Given a positive integer N, the task is to find the average of the fourth powers of the first N natural numbers.
Examples:
Input: N = 3
Output: 32.6667
Explanation:
The sum of the fourth powers of the first N natural numbers = 14 + 24 + 34 = 1 + 16 + 81 = 98.
Therefore, the average = 98 / 3 = 32.6667.Input: N = 5
Output: 12
Naive Approach: The simplest approach to solve the given problem is to find the sum of the fourth powers of first N natural numbers and print its value when divided by N.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the average of the // fourth power of first N natural numbers double findAverage( int N)
{ // Stores the sum of the fourth
// powers of first N natural numbers
double S = 0;
// Calculate the sum of fourth power
for ( int i = 1; i <= N; i++) {
S += i * i * i * i;
}
// Return the average
return S / N;
} // Driver Code int main()
{ int N = 3;
cout << findAverage(N);
return 0;
} |
// Java program for the above approach class GFG{
// Function to find the average of the // fourth power of first N natural numbers static double findAverage( int N)
{ // Stores the sum of the fourth
// powers of first N natural numbers
double S = 0 ;
// Calculate the sum of fourth power
for ( int i = 1 ; i <= N; i++)
{
S += i * i * i * i;
}
// Return the average
return S / N;
} // Driver code public static void main(String[] args)
{ int N = 3 ;
System.out.println(findAverage(N));
} } // This code is contributed by abhinavjain194 |
# Python3 program for the above approach # Function to find the average of the # fourth power of first N natural numbers def findAverage(N):
# Stores the sum of the fourth
# powers of first N natural numbers
S = 0
# Calculate the sum of fourth power
for i in range ( 1 , N + 1 ):
S + = i * i * i * i
# Return the average
return round (S / N, 4 )
# Driver Code if __name__ = = '__main__' :
N = 3
print (findAverage(N))
# This code is contributed by mohit kumar 29 |
// C# program for the above approach using System;
class GFG{
// Function to find the average of the // fourth power of first N natural numbers static double findAverage( int N)
{ // Stores the sum of the fourth
// powers of first N natural numbers
double S = 0;
// Calculate the sum of fourth power
for ( int i = 1; i <= N; i++)
{
S += i * i * i * i;
}
// Return the average
return S / N;
} // Driver Code public static void Main()
{ int N = 3;
Console.WriteLine(findAverage(N));
} } // This code is contriobuted by sanjoy_62 |
<script> // javascript program for the above approach // Function to find the average of the // fourth power of first N natural numbers function findAverage(N)
{ // Stores the sum of the fourth
// powers of first N natural numbers
var S = 0;
var i;
// Calculate the sum of fourth power
for (i = 1; i <= N; i++) {
S += i * i * i * i;
}
// Return the average
return S / N;
} // Driver Code var N = 3;
document.write(findAverage(N));
</script> |
Output:
32.6667
Time Complexity: O(N)
Auxiliary Space: O(1)
Efficient Approach: The above approach can also be optimized by finding the sum of the fourth powers of the first N natural numbers by the mathematical formula given below and then print its value when divided by N.
The mathematical formula is as follows:
=>
=>
=>
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the average of the // fourth power of first N natural numbers double findAverage( int N)
{ // Store the resultant average
// calculated using formula
double avg = ((6 * N * N * N * N)
+ (15 * N * N * N)
+ (10 * N * N) - 1)
/ 30.0;
// Return the average
return avg;
} // Driver Code int main()
{ int N = 3;
cout << findAverage(N);
return 0;
} |
// Java program for the above approach import java.util.*;
class GFG{
// Function to find the average of the // fourth power of first N natural numbers static double findAverage( int N)
{ // Store the resultant average
// calculated using formula
double avg = (( 6 * N * N * N * N) +
( 15 * N * N * N) +
( 10 * N * N) - 1 ) / 30.0 ;
// Return the average
return avg;
} // Driver Code public static void main(String args[])
{ int N = 3 ;
System.out.print(findAverage(N));
} } // This code is contributed by shivanisinghss2110 |
# Python program for the above approach # Function to find the average of the # fourth power of first N natural numbers def findAverage(N):
# Store the resultant average
# calculated using formula
avg = (( 6 * N * N * N * N) + ( 15 * N * N * N) + ( 10 * N * N) - 1 ) / 30
# Return the average
return avg
N = 3
print ( round (findAverage(N), 4 ))
# This code is contributed by avanitrachhadiya2155 |
// C# program for the above approach using System;
class GFG{
// Function to find the average of the // fourth power of first N natural numbers static double findAverage( int N)
{ // Store the resultant average
// calculated using formula
double avg = ((6 * N * N * N * N) +
(15 * N * N * N) +
(10 * N * N) - 1) / 30.0;
// Return the average
return avg;
} // Driver Code public static void Main()
{ int N = 3;
Console.WriteLine(findAverage(N));
} } // This code is contributed by ukasp |
<script> // JavaScript program for the above approach
// Function to find the average of the // fourth power of first N natural numbers function findAverage( N)
{ // Store the resultant average
// calculated using formula
let avg = ((6 * N * N * N * N)
+ (15 * N * N * N)
+ (10 * N * N) - 1)
/ 30.0;
// Return the average
return avg;
} // Driver Code let N = 3;
document.write( findAverage(N).toFixed(4));
// This code is contributed by G.Sravan Kumar (171FA07058) </script> |
Output:
32.6667
Time Complexity: O(1)
Auxiliary Space: O(1)