Problem Description:
Given an array of integer nums and an integer k, find the maximum average subarray of size k. A subarray is a contiguous sequence of elements within an array.
Input:
nums: An array of integers.
k: The size of the sliding window.
Output:
The maximum average value of a subarray of size k.
Example:
Input: nums = [1,12,-5,-6,50,3], k = 4 Output: 12.75 Explanation: The maximum average subarray is [12,-5,-6,50].
Constraints:
1 <= k <= nums.length <= 30000
-10^5 <= nums[i] <= 10^5
Note: You can solve this problem using a sliding window approach, where you maintain a window of size k and update the maximum average value as you slide the window along the array.
Q- Can you explain the problem statement using your own words? 

So you are given an array of integers and an integer k 

Your task to find the biggest array of lengths k , 
We quantify the term biggest by the average value within this array of 
Q- what is the input&output format ? 

Input : List[int] 
Output: int 

Q- can you go through an example? 

nums = [1,12,-5,-6,50,3], k = 4
The first sub_array : [1,12,-5,-6] → avg_value = 2/4 = 0.5 
The second sub_array : [12,-5,-6,50] → avg_value=51 /4 = 12.5 
** continue this for the rest of elements 
We continue sliding the window to the right, one position at a time, and calculate the average of each subarray of size 4:
[-5, -6, 50, 3] has an average of ((-5) + (-6) + 50 + 3) / 4 = 10.5.
After calculating the averages of all possible subarrays of size 4, we find that the maximum average is 12.75, corresponding to the subarray [12, -5, -6, 50].

Q- Can you comment and infer anything? 
→ so looking at the workflow in  this example we can see that we have a pattern that 
Repeat itself … each time we create some like window for the given sub_array 
Compute the average value, and move to the next window until reaching the end of the array 
Q- before i Before I continue I want you to be a pair guide  coder with me  so give me your honest feedback about my thinking process so far without telling me the exact solution just some clever and intuitive feedback

Problem Description:
Given an array of integer nums and an integer k, find the maximum average subarray of size k. A subarray is a contiguous sequence of elements within an array.
Input:
nums: An array of integers.
k: The size of the sliding window.
Output:
The maximum average value of a subarray of size k.
Example:
Input: nums = [1,12,-5,-6,50,3], k = 4 Output: 12.75 Explanation: The maximum average subarray is [12,-5,-6,50].
Constraints:
1 <= k <= nums.length <= 30000
-10^5 <= nums[i] <= 10^5
Note: You can solve this problem using a sliding window approach, where you maintain a window of size k and update the maximum average value as you slide the window along the array.
Q- Can you explain the problem statement using your own words? 

So you are given an array of integers and an integer k 

Your task to find the biggest array of lengths k , 
We quantify the term biggest by the average value within this array of 
Q- what is the input&output format ? 

Input : List[int] 
Output: int 

Q- can you go through an example? 

nums = [1,12,-5,-6,50,3], k = 4
The first sub_array : [1,12,-5,-6] → avg_value = 2/4 = 0.5 
The second sub_array : [12,-5,-6,50] → avg_value=51 /4 = 12.5 
** continue this for the rest of elements 
We continue sliding the window to the right, one position at a time, and calculate the average of each subarray of size 4:
[-5, -6, 50, 3] has an average of ((-5) + (-6) + 50 + 3) / 4 = 10.5.
After calculating the averages of all possible subarrays of size 4, we find that the maximum average is 12.75, corresponding to the subarray [12, -5, -6, 50].

Q- Can you comment and infer anything? 
→ so looking at the workflow in  this example we can see that we have a pattern that 
Repeat itself … each time we create some like window for the given sub_array 
Compute the average value, and move to the next window until reaching the end of the array 
Q- before i Before I continue I want you to be a pair guide  coder with me  so give me your honest feedback about my thinking process so far without telling me the exact solution just some clever and intuitive feedback
I'm happy to be your pair programming guide and provide feedback on your thinking process so far. You've made some excellent observations and have a good grasp of the problem. Here's my feedback:

1. Problem Understanding: You've accurately summarized the core of the problem - finding a subarray of length k with the maximum average. This shows you've understood the main objective well.

2. Input/Output Recognition: You correctly identified the input as a list of integers and k. However, the output should be a float (the maximum average), not an int. This is a small but important distinction.

3. Example Walkthrough: Your step-by-step analysis of the example is spot-on. You've demonstrated how to calculate the average for each subarray and how to slide the window. This is crucial for developing the algorithm.

4. Pattern Recognition: You've astutely noticed the repeating pattern of creating a window, computing the average, and sliding the window. This observation is key to developing an efficient solution.

5. Sliding Window Technique: Without explicitly naming it, you've described the sliding window technique, which is indeed the optimal approach for this problem. This shows good intuition for algorithmic patterns.

6. Efficiency Consideration: While you haven't mentioned it explicitly, your description implies an understanding that we don't need to recalculate the entire sum for each window, which is a crucial optimization.

Suggestions for next steps:

1. Consider how you can efficiently update the sum as you slide the window. Can you avoid recalculating the entire sum each time?

2. Think about how to handle edge cases, such as when k equals the length of the array.

3. Consider the time complexity of your approach. How many operations are you performing relative to the size of the input?

4. Think about how you'll keep track of the maximum average as you go through the array.

Your thinking process is on the right track. You've broken down the problem well and identified the key aspects. Now, try to formalize this into a step-by-step algorithm before jumping into coding. Let me know if you want to discuss your algorithm idea or if you're ready to start implementing the solution!
Q- try to answer this Question  ? 


1. Consider how you can efficiently update the sum as you slide the window. Can you avoid recalculating the entire sum each time?
—> given the slide window here is fixed by size 
For first compute the first window which start from the beginner until k oky 
Then the update logic is like removing&adding one element at the time 
→ we leverage a for loop here starting from k until n-1 (length of the input array -1) 
current_sub_array=sub_array+nums[i]-nums[i-k] 


Q
3. Consider the time complexity of your approach. How many operations are you performing relative to the size of the input?
—> Given that the worst case scenario is in the for-loop 
—> so i think the worse case scenario is O(n) 

4. Think about how you'll keep track of the maximum average as you go through the array.
—> to keep track of the maximum avg value we can initiate a varible called max_val 
Initially store the sum of the first window
→ next inside the for loop we just update it value based on the computed value of it 

→ after breaking from the loop , we just divided it by it k 

Q- finally now give your feedback about my progress so far oky ?