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Longest Sub-array with maximum average value

  • Difficulty Level : Medium
  • Last Updated : 11 May, 2021

Given an array arr[] of n integers. The task is to find the maximum length of the sub-array which has the maximum average value (average of the elements of the sub-array). 

    <strong>$$ Average = \frac{1}{n} \times\sum_{1}^{n} a_{i} $$ </strong>

Examples: 
 

Input: arr[] = {2, 3, 4, 5, 6} 
Output:
{6} is the required sub-array
Input: arr[] = {6, 1, 6, 6, 0} 
Output:
{6} and {6, 6} are the sub-arrays with maximum average value. 
 

 



Approach: 
 

  • Average of any sub-array cannot exceed the maximum value of the array.
  • The possible maximum value of the average will be the maximum element from the array.
  • So to find the maximum length sub-array with the maximum average value, we have to find the max length of the sub-array where every element of the sub-array is same and equal to the maximum element from the array.

Below is the implementation of the above approach:
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the max length of the
// sub-array that have the maximum average
// (average value of the elements)
int maxLenSubArr(int a[], int n)
{
    int count, j;
    int cm = 1, max = 0;
 
    // Finding the maximum value
    for (int i = 0; i < n; i++) {
        if (a[i] > max)
            max = a[i];
    }
 
    for (int i = 0; i < n - 1;) {
        count = 1;
 
        // If consecutive maximum found
        if (a[i] == a[i + 1] && a[i] == max) {
 
            // Find the max length of consecutive max
            for (j = i + 1; j < n; j++) {
                if (a[j] == max) {
                    count++;
                    i++;
                }
                else
                    break;
            }
 
            if (count > cm)
                cm = count;
        }
        else
            i++;
    }
 
    return cm;
}
 
// Driver code
int main()
{
    int arr[] = { 6, 1, 6, 6, 0 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    cout << maxLenSubArr(arr, n);
 
    return 0;
}

Java




// Java implementation of the approach
class GFG
{
     
// Function to return the max length of the
// sub-array that have the maximum average
// (average value of the elements)
static int maxLenSubArr(int a[], int n)
{
    int count, j;
    int cm = 1, max = 0;
 
    // Finding the maximum value
    for (int i = 0; i < n; i++)
    {
        if (a[i] > max)
            max = a[i];
    }
 
    for (int i = 0; i < n - 1; )
    {
        count = 1;
 
        // If consecutive maximum found
        if (a[i] == a[i + 1] && a[i] == max)
        {
 
            // Find the max length of consecutive max
            for (j = i + 1; j < n; j++)
            {
                if (a[j] == max)
                {
                    count++;
                    i++;
                }
                else
                    break;
            }
 
            if (count > cm)
                cm = count;
        }
        else
            i++;
    }
 
    return cm;
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 6, 1, 6, 6, 0 };
    int n = arr.length;
 
    System.out.println(maxLenSubArr(arr, n));
}
}
 
// This code is contributed by Code_Mech.

Python3




# Python3 implementation of the approach
 
# Function to return the max length of the
# sub-array that have the maximum average
# (average value of the elements)
def maxLenSubArr(a, n):
 
    cm, Max = 1, 0
 
    # Finding the maximum value
    for i in range(0, n):
        if a[i] > Max:
            Max = a[i]
             
    i = 0
    while i < n - 1:
        count = 1
 
        # If consecutive maximum found
        if a[i] == a[i + 1] and a[i] == Max:
 
            # Find the max length of
            # consecutive max
            for j in range(i + 1, n):
                if a[j] == Max:
                    count += 1
                    i += 1
                 
                else:
                    break
             
            if count > cm:
                cm = count
         
        else:
            i += 1
             
        i += 1
 
    return cm
 
# Driver code
if __name__ == "__main__":
 
    arr = [6, 1, 6, 6, 0]
    n = len(arr)
 
    print(maxLenSubArr(arr, n))
 
# This code is contributed by
# Rituraj Jain

C#




// C# implementation of the approach
using System;
 
class GFG
{
         
// Function to return the max length of the
// sub-array that have the maximum average
// (average value of the elements)
static int maxLenSubArr(int []a, int n)
{
    int count, j;
    int cm = 1, max = 0;
 
    // Finding the maximum value
    for (int i = 0; i < n; i++)
    {
        if (a[i] > max)
            max = a[i];
    }
 
    for (int i = 0; i < n - 1; )
    {
        count = 1;
 
        // If consecutive maximum found
        if (a[i] == a[i + 1] && a[i] == max)
        {
 
            // Find the max length of consecutive max
            for (j = i + 1; j < n; j++)
            {
                if (a[j] == max)
                {
                    count++;
                    i++;
                }
                else
                    break;
            }
            if (count > cm)
                cm = count;
        }
        else
            i++;
    }
    return cm;
}
 
    // Driver code
    static public void Main ()
    {
     
        int []arr = { 6, 1, 6, 6, 0 };
        int n = arr.Length;
        Console.WriteLine(maxLenSubArr(arr, n));
    }
}
 
// This code is contributed by ajit.

PHP




<?php
// PHP implementation of the approach
 
// Function to return the max length of the
// sub-array that have the maximum average
// (average value of the elements)
function maxLenSubArr($a, $n)
{
    $cm = 1 ;
    $max = 0;
 
    // Finding the maximum value
    for ($i = 0; $i < $n; $i++)
    {
        if ($a[$i] > $max)
            $max = $a[$i];
    }
 
    for ($i = 0; $i < $n - 1;)
    {
        $count = 1;
 
        // If consecutive maximum found
        if ($a[$i] == $a[$i + 1] &&
            $a[$i] == $max)
        {
 
            // Find the max length of
            // consecutive max
            for ($j = $i + 1; $j < $n; $j++)
            {
                if ($a[$j] == $max)
                {
                    $count++;
                    $i++;
                }
                else
                    break;
            }
 
            if ($count > $cm)
                $cm = $count;
        }
        else
            $i++;
    }
 
    return $cm;
}
 
// Driver code
$arr = array( 6, 1, 6, 6, 0 );
$n = sizeof($arr);
 
echo maxLenSubArr($arr, $n);
 
// This code is contributed by Ryuga
?>

Javascript




<script>
    // Javascript implementation of the approach
     
    // Function to return the max length of the
    // sub-array that have the maximum average
    // (average value of the elements)
    function maxLenSubArr(a, n)
    {
        let count, j;
        let cm = 1, max = 0;
 
        // Finding the maximum value
        for (let i = 0; i < n; i++)
        {
            if (a[i] > max)
                max = a[i];
        }
 
        for (let i = 0; i < n - 1; )
        {
            count = 1;
 
            // If consecutive maximum found
            if (a[i] == a[i + 1] && a[i] == max)
            {
 
                // Find the max length of consecutive max
                for (j = i + 1; j < n; j++)
                {
                    if (a[j] == max)
                    {
                        count++;
                        i++;
                    }
                    else
                        break;
                }
                if (count > cm)
                    cm = count;
            }
            else
                i++;
        }
        return cm;
    }
     
    let arr = [ 6, 1, 6, 6, 0 ];
    let n = arr.length;
    document.write(maxLenSubArr(arr, n));
     
</script>
Output: 
2

 

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