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# Maximum Average Subarray

Sliding Window

## Problem

Given an array consisting of `n` integers, find the contiguous subarray of given length `k` that has the maximum average value. And you need to output the maximum average value

{% hint style="info" %}
For example:

```
Input: [1,12,-5,-6,50,3], k = 4
Output: 12.75
Explanation: Maximum average is (12-5-6+50)/4
= 51/4 = 12.75
```

{% endhint %}

### Thought Process

* We can apply Sliding Window Technique since we are asked to find length of contingous subarray

* This is a static window so we are removing an element before we add a new one (this is why >= k-1)

## Solution

```
class Solution:
    def findMaxAverage(self, nums: List[int], k: int) -> float:
        maxAvg = float('-inf')
        totalAvg = 0
        start = 0
        
        for i in range(len(nums)):
            totalAvg+=nums[i]
            
            if i >= k-1:
                newAvg = totalAvg/k
                maxAvg = max(maxAvg, newAvg)
                totalAvg-=nums[start]
                start+=1
                
        return maxAvg
        
```

## Key Points

* We are using a static window of a fixed size and moving in blocks of size k

## Time Complexity

* **Time** $$O(n)$$ 
* **Space:** $$O(1)$$