Given an array of elements, find harmonic mean of numbers.
Examples:
Input : arr[] = {2.0, 1.0} Output : 1.3333 Harmonic mean = 2/(1/2.0 + 1/1.0) = (2 * 2)/3 = 1.333 Input : arr[] = {13.5, 14.5, 14.8, 15.2, 16.1} Output : 14.7707
Harmonic mean is used when average of rates is required, below is the formula.
Harmonic mean of n numbers x1, x2,
x3, . . ., xn can written as below.
Harmonic mean = n / ((1/x1) + (1/x2) + (1/x3) + . . . + (1/xn))
Below is the implementation of Harmonic Mean.
// CPP program to find harmonic mean of numbers. #include <bits/stdc++.h> using namespace std;
// Function that returns harmonic mean. float harmonicMean( float arr[], int n)
{ // Declare sum variables and initialize with zero.
float sum = 0;
for ( int i = 0; i < n; i++)
sum = sum + ( float )1 / arr[i];
return ( float )n / sum;
} // Driver code int main()
{ float arr[] = { 13.5, 14.5, 14.8, 15.2, 16.1 };
int n = sizeof (arr) / sizeof (arr[0]);
cout << harmonicMean(arr, n);
return 0;
} // This code is contributed by Aditya Kumar (adityakumar129) |
// C program to find harmonic mean of numbers. #include <stdio.h> // Function that returns harmonic mean. float harmonicMean( float arr[], int n)
{ // Declare sum variables and initialize with zero.
float sum = 0;
for ( int i = 0; i < n; i++)
sum = sum + ( float )1 / arr[i];
return ( float )n / sum;
} // Driver code int main()
{ float arr[] = { 13.5, 14.5, 14.8, 15.2, 16.1 };
int n = sizeof (arr) / sizeof (arr[0]);
printf ( "%f" ,harmonicMean(arr, n));
return 0;
} // This code is contributed by Aditya Kumar (adityakumar129) |
// JAVA program to find harmonic mean of numbers. import java.io.*;
class GFG {
// Function that returns harmonic mean.
static float harmonicMean( float arr[], int n)
{
// Declare sum variables and initialize with zero
float sum = 0 ;
for ( int i = 0 ; i < n; i++)
sum = sum + ( float ) 1 / arr[i];
return ( float )n / sum;
}
// Driver code
public static void main(String args[])
{
float arr[] = { 13 .5f, 14 .5f, 14 .8f, 15 .2f, 16 .1f };
int n = arr.length;
System.out.println(harmonicMean(arr, n));
}
} // This code is contributed by Aditya Kumar (adityakumar129) |
# Python 3 program to find harmonic # mean of numbers. # Function that returns harmonic mean. def harmonicMean(arr, n) :
# Declare sum variables and
# initialize with zero.
sm = 0
for i in range ( 0 , n) :
sm = sm + ( 1 ) / arr[i];
return n / sm
# Driver code arr = [ 13.5 , 14.5 , 14.8 , 15.2 , 16.1 ];
n = len (arr)
print (harmonicMean(arr, n))
# This code is contributed by Nikita Tiwari. |
// C# program to find harmonic // mean of numbers. using System;
class GFG {
// Function that returns harmonic mean.
static float harmonicMean( float [] arr, int n)
{
// Declare sum variables and
// initialize with zero
float sum = 0;
for ( int i = 0; i < n; i++)
sum = sum + ( float )1 / arr[i];
return ( float )n / sum;
}
// Driver code
public static void Main()
{
float [] arr = { 13.5f, 14.5f, 14.8f,
15.2f, 16.1f };
int n = arr.Length;
Console.WriteLine(harmonicMean(arr, n));
}
} /*This code is contributed by vt_m.*/ |
<?php // PHP program to find // harmonic mean of numbers. // Function that returns // harmonic mean. function harmonicMean( $arr , $n )
{ // Declare sum variables and
// initialize with zero
$sum = 0;
for ( $i = 0; $i < $n ; $i ++)
$sum = $sum + (float)
(1 / $arr [ $i ]);
return (float)( $n / $sum );
} // Driver code $arr = array (13.5, 14.5, 14.8, 15.2, 16.1);
$n = sizeof( $arr );
echo (harmonicMean( $arr , $n ));
// This code is contributed by Ajit. ?> |
<script> // Javascript program to find harmonic mean of numbers. // Function that returns harmonic mean. function harmonicMean(arr, n)
{ // Declare sum variables and initialize
// with zero.
let sum = 0;
for (let i = 0; i < n; i++)
sum = sum + (1 / arr[i]);
return n/sum;
} // Driver code let arr = [ 13.5, 14.5, 14.8, 15.2, 16.1 ]; let n = arr.length; document.write(harmonicMean(arr, n)); </script> |
Output:
14.7707
Time Complexity: O(n)
Auxiliary Space: O(1), since no extra space has been taken.
What if we are given elements and their frequencies?
If we are given n numbers and every number has some frequency then simply we use formula
Harmonic mean = (Frequency-Sum) /((f1/x1) + (f2/x2) + (f3/x3) + . . . + (fn/xn))
Where f1, f2, f3, . . ., fn are the frequencies of elements and x1, 2, x3, . . ., xn are the elements of array.
Frequency-Sum = f1 + f2 + f3, . . ., fn
Examples:
Input : num[] = {13, 14, 15, 16, 17} freq[] = {2, 5, 13, 7, 3} Output : 15.0631
// C++ program to find harmonic mean. #include <bits/stdc++.h> using namespace std;
// Function that returns harmonic mean. float harmonicMean( int arr[], int freq[], int n)
{ float sum = 0, frequency_sum = 0;
for ( int i = 0; i < n; i++) {
sum = sum + ( float )freq[i] / arr[i];
frequency_sum = frequency_sum + freq[i];
}
return frequency_sum / sum;
} // Driver code int main()
{ int num[] = { 13, 14, 15, 16, 17 };
int freq[] = { 2, 5, 13, 7, 3 };
int n = sizeof (num) / sizeof (num[0]);
cout << harmonicMean(num, freq, n);
return 0;
} |
// JAVA program to find harmonic mean. class GFG {
// Function that returns harmonic mean.
static float harmonicMean( int arr[], int freq[],
int n)
{
float sum = 0 , frequency_sum = 0 ;
for ( int i = 0 ; i < n; i++) {
sum = sum + ( float )freq[i] / arr[i];
frequency_sum = frequency_sum + freq[i];
}
return (frequency_sum / sum);
}
// Driver code
public static void main(String args[])
{
int num[] = { 13 , 14 , 15 , 16 , 17 };
int freq[] = { 2 , 5 , 13 , 7 , 3 };
int n = num.length;
System.out.println(harmonicMean(num, freq, n));
}
} /*This code is contributed by Nikita Tiwari.*/ |
// C# program to find harmonic mean. using System;
class GFG {
// Function that returns harmonic mean.
static float harmonicMean( int [] arr, int [] freq,
int n)
{
float sum = 0, frequency_sum = 0;
for ( int i = 0; i < n; i++) {
sum = sum + ( float )freq[i] / arr[i];
frequency_sum = frequency_sum + freq[i];
}
return (frequency_sum / sum);
}
// Driver code
public static void Main()
{
int [] num = { 13, 14, 15, 16, 17 };
int [] freq = { 2, 5, 13, 7, 3 };
int n = num.Length;
Console.WriteLine(harmonicMean(num, freq, n));
}
} /*This code is contributed by vt_m.*/ |
<?php // PHP program to find // harmonic mean. // Function that returns // harmonic mean. function harmonicMean( $arr , $freq , $n )
{ $sum = 0; $frequency_sum = 0;
for ( $i = 0; $i < $n ; $i ++)
{
$sum = $sum + (float)
( $freq [ $i ] / $arr [ $i ]);
$frequency_sum = $frequency_sum +
$freq [ $i ];
}
return ( $frequency_sum / $sum );
} // Driver code $num = array (13, 14, 15, 16, 17);
$freq = array (2, 5, 13, 7, 3);
$n = sizeof( $num );
echo (harmonicMean( $num , $freq , $n ));
// This code is contributed by Ajit. ?> |
<script> // Javascript program to find harmonic mean. // Function that returns harmonic mean. function harmonicMean(arr, freq, n)
{ let sum = 0, frequency_sum = 0;
for (let i = 0; i < n; i++) {
sum = sum + (freq[i] / arr[i]);
frequency_sum = frequency_sum + freq[i];
}
return frequency_sum / sum;
} // Driver code let num = [ 13, 14, 15, 16, 17 ]; let freq = [ 2, 5, 13, 7, 3 ]; let n = num.length; document.write(harmonicMean(num, freq, n)); </script> |
Output:
15.0631
Time Complexity: O(n)
Auxiliary Space: O(1)
Harmonic mean of numbers using harmonic_mean() in Python:
Simple Python program to find harmonic mean using harmonic_mean() function.
#'harmonic_mean()' new function added in 'Python3.6' onwards. #Program calculates Harmonic Mean using harmonic_mean() #imports Python statistics library import statistics
def harmonic_mean():
list = [ 13.5 , 14.5 , 14.8 , 15.2 , 16.1 ]
print (statistics.harmonic_mean( list ))
#Driver code harmonic_mean() #This code is contributed by 'Abhishek Agrawal'. |
Output: 14.770680729373778
Time Complexity: O(n)
Auxiliary Space: O(1)