Maximum average of a subarray of size of atleast X and atmost Y

Given an array arr[] and two integers X and Y. The task is to find a sub-array of size of atleast X and atmost Y with the maximum average (average of the elements of the sub-array).

Examples:

Input: arr[] = {1, 2, 3, 4, 5} X = 2, Y = 3
Output: 4.5
We can take the sub-array {4, 5} which gives us the maximum average.



Input: arr[] = {6, 7, 8, 3, 2, 4, 2} X = 2, Y = 4
Output: 7.5

Approach: Iterate over every sub-array of size starting from X to size Y and find the maximum average among all such sub-arrays. We can use two nested for loops to iterate over all sub-arrays whose size varies from X to Y. To reduce the time complexity, we can use prefix sum array to get the sum of any sub-array in O(1) complexity.

Below is the implementation of the above approach:

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the maximum average
// of the sub-array with size
// atleast x and atmost y
double maxAvgSubArray(int a[], int n, int x, int y)
{
  
    // Calculate the prefix sum array
    int prefix[n];
    prefix[0] = a[0];
    for (int i = 1; i < n; i++)
        prefix[i] = prefix[i - 1] + a[i];
  
    double maximum = 0;
  
    // Iterate over all sub-arrays
    for (int i = 0; i < n; i++) {
  
        // Sub-arrays of size X to Y
        for (int j = i + x - 1; j < i + y && j < n; j++) {
  
            // Get the sum of the sub-array
            double sum = prefix[j];
            if (i > 0)
                sum -= prefix[i - 1];
  
            // Find average of sub-array
            double current = sum / (double)(j - i + 1);
  
            // Store the maximum of average
            maximum = max(maximum, current);
        }
    }
  
    return maximum;
}
  
// Driver code
int main()
{
    int a[] = { 6, 7, 8, 3, 2, 4, 2 };
    int X = 2, Y = 4;
    int n = sizeof(a) / sizeof(a[0]);
    cout << maxAvgSubArray(a, n, X, Y);
  
    return 0;
}
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation of the approach
class GfG {
  
    // Function to return the maximum average
    // of the sub-array with size
    // atleast x and atmost y
    static double maxAvgSubArray(int a[], int n, int x, int y)
    {
  
        // Calculate the prefix sum array
        int prefix[] = new int[n];
        prefix[0] = a[0];
        for (int i = 1; i < n; i++)
            prefix[i] = prefix[i - 1] + a[i];
  
        double maximum = 0;
  
        // Iterate over all sub-arrays
        for (int i = 0; i < n; i++) {
  
            // Sub-arrays of size X to Y
            for (int j = i + x - 1; j < i + y && j < n; j++) {
  
                // Get the sum of the sub-array
                double sum = prefix[j];
                if (i > 0)
                    sum -= prefix[i - 1];
  
                // Find average of sub-array
                double current = sum / (double)(j - i + 1);
  
                // Store the maximum of average
                maximum = Math.max(maximum, current);
            }
        }
  
        return maximum;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int a[] = { 6, 7, 8, 3, 2, 4, 2 };
        int X = 2, Y = 4;
        int n = a.length;
        System.out.println(maxAvgSubArray(a, n, X, Y));
    }
}
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 implementation of the approach 
  
# Function to return the maximum average 
# of the sub-array with size 
# atleast x and atmost y 
def maxAvgSubArray(a, n, x, y) : 
  
    # Calculate the prefix sum array 
    prefix = [0] * n ;
    prefix[0] = a[0];
    for i in range(1, n) :
        prefix[i] = prefix[i - 1] + a[i];
          
    maximum = 0;
      
    # Iterate over all sub-arrays
    for i in range(n) :
        j = i + x - 1
          
        # Sub-arrays of size X to Y
        while(j < i + y and j < n) :
              
            # Get the sum of the sub-array
            sum = prefix[j];
              
            if (i > 0) :
                sum -= prefix[i - 1];
              
            # Find average of sub-array 
            current = sum / (j - i + 1);
          
            # Store the maximum of average
            maximum = max(maximum, current);
              
            j += 1
    return maximum; 
  
# Driver code 
if __name__ == "__main__"
  
    a = [ 6, 7, 8, 3, 2, 4, 2 ];
    X = 2; Y = 4;
      
    n = len(a);
    print(maxAvgSubArray(a, n, X, Y)); 
  
# This code is contributed by Ryuga
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation of the approach 
using System;
  
class GFG
{
  
    // Function to return the maximum 
    // average of the sub-array with 
    // size atleast x and atmost y 
    public static double maxAvgSubArray(int[] a, int n, 
                                        int x, int y)
    {
  
        // Calculate the prefix sum array 
        int[] prefix = new int[n];
        prefix[0] = a[0];
        for (int i = 1; i < n; i++)
        {
            prefix[i] = prefix[i - 1] + a[i];
        }
  
        double maximum = 0;
  
        // Iterate over all sub-arrays 
        for (int i = 0; i < n; i++)
        {
  
            // Sub-arrays of size X to Y 
            for (int j = i + x - 1; 
                     j < i + y && j < n; j++)
            {
  
                // Get the sum of the sub-array 
                double sum = prefix[j];
                if (i > 0)
                {
                    sum -= prefix[i - 1];
                }
  
                // Find average of sub-array 
                double current = sum / (double)(j - i + 1);
  
                // Store the maximum of average 
                maximum = Math.Max(maximum, current);
            }
        }
  
        return maximum;
    }
  
    // Driver code 
    public static void Main(string[] args)
    {
        int[] a = new int[] {6, 7, 8, 3, 2, 4, 2};
        int X = 2, Y = 4;
        int n = a.Length;
        Console.WriteLine(maxAvgSubArray(a, n, X, Y));
    }
}
  
// This code is contributed by Shrikant13
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP implementation of the approach
  
// Function to return the maximum average
// of the sub-array with size
// atleast x and atmost y
function maxAvgSubArray($a, $n, $x, $y)
{
  
    // Calculate the prefix sum array
    $prefix = array();
    $prefix[0] = $a[0];
    for ($i = 1; $i < $n; $i++)
        $prefix[$i] = $prefix[$i - 1] + $a[$i];
  
    $maximum = 0;
  
    // Iterate over all sub-arrays
    for ($i = 0; $i < $n; $i++) 
    {
  
        // Sub-arrays of size X to Y
        for ($j = $i + $x - 1; 
            $j < $i + $y && $j < $n; $j++)
        {
  
            // Get the sum of the sub-array
            $sum = $prefix[$j];
            if ($i > 0)
                $sum -= $prefix[$i - 1];
  
            // Find average of sub-array
            $current = ($sum / ($j - $i + 1));
  
            // Store the maximum of average
            $maximum = max($maximum, $current);
        }
    }
  
    return $maximum;
}
  
// Driver code
$a = array(6, 7, 8, 3, 2, 4, 2);
$X = 2; $Y = 4;
$n = sizeof($a);
echo maxAvgSubArray($a, $n, $X, $Y);
  
// This code is contributed by Akanksha Rai
?>
chevron_right

Output:
7.5

Time Complexity: O(N * (Y-X))
Auxiliary Space: O(N)




Striver(underscore)79 at Codechef and codeforces D

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.





Article Tags :
Practice Tags :