Average of even numbers till a given even number

Given an even number n, find the average of even numbers from 1 to n.
Examples : 

Input : 10
Output : 6
Explanation:
(2 + 4 + 6 + 8 + 10 )/5
= 30/5
= 6 
 
Input : 100
Output : 51

Method 1
We can calculate average by adding each even numbers till n and then dividing sum by count.

C++

// Program to find average of even numbers
// till a given even number.
#include <stdio.h>

// Function to calculate the average
// of even numbers
int averageEven(int n)
{
    if (n % 2 != 0) {
        printf("Invalid Input");
        return -1;
    }

    int sum = 0, count = 0;
    while (n >= 2) {

        // count even numbers
        count++;

        // store the sum of even numbers
        sum += n;

        n = n - 2;
    }
    return sum / count;
}

// driver function
int main()
{
    int n = 16;
    printf("%d", averageEven(n));
    return 0;
}

Java

// Program to find average of even numbers
// till a given even number.
import java.io.*;

class GFG {

    // Function to calculate the average
    // of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        System.out.println("Invalid Input");
            return -1;
        }

        int sum = 0, count = 0;
        while (n >= 2) {

         // count even numbers
         count++;

         // store the sum of even numbers
         sum += n;

         n = n - 2;
        }
        return sum / count;
    }

    // driver function
    public static void main(String args[])
    {
        int n = 16;
        System.out.println(averageEven(n));
    }
}

/*This code is contributed by Nikita Tiwari.*/

Python3

# Program to find average of
# even numbers till a given
# even number.

# Function to calculate the
# average of even numbers
def averageEven(n) :

    if (n % 2 != 0) :
        print("Invalid Input")
        return -1

    sm = 0
    count = 0

    while (n >= 2) :

        # count even numbers
        count = count + 1

        # store the sum of even
        # numbers
        sm = sm + n

        n = n - 2

    return sm // count

# driver function
n = 16
print(averageEven(n))

# This code is contributed by Nikita Tiwari.

C#

// C# Program to find average
// of even numbers till a
// given even number.
using System;

class GFG {

    // Function to calculate the
    // average of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        Console.Write("Invalid Input");
            return -1;
        }

        int sum = 0, count = 0;
        while (n >= 2) {

        // count even numbers
        count++;

        // store the sum of even numbers
        sum += n;

        n = n - 2;
        }
        return sum / count;
    }

    // driver function
    public static void Main()
    {
        int n = 16;
        Console.Write(averageEven(n));
    }
}

/*This code is contributed by vt_m.*/

PHP

<?php
// PHP Program to find average of even
// numbers till a given even number.

// Function to calculate the
// average of even numbers
function averageEven( $n)
{
    if ($n % 2 != 0)
    {
        echo("Invalid Input");
        return -1;
    }

    $sum = 0;
    $count = 0;
    while ($n >= 2)
    {

        // count even numbers
        $count++;

        // store the sum of
        // even numbers
        $sum += $n;

        $n = $n - 2;
    }
    return $sum / $count;
}

    // Driver Code
    $n = 16;
    echo(averageEven($n));

//This code is contributed by vt_m.
?>

Javascript

<script>

// javascript Program to find average of even numbers
// till a given even number.


// Function to calculate the average
// of even numbers
function averageEven( n)
{
    if (n % 2 != 0) {
        document.write("Invalid Input");
        return -1;
    }

    let sum = 0, count = 0;
    while (n >= 2) {

        // count even numbers
        count++;

        // store the sum of even numbers
        sum += n;

        n = n - 2;
    }
    return sum / count;
}

// driver function
let n = 16;
    document.write( averageEven(n));

// This code is contributed by todaysgaurav


</script>

Output: 

9

Time Complexity: O(n)

Auxiliary Space: O(1)
Method 2
The average of even numbers can be find out only in single steps 
by using the following formula :- 
[n + 2 ] / 2 where n is last even number.
How does this formula work?
We know there are (n)/2 even numbers till n. For example there are two even number till 4 and there are three even numbers till 6.
Sum of first k even numbers is k * (k + 1)
Putting k = n/2, we get sum of first n/2 even numbers as n/2(n/2 + 1)
Average of first n/2 even numbers (or even numbers till n) = (n + 2)/2

C++

// Program to find average of even numbers
// till a given even nend number.
#include <bits/stdc++.h>
using namespace std;

// Function to calculate the average
// of even numbers
int averageEven(int n)
{
    if (n % 2 != 0) {
        cout<<"Invalid Input";
        return -1;
    }

    return (n + 2) / 2;
}

// driver function
int main()
{
    int n = 16;
    cout<<averageEven(n)<<endl;
    return 0;
}

// This code is contributed by noob2000.

C

// Program to find average of even numbers
// till a given even number.
#include <stdio.h>

// Function to calculate the average
// of even numbers
int averageEven(int n)
{
    if (n % 2 != 0) {
        printf("Invalid Input");
        return -1;
    }

    return (n + 2) / 2;
}

// driver function
int main()
{
    int n = 16;
    printf("%d", averageEven(n));
    return 0;
}

Java

// Program to find average of even numbers
// till a given even number.
import java.io.*;

class GFG {

    // Function to calculate the average
    // of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        System.out.println("Invalid Input");
            return -1;
        }

        return (n + 2) / 2;
    }

    // driver function
    public static void main(String args[])
    {
        int n = 16;
        System.out.println(averageEven(n));
    }
}

/*This code is contributed by Nikita Tiwari.*/

Python3

# Python3 program to find average of even
# numbers till a given even number.

# Function to calculate the
# average of even numbers
def averageEven(n) :
    if (n % 2 != 0) :
        print("Invalid Input")
        return -1

    return (n + 2) // 2

# Driver function
n = 16
print(averageEven(n))

# This code is contributed by Nikita Tiwari.

C#

// C# Program to find average
// of even numbers till a
// given even number.
using System;

class GFG {

    // Function to calculate the
    // average of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        Console.Write("Invalid Input");
            return -1;
        }

        return (n + 2) / 2;
    }

    // driver function
    public static void Main()
    {
        int n = 16;
        Console.Write(averageEven(n));
    }
}

/*This code is contributed by vt_m.*/

PHP

<?php
// PHP Program to find average of even
// numbers till a given even number.

// Function to calculate the average
// of even numbers
function averageEven( $n)
{
    if ($n % 2 != 0)
    {
        echo("Invalid Input");
        return -1;
    }

    return ($n + 2) / 2;
}

    // Driver Code
    $n = 16;
    echo (averageEven($n));
    return 0;

// This code is contributed by vt_m.
?>

Javascript

<script>
// javascript Program to find average of even numbers
// till a given even number.

// Function to calculate the average
// of even numbers
function averageEven( n)
{
    if (n % 2 != 0)
    {
        document.write("Invalid Input");
        return -1;
    }
    return (n + 2) / 2;
}

// driver function
    let n = 16;
     document.write(averageEven(n));

// This code is contributed by Rajput-Ji

</script>

Output : 

9

Time complexity: O(1) since performing constant operations

Space Complexity: O(1) since using constant variables