function to calculate arithmetic
    // mean, geometric mean and harmonic mean
    static double compute(int a, int b)
    {
 
        double AM, GM, HM;
 
        AM = (a + b) / 2;
        GM = Math.Sqrt(a * b);
        HM = (GM * GM) / AM;
        return HM;
    }
     
    // Driver function
    public static void Main()
    {
        int a = 5, b = 15;
        double HM = compute(a, b);
        Console.WriteLine("Harmonic Mean between "
                        + a + " and " + b + " is "
                        +HM);
    }
}
// This code is contributed by mits

<?php
// PHP implementation of computation  of
// arithmetic mean, geometric mean
// and harmonic mean
 
// Function to calculate arithmetic
// mean, geometric mean and harmonic mean
function compute( $a, $b)
{
 
    $AM;
    $GM;
    $HM;
 
    $AM = ($a + $b) / 2;
    $GM = sqrt($a * $b);
    $HM = ($GM * $GM) / $AM;
    return $HM;
}
 
// Driver Code
    $a = 5;
    $b = 15;
    $HM = compute($a, $b);
    echo"Harmonic Mean between " .$a.
        " and " .$b. " is " .$HM ;
    return 0;
// This code is contributed by nitin mittal.
?>

<script>
  
// Javascript implementation of computation
// of arithmetic mean, geometric mean
// and harmonic mean
  
// Function to calculate arithmetic
// mean, geometric mean and harmonic mean
function compute(a, b)
{
    var AM = (a + b) / 2;
    var GM = Math.sqrt(a * b);
    var HM = (GM * GM) / AM;
     
    return HM;
}
 
// Driver Code
var a = 5;
var b = 15;
var HM = compute(a, b)
 
document.write("Harmonic Mean between " +
               a + " and " +  b  + " is " +
               HM.toFixed(3));
                
// This code is contributed by bunnyram19
 
</script>

Producción: 

Harmonic Mean between 5 and 15 is 7.500

Complejidad de tiempo: O (log (a * b)), para usar la función sqrt donde a y b representan los números enteros dados.
Espacio auxiliar: O(1), no se requiere espacio adicional, por lo que es una constante.