Maximum even numbers present in any subarray of size K

Given an array arr[] of size N and an integer K, the task is to find the maximum number of even numbers present in any subarray of size K.

Examples:

Input: arr[] = {2, 3, 5, 4, 7, 6}, K = 3 
Output: 2 
Explanation:
Subarrays of size K(=3) with maximum count of even numbers are { arr[3], arr[4], arr[5] } 
Therefore, the required output is 2

Input: arr[] = {4, 3, 2, 6}, K = 2 
Output: 2

Naive Approach: The simplest approach to solve this problem is to generate all possible subarrays of size K and count the even numbers in the subarray. Finally, print the maximum count obtained.

Below is the implementation of the above approach:

C++

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

// Function to find the maximum count of
// even numbers from all the subarrays of
// size K
int maxEvenIntegers(int arr[], int N, int M)
{

    // Stores the maximum count of even numbers
    // from all the subarrays of size K
    int ans = 0;

    // Generate all subarrays of size K
    for (int i = 0; i <= N - M; i++) {

        // Store count of even numbers
        // in current subarray of size K
        int cnt = 0;

        // Traverse the current subarray
        for (int j = 0; j < M; j++) {

            // If current element
            // is an even number
            if (arr[i + j] % 2 == 0)
                cnt++;
        }

        // Update the answer
        ans = max(ans, cnt);
    }

    // Return answer
    return ans;
}

// Driver Code
int main()
{

    int arr[] = { 2, 3, 5, 4, 7, 6 };
    int K = 3;

    // Size of the input array
    int N = sizeof(arr) / sizeof(arr[0]);

    cout << maxEvenIntegers(arr, N, K) << endl;

    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;
class GFG
{

// Function to find the maximum count of
// even numbers from all the subarrays of
// size K
static int maxEvenIntegers(int arr[], int N, int M)
{

    // Stores the maximum count of even numbers
    // from all the subarrays of size K
    int ans = 0;

    // Generate all subarrays of size K
    for (int i = 0; i <= N - M; i++)
    {

        // Store count of even numbers
        // in current subarray of size K
        int cnt = 0;

        // Traverse the current subarray
        for (int j = 0; j < M; j++)
        {

            // If current element
            // is an even number
            if (arr[i + j] % 2 == 0)
                cnt++;
        }

        // Update the answer
        ans = Math.max(ans, cnt);
    }

    // Return answer
    return ans;
}

// Driver Code
public static void main(String[] args)
{
    int arr[] = { 2, 3, 5, 4, 7, 6 };
    int K = 3;

    // Size of the input array
    int N = arr.length;
    System.out.print(maxEvenIntegers(arr, N, K) +"\n");

}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement
# the above approach

# Function to find the maximum count of
# even numbers from all the subarrays of
# size K
def maxEvenIntegers(arr, N, K):

    # Stores the maximum count of even numbers
    # from all the subarrays of size K
    ans = 0
    # Generate all subarrays of size K
    for i in range(N-K+1):
        # Store count of even numbers
        # in current subarray of size K
        cnt = 0

        # Traverse the current subarray
        for j in range(0, K):
            if arr[i+j] % 2 == 0:
                cnt += 1
        # Update the answer
        ans = max(cnt, ans)
    # Return answer
    return ans


# Driver Code
if __name__ == '__main__':
    arr = [2, 3, 5, 4, 7, 6]
    K = 3
    # Size of the input array
    N = len(arr)
    print(maxEvenIntegers(arr, N, K))

# This code is contributed by MuskanKalra1

C#

// C# program to implement
// the above approach
using System;

class GFG
{

    // Function to find the maximum count of
    // even numbers from all the subarrays of
    // size K
    static int maxEvenIntegers(int []arr, int N, int M)
    {

        // Stores the maximum count of even numbers
        // from all the subarrays of size K
        int ans = 0;

        // Generate all subarrays of size K
        for (int i = 0; i <= N - M; i++)
        {

            // Store count of even numbers
            // in current subarray of size K
            int cnt = 0;

            // Traverse the current subarray
            for (int j = 0; j < M; j++)
            {

                // If current element
                // is an even number
                if (arr[i + j] % 2 == 0)
                    cnt++;
            }

            // Update the answer
            ans = Math.Max(ans, cnt);
        }

        // Return answer
        return ans;
    }

    // Driver Code
    public static void Main(string[] args)
    {
        int []arr = { 2, 3, 5, 4, 7, 6 };
        int K = 3;

        // Size of the input array
        int N = arr.Length;
        Console.WriteLine(maxEvenIntegers(arr, N, K));
    }
}

// This code is contributed by AnkThon

Javascript

<script>
// Java script program to implement
// the above approach


// Function to find the maximum count of
// even numbers from all the subarrays of
// size K
function maxEvenIntegers(arr,  N,  M)
{

    // Stores the maximum count of even numbers
    // from all the subarrays of size K
    let ans = 0;

    // Generate all subarrays of size K
    for (let i = 0; i <= N - M; i++)
    {

        // Store count of even numbers
        // in current subarray of size K
        let cnt = 0;

        // Traverse the current subarray
        for (let j = 0; j < M; j++)
        {

            // If current element
            // is an even number
            if (arr[i + j] % 2 == 0)
                cnt++;
        }

        // Update the answer
        ans = Math.max(ans, cnt);
    }

    // Return answer
    return ans;
}

// Driver Code

    let arr = [ 2, 3, 5, 4, 7, 6 ];
    let K = 3;

    // Size of the input array
    let N = arr.length;
    document.write(maxEvenIntegers(arr, N, K) +"<br>");

//contributed by bobby

</script>

Output:

2

Time Complexity: O(N * K)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized using the Sliding window technique. Follow the steps below to solve the problems:

• Initialize a variable, say cntMaxEven, to store the maximum count of even numbers in a subarray of size K.
• Calculate the count of even numbers in the subarray { arr[0], … arr[K – 1] } and store it into cntMaxEven.
• Traverse the remaining subarrays of size K by iterating over the range [K, N – 1]. For every i^th iteration remove the first element of the subarray and insert the current i^th element of the array into the current subarray.
• Count the even numbers in the current subarray and update cntMaxEven to the maximum count of even numbers in the current subarray and cntMaxEven.
• Finally, print the value of cntMaxEven.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

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

// Function to find the maximum count of
// even numbers from all the subarrays of
// size K
int maxEvenIntegers(int arr[], int N, int M)
{

    // Stores the count of even numbers
    // in a subarray of size K
    int curr = 0;

    // Calculate the count of even numbers
    // in the current subarray
    for (int i = 0; i < M; i++) {

        // If current element is
        // an even number
        if (arr[i] % 2 == 0)
            curr++;
    }

    // Stores the maximum count of even numbers
    // from all the subarrays of size K
    int ans = curr;

    // Traverse remaining subarrays of size K
    // using sliding window technique
    for (int i = M; i < N; i++) {

        // If the first element of
        // the subarray is even
        if (arr[i - M] % 2 == 0) {

            // Update curr
            curr--;
        }

        // If i-th element is even increment
        // the count
        if (arr[i] % 2 == 0)
            curr++;

        // Update the answer
        ans = max(ans, curr);
    }

    // Return answer
    return ans;
}

// Driver Code
int main()
{
    int arr[] = { 2, 3, 5, 4, 7, 6 };
    int M = 3;

    // Size of the input array
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    cout << maxEvenIntegers(arr, N, M) << endl;

    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;

class GFG
{

  // Function to find the maximum count of
  // even numbers from all the subarrays of
  // size K
  static int maxEvenIntegers(int arr[], int N, int M)
  {

    // Stores the count of even numbers
    // in a subarray of size K
    int curr = 0;

    // Calculate the count of even numbers
    // in the current subarray
    for (int i = 0; i < M; i++)
    {

      // If current element is
      // an even number
      if (arr[i] % 2 == 0)
        curr++;
    }

    // Stores the maximum count of even numbers
    // from all the subarrays of size K
    int ans = curr;

    // Traverse remaining subarrays of size K
    // using sliding window technique
    for (int i = M; i < N; i++)
    {

      // If the first element of
      // the subarray is even
      if (arr[i - M] % 2 == 0)
      {

        // Update curr
        curr--;
      }

      // If i-th element is even increment
      // the count
      if (arr[i] % 2 == 0)
        curr++;

      // Update the answer
      ans = Math.max(ans, curr);
    }

    // Return answer
    return ans;
  }

  // Driver Code
  public static void main(String[] args)
  {
    int arr[] = { 2, 3, 5, 4, 7, 6 };
    int M = 3;

    // Size of the input array
    int N = arr.length;

    // Function call
    System.out.print(maxEvenIntegers(arr, N, M) +"\n");

  }
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement
# the above approach

# Function to find the maximum count of
# even numbers from all the subarrays of
# size M
def maxEvenIntegers(arr, N, M):

    # Stores the count of even numbers
    # in a subarray of size M
    curr = 0

    # Calculate the count of even numbers
    # in the current subarray
    for i in range(0, M):

        # If current element is
        # an even number
        if(arr[i] % 2 == 0):
            curr += 1

    # Stores the maximum count of even numbers
    # from all the subarrays of size M
    ans = curr

    # Traverse remaining subarrays of size M
    # using sliding window technique
    for i in range(M, N):

        # If the first element of
        # the subarray is even
        if(arr[i - M] % 2 == 0):

            # update curr
            curr -= 1

        # If i-th element is even increment
        # the count
        if(arr[i] % 2 == 0):
            curr += 1

            # update the answer
            ans = max(curr, ans)

    # Return answer
    return ans

# Driver Code
if __name__ == '__main__':
    arr = [2, 3, 5, 4, 7, 6]
    M = 3

    # Size of the input array
    N = len(arr)

    # Function call
    print(maxEvenIntegers(arr, N, M))

# This code is contributed by MuskanKalra1

C#

// C# program to implement
// the above approach
using System;

class GFG
{

  // Function to find the maximum count of
  // even numbers from all the subarrays of
  // size K
  static int maxEvenints(int []arr, int N, int M)
  {

    // Stores the count of even numbers
    // in a subarray of size K
    int curr = 0;

    // Calculate the count of even numbers
    // in the current subarray
    for (int i = 0; i < M; i++)
    {

      // If current element is
      // an even number
      if (arr[i] % 2 == 0)
        curr++;
    }

    // Stores the maximum count of even numbers
    // from all the subarrays of size K
    int ans = curr;

    // Traverse remaining subarrays of size K
    // using sliding window technique
    for (int i = M; i < N; i++)
    {

      // If the first element of
      // the subarray is even
      if (arr[i - M] % 2 == 0)
      {

        // Update curr
        curr--;
      }

      // If i-th element is even increment
      // the count
      if (arr[i] % 2 == 0)
        curr++;

      // Update the answer
      ans = Math.Max(ans, curr);
    }

    // Return answer
    return ans;
  }

  // Driver Code
  public static void Main(String[] args)
  {
    int []arr = { 2, 3, 5, 4, 7, 6 };
    int M = 3;

    // Size of the input array
    int N = arr.Length;

    // Function call
    Console.Write(maxEvenints(arr, N, M) +"\n");
  }
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// Javascript program to implement
// the above approach

  // Function to find the maximum count of
  // even numbers from all the subarrays of
  // size K
  function maxEvenLetegers(arr, N, M)
  {

    // Stores the count of even numbers
    // in a subarray of size K
    let curr = 0;

    // Calculate the count of even numbers
    // in the current subarray
    for (let i = 0; i < M; i++)
    {

      // If current element is
      // an even number
      if (arr[i] % 2 == 0)
        curr++;
    }

    // Stores the maximum count of even numbers
    // from all the subarrays of size K
    let ans = curr;

    // Traverse remaining subarrays of size K
    // using sliding window technique
    for (let i = M; i < N; i++)
    {

      // If the first element of
      // the subarray is even
      if (arr[i - M] % 2 == 0)
      {

        // Update curr
        curr--;
      }

      // If i-th element is even increment
      // the count
      if (arr[i] % 2 == 0)
        curr++;

      // Update the answer
      ans = Math.max(ans, curr);
    }

    // Return answer
    return ans;
  }

// Driver Code

    let arr = [ 2, 3, 5, 4, 7, 6 ];
    let M = 3;

    // Size of the input array
    let N = arr.length;

    // Function call
    document.write(maxEvenLetegers(arr, N, M) +"\n");

     // This code is contributed by souravghosh0416.
</script>

Output:

2

Time Complexity: O(N)

Auxiliary Space: O(1)