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:

C++

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// 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;
}

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Java

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// 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));
    }
}

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Python3

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# 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

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C#

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// 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

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PHP

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<?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
?>

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Output:

7.5

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



My Personal Notes arrow_drop_up

Striver(underscore)79 at Codechef and codeforces D

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