# Maximum average of a subarray of size of at least X and at most Y in C++

C++Server Side ProgrammingProgramming

## Problem statement

Given an array arr[] and two integers X and Y. The task is to find a sub-array of size of at least X and at most Y with the maximum average

## Example

If input array is {2, 10, 15, 7, 8, 4} and x = 3 and Y = 3 then we can obtain maximum average 12.5 as follows −

(10 + 15) / 2 = 12.5

## Algorithm

• Iterate over every sub-array of size starting from X to size Y and find the maximum average among all such sub-arrays.
• To reduce the time complexity, we can use prefix sum array to get the sum of any sub-array in O(1) complexity

## Example

Let us now see an example −

Live Demo

#include <bits/stdc++.h>
using namespace std;
double getMaxAverage(int *arr, int n, int x, int y) {
int prefix[n];
prefix = arr;
for (int i = 1; i < n; ++i) {
prefix[i] = prefix[i - 1] + arr[i];
}
double maxAverage = 0;
for (int i = 0; i < n; ++i) {
for (int j = i + x - 1; j < i + y && j < n; ++j) {
double sum = prefix[j];
if (i > 0) {
sum = sum - prefix[i - 1];
double current = sum / double(j - i + 1);
maxAverage = max(maxAverage,current);
}
}
}
return maxAverage;
}
int main() {
int arr[] = {2, 10, 15, 7, 8, 4};
int x = 2;
int y = 3;
int n = sizeof(arr) / sizeof(arr);
cout << "Maximum average = " << getMaxAverage(arr, n, x, y) << endl;
return 0;
}

## Output

Maximum average = 12.5