自然数平方的平均值
原文:https://www . geesforgeks . org/average-squares-natural-numbers/
给定一个数 n，求自然数平方的平均值直到 n 例:
Input : n = 2
Output :2.5
12 + 22 = 2.5
Input : n = 3
Output : 4.666667
12 + 22 + 32 = 4.666667
天真的方法: 天真的方法是运行一个从 1 到 n 的循环，并找出所有平方的平均值。
C
// C program to calculate 1^2+2^2+3^2+... average
// of square number
#include <stdio.h>
// Function to calculate average of square number
float AvgofSquareN(int n)
{
float sum = 0;
for (int i = 1; i <= n; i++)
sum += (i * i);
return sum/n;
}
// Driver code
int main()
{
int n = 2;
printf("%f", AvgofSquareN(n));
return 0;
}
C++
// C++ program to calculate 1^2+2^2+3^2+...
// average of square number
#include<bits/stdc++.h>
using namespace std;
// Function to calculate average of squares
float AvgofSquareN(int n)
{
float sum = 0;
for (int i = 1; i <= n; i++)
sum += (i * i);
return sum/n;
}
// Driver code
int main()
{
int n = 2;
cout << AvgofSquareN(n) ;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to calculate 1^2+2^2+3^2+
// ... average of square number
import java.io.*;
public class GFG{
// Function to calculate average
// of square number
static float AvgofSquareN(int n)
{
float sum = 0;
for (int i = 1; i <= n; i++)
sum += (i * i);
return sum / n;
}
// Driver code
static public void main (String[] args)
{
int n = 2;
System.out.println(AvgofSquareN(n));
}
}
// This code is contributed by vt_m.
Python 3
# Python program to
# calculate 1^2+2^2+3^2+...
# average of square number
# Function to calculate
# average of square number
def AvgofSquareN(n) :
sum = 0
for i in range(1, n + 1) :
sum += (i * i)
return sum/n
# Driver code
n = 2
print (AvgofSquareN(n))
# This code is contributed by
# Manish Shaw(manishshaw1)
C
// C# program to calculate 1^2+2^2+3^2+
// ... average of square number
using System;
public class GFG{
// Function to calculate average
// of square number
static float AvgofSquareN(int n)
{
float sum = 0;
for (int i = 1; i <= n; i++)
sum += (i * i);
return sum / n;
}
// Driver code
static public void Main (String []args)
{
int n = 2;
Console.WriteLine(AvgofSquareN(n));
}
}
// This code is contributed by vt_m.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to calculate 1^2+2^2+3^2+...
// average of square number
// Function to calculate average
// of square number
function AvgofSquareN( $n)
{
$sum = 0;
for ($i = 1; $i <= $n; $i++)
$sum += ($i * $i);
return $sum/$n;
}
// Driver code
$n = 2;
echo(AvgofSquareN($n));
// This code is contributed by vt_m.
?>
java 描述语言
<script>
// javascript program to calculate 1^2+2^2+3^2+... average
// of square number
// Function to calculate average of square number
function AvgofSquareN( n)
{
let sum = 0;
for (let i = 1; i <= n; i++)
sum += (i * i);
return sum/n;
}
// Driver code
let n = 2;
document.write(AvgofSquareN(n).toFixed(6));
// This code is contributed by todaysgaurav
</script>
输出:
2.500000
时间复杂度: O(n) 空间复杂度: O(1) 高效逼近: 自然数平方和 (n + 1)(2n + 1) / 6 。因此平均值为 n(n + 1)(2n + 1) / 6 * n = (n + 1)(2n + 1) / 6。
C
// C program to get the Average of Square
// of first n natural numbers
#include <stdio.h>
float AvgofSquareN(int n)
{
return (float)((n + 1) * (2 * n + 1)) / 6;
}
// Driver Code
int main()
{
int n = 10;
printf("%f", AvgofSquareN(n));
return 0;
}
C++
// C++ program to get the Average of Square
// of first n natural numbers
#include<bits/stdc++.h>
using namespace std;
float AvgofSquareN(int n)
{
return (float)((n + 1) * (2 * n + 1)) / 6;
}
// Driver Code
int main()
{
int n = 10;
cout << AvgofSquareN(n) ;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to get the Average of
// square of first n natural numbers
import java.io.*;
public class GFG{
// Function to get the average
static float AvgofSquareN(int n)
{
return (float)((n + 1) * (2 *
n + 1)) / 6;
}
// Driver Code
static public void main (String[] args)
{
int n = 2;
System.out.println(AvgofSquareN(n));
}
}
// This code is contributed by vt_m.
Python 3
# PHP program to get the Average of
# Square of first n natural numbers
def AvgofSquareN(n) :
return ((n + 1) * (2 * n + 1)) / 6;
# Driver Code
n = 2;
print (AvgofSquareN(n));
# This code is contributed by Manish Shaw
# (manishshaw1)
C
// C# program to get the Average of
// squareof first n natural numbers
using System;
public class GFG{
// Function to calculate average
static float AvgofSquareN(int n)
{
return (float)((n + 1) * (2 *
n + 1)) / 6;
}
// Driver Code
static public void Main (String []args)
{
int n = 2;
Console.WriteLine(AvgofSquareN(n));
}
}
// This code is contributed by vt_m.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to get the Average of
// Square of first n natural numbers
function AvgofSquareN( $n)
{
return (($n + 1) * (2 * $n + 1)) / 6;
}
// Driver Code
$n = 2;
echo(AvgofSquareN($n));
// This code is contributed by vt_m.
?>
java 描述语言
<script>
// javascript program to get the Average of
// square of first n natural numberspublic
// Function to get the average
function AvgofSquareN(n)
{
return ((n + 1) * (2 *
n + 1)) / 6;
}
// Driver Code
var n = 2;
document.write(AvgofSquareN(n));
// This code is contributed by Amit Katiyar
</script>
2.500000
时间复杂度: O(1) 空间复杂度: O(1)
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