Find Harmonic mean using Arithmetic mean and Geometric mean (original) (raw)

Last Updated : 17 Feb, 2023

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 GM^2 = AM * HM

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

JavaScript

`

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.