Dado un entero positivo N , la tarea es encontrar el promedio de las cuartas potencias de los primeros N números naturales .
Ejemplos:
Entrada: N = 3
Salida: 32,6667
Explicación:
La suma de las cuartas potencias de los primeros N números naturales = 1 4 + 2 4 + 3 4 = 1 + 16 + 81 = 98.
Por tanto, la media = 98 / 3 = 32,6667 .Entrada: N = 5
Salida: 12
Enfoque ingenuo: el enfoque más simple para resolver el problema dado es encontrar la suma de las cuartas potencias de los primeros N números naturales e imprimir su valor cuando se divide por N.
A continuación se muestra la implementación del enfoque anterior:
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 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
// 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
# 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#
// 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
Javascript
<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>
Producción:
32.6667
Complejidad temporal: O(N)
Espacio auxiliar: O(1)
Enfoque eficiente: el enfoque anterior también se puede optimizar al encontrar la suma de las cuartas potencias de los primeros N números naturales mediante la fórmula matemática que se proporciona a continuación y luego imprimir su valor cuando se divide por N .
La fórmula matemática es la siguiente:
=>
=>
=>
A continuación se muestra la implementación del enfoque anterior:
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 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
// 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
Python3
# 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#
// 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
Javascript
<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>
Producción:
32.6667
Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)