Longest subsequence of even numbers in an Array

Given an array arr[] containing N integers, the task is to print the length of the longest subsequence of even numbers in the array.

Examples:

Input: arr[] = {3, 4, 11, 2, 9, 21} 
Output: 2 
Explanation:
The longest subsequence containing even numbers is {4, 2}. 
Hence, the answer is 2.

Input: arr[] = {6, 4, 10, 13, 9, 25} 
Output: 3 
The longest subsequence containing even numbers is {6, 4, 10}. 
Hence, the answer is 3.  

Approach: One observation that needs to be made from the array is that the longest subsequence containing only an even number will be the total count of all the even numbers. Therefore, the following steps are followed to compute the answer:  

• Traverse through the given array element by element.
• If the element is an even number, then increase the length of the resulting subsequence.
• When the traversal is completed, the required length of the longest subsequence containing only even numbers is stored in the counter.

Below is the implementation of the above approach:  

C++

// C++ program to find the length of the
// longest subsequence which contains
// all even numbers

#include <bits/stdc++.h>
using namespace std;
#define N 100000

// Function to find the length of the
// longest subsequence
// which contain all even numbers
int longestEvenSubsequence(int arr[], int n)
{
    // Counter to store the
    // length of the subsequence
    int answer = 0;

    // Iterating through the array
    for (int i = 0; i < n; i++) {

        // Checking if the element is
        // even or not
        if (arr[i] % 2 == 0) {

            // If it is even, then
            // increment the counter
            answer++;
        }
    }

    return answer;
}

// Driver code
int main()
{
    int arr[] = { 3, 4, 11, 2, 9, 21 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << longestEvenSubsequence(arr, n)
         << endl;

    return 0;
}

Java

// Java program to find the length of the
// longest subsequence which contains
// all even numbers
import java.util.*;
class GFG{

// Function to find the length of the
// longest subsequence
// which contain all even numbers
static int longestEvenSubsequence(int arr[], int n)
{
    // Counter to store the
    // length of the subsequence
    int answer = 0;

    // Iterating through the array
    for (int i = 0; i < n; i++)
    {

        // Checking if the element is
        // even or not
        if (arr[i] % 2 == 0)
        {

            // If it is even, then
            // increment the counter
            answer++;
        }
    }
    return answer;
}

// Driver code
public static void main(String args[])
{
    int []arr = { 3, 4, 11, 2, 9, 21 };
    int n = arr.length;

    System.out.print(longestEvenSubsequence(arr, n));
}
}

// This code is contributed by Akanksha_Rai

Python3

# Python3 program to find the length
# of the longest subsequence which
# contains all even numbers

N = 100000

# Function to find the length
# of the longest subsequence
# which contain all even numbers
def longestEvenSubsequence(arr, n):

    # Counter to store the
    # length of the subsequence
    answer = 0

    # Iterating through the array
    for i in range(n):

        # Checking if the element
        # is even or not
        if (arr[i] % 2 == 0):

            # If it is even, then
            # increment the counter
            answer += 1

    return answer

# Driver code
if __name__ == "__main__":

    arr = [ 3, 4, 11, 2, 9, 21 ]
    n = len(arr)

    print(longestEvenSubsequence(arr, n))

# This code is contributed by chitranayal

C#

// C# program to find the length of the
// longest subsequence which contains
// all even numbers
using System;
class GFG{

// Function to find the length of the
// longest subsequence
// which contain all even numbers
static int longestEvenSubsequence(int []arr, int n)
{
    // Counter to store the
    // length of the subsequence
    int answer = 0;

    // Iterating through the array
    for (int i = 0; i < n; i++)
    {

        // Checking if the element is
        // even or not
        if (arr[i] % 2 == 0)
        {

            // If it is even, then
            // increment the counter
            answer++;
        }
    }
    return answer;
}

// Driver code
public static void Main()
{
    int []arr = { 3, 4, 11, 2, 9, 21 };
    int n = arr.Length;

    Console.WriteLine(longestEvenSubsequence(arr, n));
}
}

// This code is contributed by Nidhi_Biet

Javascript

<script>
// Javascript program to find the length of the
// longest subsequence which contains
// all even numbers

let N = 100000;

// Function to find the length of the
// longest subsequence
// which contain all even numbers
function longestEvenSubsequence(arr, n) {
    // Counter to store the
    // length of the subsequence
    let answer = 0;

    // Iterating through the array
    for (let i = 0; i < n; i++) {

        // Checking if the element is
        // even or not
        if (arr[i] % 2 == 0) {

            // If it is even, then
            // increment the counter
            answer++;
        }
    }

    return answer;
}

// Driver code
let arr = [3, 4, 11, 2, 9, 21];
let n = arr.length;

document.write(longestEvenSubsequence(arr, n) + "<br>");

// This code is contributed by _saurabh_jaiswal
</script>

Output:

2

Time Complexity: O(N), where N is the length of the array. 
Auxiliary Space: O(1)