Count of subarrays of size K with average at least M

Given an array arr[] consisting of N integers and two positive integers K and M, the task is to find the number of subarrays of size K whose average is at least M.

Examples:

Input: arr[] = {2, 3, 3, 4, 4, 4, 5, 6, 6}, K = 3, M = 4
Output: 4
Explanation:
Below are the subarrays of size K(= 3) whose average is at least M(= 4) as:

1. arr[3, 5]: The average is 4 which is at least M(= 4).
2. arr[4, 6]: The average is 4.33 which is at least M(= 4).
3. arr[5, 7]: The average is 5 which is at least M(= 4).
4. arr[6, 8]: The average is 5.66 which is at least M(= 4).

Therefore, the count of the subarray is given by 4.

Input: arr[] = {3, 6, 3, 2, 1, 3, 9] K = 2, M = 4
Output: 3

Approach: The given problem can be solved by using the Two Pointers and Sliding Window Technique. Follow the steps below to solve the given problem:

• Initialize a variable, say count as 0 that stores the count of all possible subarrays.
• Initialize a variable, say sum as 0 that stores the sum of elements of the subarray of size K.
• Find the sum of the first K array elements and store it in the variable sum. If the value of sum is at least M*K, then increment the value of count by 1.
• Traverse the given array arr[] over the range [K, N - 1] using the variable i and perform the following steps:
  • Add the value of arr[i] to the variable sum and subtract the value of arr[i - K] from the sum.
  • If the value of sum is at least M*K, then increment the value of count by 1.
• After completing the above steps, print the value of count as the resultant count of subarrays.

Below is the implementation of the above approach:

// C++ program for the above approach

#include <iostream>
using namespace std;

// Function to count the subarrays of
// size K having average at least M
int countSubArrays(int arr[], int N,
                   int K, int M)
{
    // Stores the resultant count of
    // subarray
    int count = 0;

    // Stores the sum of subarrays of
    // size K
    int sum = 0;

    // Add the values of first K elements
    // to the sum
    for (int i = 0; i < K; i++) {
        sum += arr[i];
    }

    // Increment the count if the
    // current subarray is valid
    if (sum >= K * M)
        count++;

    // Traverse the given array
    for (int i = K; i < N; i++) {

        // Find the updated sum
        sum += (arr[i] - arr[i - K]);

        // Check if current subarray
        // is valid or not
        if (sum >= K * M)
            count++;
    }

    // Return the count of subarrays
    return count;
}

// Driver Code
int main()
{
    int arr[] = { 3, 6, 3, 2, 1, 3, 9 };
    int K = 2, M = 4;
    int N = sizeof(arr) / sizeof(arr[0]);

    cout << countSubArrays(arr, N, K, M);

    return 0;
}

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

class GFG 
{
  
    // Driver Code
    public static void main(String[] args)
    {
        int[] arr = { 3, 6, 3, 2, 1, 3, 9 };
        int K = 2, M = 4;
        System.out.println(countSubArrays(arr, K, M));
    }
  
    // Function to count the subarrays of
    // size K having average at least M
    public static int countSubArrays(int[] arr, int K,
                                     int M)
    {
      
        // Stores the resultant count of
        // subarray
        int count = 0;

        // Stores the sum of subarrays of
        // size K
        int sum = 0;

        // Add the values of first K elements
        // to the sum
        for (int i = 0; i < K; i++) {
            sum += arr[i];
        }

        // Increment the count if the
        // current subarray is valid
        if (sum >= K * M)
            count++;

        // Traverse the given array
        for (int i = K; i < arr.length; i++) {

            // Find the updated sum
            sum += (arr[i] - arr[i - K]);

            // Check if current subarray
            // is valid or not
            if (sum >= K * M)
                count++;
        }

        // Return the count of subarrays
        return count;
    }
}

// This code is contributed by Kdheeraj.

# Python 3 code for the above approach

# Function to count the subarrays of
# size K having average at least M
def countSubArrays(arr, N, K, M):
  
    # Stores the resultant count of
    # subarray
    count = 0

    # Stores the sum of subarrays of
    # size K
    sum = 0

    # Add the values of first K elements
    # to the sum
    for i in range(K):
        sum += arr[i]

    # Increment the count if the
    # current subarray is valid
    if sum >= K*M:
        count += 1

    # Traverse the given array
    for i in range(K, N):

        # Find the updated sum
        sum += (arr[i] - arr[i - K])

        # Check if current subarray
        # is valid or not
        if sum >= K*M:
            count += 1

    # Return the count of subarrays
    return count

# Driver Code
if __name__ == '__main__':
    arr = [3, 6, 3, 2, 1, 3, 9]
    K = 2
    M = 4
    N = len(arr)
    count = countSubArrays(arr, N, K, M)
    print(count)

    # This code is contributed by Kdheeraj.

// C# program for the above approach

using System;

public class GFG 
{
  
    // Driver Code
    public static void Main(String[] args)
    {
        int[] arr = { 3, 6, 3, 2, 1, 3, 9 };
        int K = 2, M = 4;
        Console.WriteLine(countSubArrays(arr, K, M));
    }
  
    // Function to count the subarrays of
    // size K having average at least M
    public static int countSubArrays(int[] arr, int K,
                                     int M)
    {
      
        // Stores the resultant count of
        // subarray
        int count = 0;

        // Stores the sum of subarrays of
        // size K
        int sum = 0;

        // Add the values of first K elements
        // to the sum
        for (int i = 0; i < K; i++) {
            sum += arr[i];
        }

        // Increment the count if the
        // current subarray is valid
        if (sum >= K * M)
            count++;

        // Traverse the given array
        for (int i = K; i < arr.Length; i++) {

            // Find the updated sum
            sum += (arr[i] - arr[i - K]);

            // Check if current subarray
            // is valid or not
            if (sum >= K * M)
                count++;
        }

        // Return the count of subarrays
        return count;
    }
}

// This code is contributed by AnkThon

 <script>
        // JavaScript Program to implement
        // the above approach

        // Function to count the subarrays of
        // size K having average at least M
        function countSubArrays(arr, N,
            K, M) 
        {
            // Stores the resultant count of
            // subarray
            let count = 0;

            // Stores the sum of subarrays of
            // size K
            let sum = 0;

            // Add the values of first K elements
            // to the sum
            for (let i = 0; i < K; i++) {
                sum += arr[i];
            }

            // Increment the count if the
            // current subarray is valid
            if (sum >= K * M)
                count++;

            // Traverse the given array
            for (let i = K; i < N; i++) {

                // Find the updated sum
                sum += (arr[i] - arr[i - K]);

                // Check if current subarray
                // is valid or not
                if (sum >= K * M)
                    count++;
            }

            // Return the count of subarrays
            return count;
        }

        // Driver Code
        let arr = [3, 6, 3, 2, 1, 3, 9];
        let K = 2, M = 4;
        let N = arr.length;

        document.write(countSubArrays(arr, N, K, M));

     // This code is contributed by Potta Lokesh

    </script>

3

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

kdheeraj

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Article Tags :

• Mathematical
• DSA
• Arrays
• subarray
• sliding-window
• two-pointer-algorithm
• subarray-sum

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Practice Tags :

• Arrays
• Mathematical
• sliding-window
• two-pointer-algorithm