Find Harmonic mean using Arithmetic mean and Geometric mean

Given two numbers, first calculate arithmetic mean and geometric mean of these two numbers. Using the arithmetic mean and geometric mean so calculated, find the harmonic mean between the two numbers.

Examples: 

Input : a = 2
        b = 4
Output : 2.666

Input : a = 5
        b = 15
Output : 7.500

Arithmetic Mean: Arithmetic Mean ‘AM’ between two numbers a and b is such a number that AM-a = b-AM. Thus, if we are given these two numbers, the arithmetic mean AM = 1/2(a+b)
Geometric Mean: Geometric Mean ‘GM’ between two numbers a and b is such a number that GM/a = b/GM. Thus, if we are given these two numbers, the geometric mean GM = sqrt(a*b)
Harmonic Mean: Harmonic Mean ‘HM’ between two numbers a and b is such a number that 1/HM – 1/a = 1/b – 1/HM. Thus, if we are given these two numbers, the harmonic mean HM = 2ab/a+b
Now, we also know that 

C++

// 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

// 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));
    }
}

Python3

# 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#

// 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
// 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.
?>

Javascript

<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>

Output:

Harmonic Mean between 5 and 15 is 7.500

Time Complexity: O(log(a*b)), for using sqrt function where a and b represents the given integers. 
Auxiliary Space: O(1), no extra space is required, so it is a constant.