前 N 个自然数立方体的平均值

原文:https://www . geeksforgeeks . org/第一个 n 个自然数的立方平均数/

给定一个正整数 N ，任务是求第一个 N 自然数的立方的平均值。 例:

输入: N = 2 输出: 4.5 解释: 对于整数 N = 2， 我们有(13+23)= 1+8 = 9 平均值= 9 / 2 即 4.5 输入: N = 3 输出: 12

我们有(13+23+23+23+33+23)= 27+8+1 = 36 平均值= 36 / 3 也就是 12

天真法:天真法是求前 N 个自然数的立方之和，除以 N 。 以下是上述方法的实施:

C

// C program for the above approach
#include <stdio.h>

// Function to find average of cubes
double findAverageOfCube(int n)
{
    // Store sum of cubes of
    // numbers in the sum
    double sum = 0;

    // Calculate sum of cubes
    int i;
    for (i = 1; i <= n; i++) {
        sum += i * i * i;
    }

    // Return average
    return sum / n;
}

// Driver Code
int main()
{
    // Given number
    int n = 3;

    // Function Call
    printf("%lf", findAverageOfCube(n));
    return 0;
}

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find average of cubes
double findAverageOfCube(int n)
{
    // Storing sum of cubes
    // of numbers in sum
    double sum = 0;

    // Calculate sum of cubes
    for (int i = 1; i <= n; i++) {
        sum += i * i * i;
    }

    // Return average
    return sum / n;
}

// Driver Code
int main()
{
    // Given Number
    int n = 3;

    // Function Call
    cout << findAverageOfCube(n);
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java program for the above approach
import java.util.*;
import java.io.*;
class GFG{

// Function to find average of cubes
static double findAverageOfCube(int n)
{
    // Storing sum of cubes
    // of numbers in sum
    double sum = 0;

    // Calculate sum of cubes
    for (int i = 1; i <= n; i++)
    {
        sum += i * i * i;
    }

    // Return average
    return sum / n;
}

// Driver Code
public static void main(String[] args)
{
    // Given Number
    int n = 3;

    // Function Call
    System.out.print(findAverageOfCube(n));
}
}

// This code is contributed by shivanisinghss2110

Python 3

# Python3 program for the above approach

# Function to find average of cubes
def findAverageOfCube(n):

    # Storing sum of cubes
    # of numbers in sum
    sum = 0

    # Calculate sum of cubes
    for i in range(1, n + 1):
        sum += i * i * i

    # Return average
    return round(sum / n, 6)

# Driver Code
if __name__ == '__main__':

    # Given Number
    n = 3

    # Function Call
    print(findAverageOfCube(n))

# This code is contributed by mohit kumar 29

C

// C# program for the above approach
using System;
class GFG{

// Function to find average of cubes
static double findAverageOfCube(int n)
{
    // Storing sum of cubes
    // of numbers in sum
    double sum = 0;

    // Calculate sum of cubes
    for (int i = 1; i <= n; i++)
    {
        sum += i * i * i;
    }

    // Return average
    return sum / n;
}

// Driver Code
public static void Main()
{
    // Given Number
    int n = 3;

    // Function Call
    Console.Write(findAverageOfCube(n));
}
}

// This code is contributed by Nidhi_biet

java 描述语言

<script>
// javascript program for the above approach

// Function to find average of cubes
function findAverageOfCube( n)
{

    // Store sum of cubes of
    // numbers in the sum
    let sum = 0;

    // Calculate sum of cubes
    let i;
    for (i = 1; i <= n; i++) {
        sum += i * i * i;
    }

    // Return average
    return sum / n;
}

// Driver Code

    // Given number
    let n = 3;

    // Function Call
    document.write(findAverageOfCube(n).toFixed(6));

// This code is contributed by todaysgaurav

</script>

Output: 

12.000000

时间复杂度:O(N) T5】高效进场:

我们知道， 第一个 N 自然数的立方之和=

(\frac{N*(N+1)}{2})^{2}

的平均值由下式给出: => \frac{\text{Sum of cubes of first N natural numbers}}{N}

=> \frac{(\frac{N*(N+1)}{2})^{2}}{N}

=> \frac{N^{2}*(N+1)^{2}}{4*N}

=> \frac{N*(N+1)^{2}}{4}

因此，第一个 N 个自然数的立方和的平均值由 \frac{N*(N+1)^{2}}{4}

给出，以下是上述方法的实现:

C

// C program for the above approach
#include <stdio.h>

// Function to find average of cubes
double findAverageOfCube(int n)
{
    // Store sum of cubes of
    // numbers in the sum
    double sum = 0;

    // Calculate sum of cubes
    int i;
    for (i = 1; i <= n; i++) {
        sum += i * i * i;
    }

    // Return average
    return sum / n;
}

// Driver Code
int main()
{
    // Given number
    int n = 3;

    // Function Call
    printf("%lf", findAverageOfCube(n));

    return 0;
}

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// function to find an average of cubes
double findAverageofCube(double n)
{
    // Apply the formula n(n+1)^2/4
    int ans = (n * (n + 1) * (n + 1)) / 4;
    return ans;
}

// Driver Code
int main()
{
    // Given Number
    int n = 3;

    // Function Call
    cout << findAverageofCube(n);

    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java program for the above approach
class GFG{

// function to find an average of cubes
static double findAverageofCube(double n)
{
    // Apply the formula n(n+1)^2/4
    int ans = (int)((n * (n + 1) * (n + 1)) / 4);
    return ans;
}

// Driver Code
public static void main(String[] args)
{
    // Given Number
    int n = 3;

    // Function Call
    System.out.print(findAverageofCube(n));
}
}

// This code is contributed by shivanisinghss2110

Python 3

# Python3 program for the above approach

# Function to find average of cubes
def findAverageOfCube (n):

    # Apply the formula n*(n+1)^2/4
    ans = (n * (n + 1) * (n + 1)) / 4
    return ans

# Driver code
if __name__ == '__main__':

    # Given number
    n = 3

    # Function call
    print(findAverageOfCube(n))

# This code is contributed by himanshu77

C

// C# program for the above approach
using System;
class GFG{

// function to find an average of cubes
static double findAverageofCube(double n)
{
    // Apply the formula n(n+1)^2/4
    int ans = (int)((n * (n + 1) * (n + 1)) / 4);
    return ans;
}

// Driver Code
public static void Main()
{
    // Given Number
    int n = 3;

    // Function Call
    Console.Write(findAverageofCube(n));
}
}

// This code is contributed by Code_Mech

java 描述语言

<script>
// javascript program for the above approach
// function to find an average of cubes
function findAverageofCube(n)
{
    // Apply the formula n(n+1)^2/4
    var ans = parseInt(((n * (n + 1) * (n + 1)) / 4));
    return ans;
}

// Driver Code

// Given Number
var n = 3;

// Function Call
document.write(findAverageofCube(n));

// This code is contributed by Amit Katiyar
</script>

Output: 

12.000000

时间复杂度: O(1)

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