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++
// 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 numbersdouble 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 Codeint main(){ int N = 3; cout << findAverage(N); return 0;} |
Java
// Java program for the above approachclass GFG{// Function to find the average of the// fourth power of first N natural numbersstatic 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 codepublic static void main(String[] args){ int N = 3; System.out.println(findAverage(N));}}// This code is contributed by abhinavjain194 |
Python3
# Python3 program for the above approach# Function to find the average of the# fourth power of first N natural numbersdef 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 Codeif __name__ == '__main__': N = 3 print(findAverage(N))# This code is contributed by mohit kumar 29 |
C#
// C# program for the above approachusing System;class GFG{// Function to find the average of the// fourth power of first N natural numbersstatic 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 Codepublic static void Main(){ int N = 3; Console.WriteLine(findAverage(N));}}// This code is contriobuted by sanjoy_62 |
Javascript
<script>// javascript program for the above approach// Function to find the average of the// fourth power of first N natural numbersfunction 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++
// 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 numbersdouble 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 Codeint main(){ int N = 3; cout << findAverage(N); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{ // Function to find the average of the// fourth power of first N natural numbersstatic 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 Codepublic static void main(String args[]){ int N = 3; System.out.print(findAverage(N));}}// This code is contributed by shivanisinghss2110 |
Python3
# Python program for the above approach# Function to find the average of the# fourth power of first N natural numbersdef 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 avgN = 3print(round(findAverage(N),4)) # This code is contributed by avanitrachhadiya2155 |
C#
// C# program for the above approachusing System;class GFG{ // Function to find the average of the// fourth power of first N natural numbersstatic 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 Codepublic static void Main(){ int N = 3; Console.WriteLine(findAverage(N));}}// This code is contributed by ukasp |
Javascript
<script> // JavaScript program for the above approach// Function to find the average of the// fourth power of first N natural numbersfunction 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)
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