前 n 个偶数自然数的平均值
给定一个数 n，然后求前 n 个偶数自然数的平均值 Ex。= 2+4+6+8+10+12+……+2n。 例:
Input : 7
Output : 8
(2 + 4 + 6 + 8 + 10 + 12 + 14)/7 = 8
Input : 5
Output : 6
(2 + 4 + 6 + 8 + 10)/5 = 6
天真的方法:- 在这个程序中迭代循环，找到前 N 个偶数的总和并除以 N，需要 0(N)个时间。
C++
// C++ implementation to find Average
// of sum of first n natural even numbers
#include <bits/stdc++.h>
using namespace std;
// function to find average of
// sum of first n even numbers
int avg_of_even_num(int n)
{
// sum of first n even numbers
int sum = 0;
for (int i = 1; i <= n; i++)
sum += 2*i;
// calculating Average
return sum/n;
}
// Driver Code
int main()
{
int n = 9;
cout << avg_of_even_num(n);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// java implementation to find Average
// of sum of first n natural even number
import java.io.*;
class GFG {
// function to find average of
// sum of first n even numbers
static int avg_of_even_num(int n)
{
// sum of first n even numbers
int sum = 0;
for (int i = 1; i <= n; i++)
sum += 2*i;
// calculating Average
return (sum / n);
}
public static void main (String[] args) {
int n = 9;
System.out.print(avg_of_even_num(n));
}
}
// this code is contributed by 'vt_m'
Python 3
# Python3 implementation to
# find Average of sum of
# first n natural even
# number
# Function to find average
# of sum of first n even
# numbers
def avg_of_even_num(n):
# sum of first n even
# numbers
sum=0
for i in range(1, n + 1):
sum=sum + 2 * i
# calculating Average
return sum / n
n=9
print(avg_of_even_num(n))
# This code is contributed by upendra singh bartwal
C
// C# implementation to find
// Average of sum of first
// n natural even number
using System;
class GFG {
// function to find average of
// sum of first n even numbers
static int avg_of_even_num(int n)
{
// sum of first n even numbers
int sum = 0;
for (int i = 1; i <= n; i++)
sum += 2 * i;
// calculating Average
return (sum / n);
}
// driver code
public static void Main () {
int n = 9;
Console.Write(avg_of_even_num(n));
}
}
// This code is contributed by 'vt_m'
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP implementation to find Average
// of sum of first n natural even numbers
// function to find average of
// sum of first n even numbers
function avg_of_even_num($n)
{
// sum of first n even numbers
$sum = 0;
for ($i = 1; $i <= $n; $i++)
$sum += 2 * $i;
// calculating Average
return $sum / $n;
}
// Driver Code
$n = 9;
echo(avg_of_even_num($n));
// This code is contributed by Ajit.
?>
java 描述语言
<script>
// javascript implementation to find Average
// of sum of first n natural even numbers
// function to find average of
// sum of first n even numbers
function avg_of_even_num( n)
{
// sum of first n even numbers
let sum = 0;
for (let i = 1; i <= n; i++)
sum += 2*i;
// calculating Average
return sum/n;
}
// Driver Code
let n = 9;
document.write(avg_of_even_num(n));
// This code is contributed by todaysgaurav
</script>
输出:
10
时间复杂度:O(N) 方法二:- 思路是前 N 个偶数之和为 n(n+1)，用于求前 N 个偶数除以 N 的平均值，故公式为 n(n + 1) / n = ( n + 1) 。即前 n 个偶数的平均值为 n+1 。它需要 0(1)时间。
Avg of sum of N even natural number = (N + 1)
证明T2】
Sum of first n terms of an A.P.(Arithmetic Progression)
= (n/2) * [2*a + (n-1)*d].....(i)
where, a is the first term of the series and d is
the difference between the adjacent terms of the series.
Here, a = 2, d = 2, applying these values to eq.(i), get
Sum = (n/2) * [2*2 + (n-1)*2]
= (n/2) * [4 + 2*n - 2]
= (n/2) * (2*n + 2)
= n * (n + 1)
finding the Avg so divided by n = n*(n+1)/n
= (n+1)
C++
// CPP Program to find the average
// of sum of first n even numbers
#include <bits/stdc++.h>
using namespace std;
// Return the average of sum
// of first n even numbers
int avg_of_even_num(int n)
{
return n+1;
}
// Driver Code
int main()
{
int n = 8;
cout << avg_of_even_num(n) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to find the average
// of sum of first n even numbers
import java.io.*;
class GFG
{
// Return the average of sum
// of first n even numbers
static int avg_of_even_num(int n)
{
return n + 1;
}
public static void main (String[] args) {
int n = 8;
System.out.println(avg_of_even_num(n));
}
}
// This code is contributed by vt_m
Python 3
# Python 3 Program to
# find the average
# of sum of first n
# even numbers
# Return the average of sum
# of first n even numbers
def avg_of_even_num(n) :
return n+1
# Driven Program
n = 8
print(avg_of_even_num(n))
# This code is contributed
# by Nikita Tiwari.
C
// C# Program to find the average
// of sum of first n even numbers
using System;
class GFG {
// Return the average of sum
// of first n even numbers
static int avg_of_even_num(int n)
{
return n + 1;
}
// driver code
public static void Main () {
int n = 8;
Console.Write(avg_of_even_num(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 find the average
// of sum of first n even numbers
// Return the average of sum
// of first n even numbers
function avg_of_even_num($n)
{
return $n + 1;
}
// Driver Code
$n = 8;
echo(avg_of_even_num($n));
// This code is contributed by Ajit.
?>
java 描述语言
<script>
// javascript Program to find the average
// of sum of first n even numbers
// Return the average of sum
// of first n even numbers
function avg_of_even_num(n)
{
return n + 1;
}
var n = 8;
document.write(avg_of_even_num(n));
// This code is contributed by Amit Katiyar
</script>
输出:
9
时间复杂度:O(1)
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