Given an array of n elements, we need to find the geometric mean of the numbers. Generally geometric mean of n numbers is the nth root of their product.
If there are n elements x1, x2, x3, . . ., xn
in an array and if we want to calculate the
geometric mean of the array elements is
Geometric mean = (x1 * x2 * x3 * . . . * xn)1/n
Examples:
Input : arr[] = {1, 2, 3, 4, 5, 6, 7, 8}
Output : 3.76435
= (1 * 2 * 3 * 4 * 5 * 6 * 7 * 8)1/8
= 403201/8
= 3.76435
Input : arr[] = {15, 12, 13, 19, 10}
Output : 13.447
= (15 * 12 * 13 * 19 * 10)1/5
= 4446001/5
= 13.477
A simple solution is to multiply all numbers first, then find (1/n)-th power of the multiplication.
// Program to calculate the geometric mean
// of the given array elements.
#include <bits/stdc++.h>
using namespace std;
// function to calculate geometric mean
// and return float value.
float geometricMean(int arr[], int n)
{
// declare product variable and
// initialize it to 1.
float product = 1;
// Compute the product of all the
// elements in the array.
for (int i = 0; i < n; i++)
product = product * arr[i];
// compute geometric mean through formula
// pow(product, 1/n) and return the value
// to main function.
float gm = pow(product, (float)1 / n);
return gm;
}
// Driver function
int main()
{
int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << geometricMean(arr, n);
return 0;
}
// Program to calculate the geometric mean
// of the given array elements.
import java.math.*;
class GFG{
// function to calculate geometric mean
// and return float value.
static float geometricMean(int arr[], int n)
{
// declare product variable and
// initialize it to 1.
float product = 1;
// Compute the product of all the
// elements in the array.
for (int i = 0; i < n; i++)
product = product * arr[i];
// compute geometric mean through
// formula pow(product, 1/n) and
// return the value to main function.
float gm = (float)Math.pow(product, (float)1 / n);
return gm;
}
// Driver function
public static void main(String args[])
{
int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
int n = arr.length ;
System.out.println(geometricMean(arr, n));
}
}
/*This code is contributed by Nikita Tiwari*/
# Python Program to calculate the
# geometric mean of the given
# array elements.
import math
# function to calculate geometric
# mean and return float value.
def geometricMean(arr, n) :
# declare product variable and
# initialize it to 1.
product = 1
# Compute the product of all the
# elements in the array.
for i in range(0,n) :
product = product * arr[i]
# compute geometric mean through
# formula pow(product, 1/n) and
# return the value to main function.
gm = (float)(math.pow(product, (1 / n)))
return (float)(gm)
# Driver function
arr = [ 1, 2, 3, 4, 5, 6, 7, 8]
n = len(arr)
# to print 6 digits after decimal
print ('{0:.6f}'.format(geometricMean(arr, n)))
# This code is contributed by Nikita Tiwari
// Program to calculate the geometric mean
// of the given array elements.
using System;
class GFG{
// function to calculate geometric mean
// and return float value.
static float geometricMean(int []arr, int n)
{
// declare product variable and
// initialize it to 1.
float product = 1;
// Compute the product of all the
// elements in the array.
for (int i = 0; i < n; i++)
product = product * arr[i];
// compute geometric mean through
// formula pow(product, 1/n) and
// return the value to main function.
float gm = (float)Math.Pow(product, (float)1 / n);
return gm;
}
// Driver function
public static void Main()
{
int []arr = { 1, 2, 3, 4, 5, 6, 7, 8 };
int n = arr.Length ;
Console.WriteLine(geometricMean(arr, n));
}
}
/*This code is contributed by vt_m*/
<script>
// Javascript program to calculate the geometric mean
// of the given array elements.
// function to calculate geometric mean
// and return float value.
function geometricMean(arr, n)
{
// declare product variable and
// initialize it to 1.
let product = 1;
// Compute the product of all the
// elements in the array.
for (let i = 0; i < n; i++)
product = product * arr[i];
// compute geometric mean through
// formula pow(product, 1/n) and
// return the value to main function.
let gm = Math.pow(product, 1 / n);
return gm;
}
// driver function
let arr = [ 1, 2, 3, 4, 5, 6, 7, 8 ];
let n = arr.length ;
document.write(geometricMean(arr, n));
// This code is contributed by code_hunt.
</script>
<?php
// Program to calculate the geometric mean
// of the given array elements.
// function to calculate geometric mean
// and return float value.
function geometricMean($arr, $n)
{
// declare product variable and
// initialize it to 1.
$product = 1;
// Compute the product of all the
// elements in the array.
for ($i = 0; $i < $n; $i++)
$product = $product * $arr[$i];
// compute geometric mean through formula
// pow(product, 1/n) and return the value
// to main function.
$gm = pow($product, (float)(1 / $n));
return $gm;
}
// Driver Code
$arr = array(1, 2, 3, 4, 5, 6, 7, 8);
$n = sizeof($arr);
echo(geometricMean($arr, $n));
// This code is contributed by Ajit.
?>
Output:
3.76435
Time Complexity: O(n) where n is size of given array
Auxiliary Space: O(1)
The above solution simply causes overflow. A better solution is to use log. There are n numbers and we need to calculate geometric mean using the formula :
Geometric mean = Antilog((log(x1) + log(x2) +
log(x3) + . . . + log(xn))/n)
For calculating the Antilog in programming we use exponent function (exp()).
// Program to calculate the geometric mean
// of the given array elements.
#include <bits/stdc++.h>
using namespace std;
// function to calculate geometric mean
// and return float value.
float geometricMean(int arr[], int n)
{
// declare sum variable and
// initialize it to 1.
float sum = 0;
// Compute the sum of all the
// elements in the array.
for (int i = 0; i < n; i++)
sum = sum + log(arr[i]);
// compute geometric mean through formula
// antilog(((log(1) + log(2) + . . . + log(n))/n)
// and return the value to main function.
sum = sum / n;
return exp(sum);
}
// Driver function
int main()
{
int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
int n = sizeof(arr) / sizeof(arr[0]);
// function call
cout << geometricMean(arr, n);
return 0;
}
// Java Program to calculate the geometric mean
// of the given array elements.
import java.io.*;
class GFG
{
// function to calculate geometric mean
// and return float value.
static float geometricMean(int []arr, int n)
{
// declare sum variable and
// initialize it to 1.
float sum = 0;
// Compute the sum of all the
// elements in the array.
for (int i = 0; i < n; i++)
sum = sum + (float)Math.log(arr[i]);
// compute geometric mean through formula
// antilog(((log(1) + log(2) + . . . + log(n))/n)
// and return the value to main function.
sum = sum / n;
return (float)Math.exp(sum);
}
// Driver function
public static void main (String[] args)
{
int []arr = { 1, 2, 3, 4, 5, 6, 7, 8 };
int n = arr.length;
// function call
System.out.println(geometricMean(arr, n));
}
}
// This code is contributed by vt_m.
# Program to calculate the
# geometric mean of the
# given array elements.
import math
# function to calculate
# geometric mean and
# return float value.
def geometricMean(arr, n):
# declare sum variable and
# initialize it to 1.
sum = 0;
# Compute the sum of all
# the elements in the array.
for i in range(n):
sum = sum + math.log(arr[i]);
# compute geometric mean
# through formula antilog
# (((log(1) + log(2) + . .
# ... + log(n))/n)
# and return the value to
# main function.
sum = sum / n;
return math.exp(sum);
# Driver Code
arr= [ 1, 2, 3, 4, 5, 6, 7, 8 ];
n = len(arr);
# function call
print(geometricMean(arr, n));
# This code is contributed by mits.
// Program to calculate the geometric mean
// of the given array elements.
using System;
class GFG {
// function to calculate geometric mean
// and return float value.
static float geometricMean(int []arr, int n)
{
// declare sum variable and
// initialize it to 1.
float sum = 0;
// Compute the sum of all the
// elements in the array.
for (int i = 0; i < n; i++)
sum = sum + (float)Math.Log(arr[i]);
// compute geometric mean through formula
// antilog(((log(1) + log(2) + . . . + log(n))/n)
// and return the value to main function.
sum = sum / n;
return (float)Math.Exp(sum);
}
// Driver function
public static void Main ()
{
int []arr = { 1, 2, 3, 4, 5, 6, 7, 8 };
int n = arr.Length;
// function call
Console.WriteLine(geometricMean(arr, n));
}
}
// This code is contributed by vt_m.
<script>
// Program to calculate the geometric mean
// of the given array elements.
// function to calculate geometric mean
// and return float value.
function geometricMean(arr, n)
{
// declare sum variable and
// initialize it to 1.
var sum = 0;
// Compute the sum of all the
// elements in the array.
for (var i = 0; i < n; i++)
sum = sum + Math.log(arr[i]);
// compute geometric mean through formula
// antilog(((log(1) + log(2) + . . . + log(n))/n)
// and return the value to main function.
sum = sum / n;
return Math.exp(sum);
}
// Driver function
var arr = [ 1, 2, 3, 4, 5, 6, 7, 8 ];
var n = arr.length;
// function call
document.write(geometricMean(arr, n).toFixed(5));
// This code is contributed by bunnyram19.
</script>
<?php
// Program to calculate the geometric mean
// of the given array elements.
// function to calculate geometric mean
// and return float value.
function geometricMean($arr, $n)
{
// declare sum variable and
// initialize it to 1.
$sum = 0;
// Compute the sum of all the
// elements in the array.
for($i = 0; $i < $n; $i++)
$sum = $sum + log($arr[$i]);
// compute geometric mean
// through formula
// antilog(((log(1) + log(2) +
// . . . + log(n))/n)
// and return the value
$sum = $sum / $n;
return exp($sum);
}
// Driver Code
$arr = array(1, 2, 3, 4, 5, 6, 7, 8);
$n = count($arr);
// function call
echo geometricMean($arr, $n);
// This code is contributed by anuj_67.
?>
Output:
3.76435
Time Complexity: O(n)
Auxiliary Space: O(1)
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