前 N 个自然数的四次方的平均值
给定一个正整数N ,任务是求前N个自然数的四次方的平均值。
例子:
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
朴素方法:解决给定问题的最简单方法是找到前 N 个自然数的四次方之和,并在除以N时打印其值。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
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
C++
// C++ program for the above approach
#include
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
输出:
32.6667
时间复杂度: O(N)
辅助空间: O(1)
有效方法:上述方法也可以通过以下给出的数学公式找到前N个自然数的四次方之和,然后在除以N时打印其值来优化。
数学公式如下:
=>
=>
=>
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
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
输出:
32.6667
时间复杂度: O(1)
辅助空间: O(1)