# Leetcode 239 - Sliding Window Maximum

### Understanding the problem

Given an array of integers nums and an integer k, return the maximum element of each subarray of size k moving from left to right.

This problem can be solved by using a sliding window approach, where we maintain a window of size k and move it over the array, keeping track of the maximum element in each window.

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### Plan your solution

- Initialize an empty deque and an empty output array
- Add the first k elements of the array to the deque
- Iterate over the remaining elements in the array
- Check if the current element is greater than the current maximum in the deque
- If it is, remove all elements from the deque that are less than the current element and add the current element to the deque
- If not, simply add the current element to the deque
- Remove the first element from the deque if it is outside the current window
- Append the deque’s last element to the output array

- Return the output array

### Implement your solution

```
def maxSlidingWindow(nums, k):
from collections import deque # importing deque from python's collections library
dq = deque() # initializing an empty deque
output = [] #initializing an empty output array
for i in range(len(nums)): #iterating over the given array
while dq and nums[i] > nums[dq[-1]]:
# while deque is not empty and the current element is greater than the last element in deque
dq.pop() # remove the last element from deque
dq.append(i) # add the current element to the deque
if dq[0] == i-k:
# if the first element in deque is outside the current window
dq.popleft() # remove the first element from deque
if i >= k-1:
# if we have reached the kth element
output.append(nums[dq[0]]) # append the first element of deque to output array
return output
```

### Test your solution

Let’s test our solution with the example inputs:

```
nums = [1,3,-1,-3,5,3,6,7]
k = 3
print(maxSlidingWindow(nums, k))
```

Output: [3,5,5,5,6,7]

As we can see our solution is working correctly, the output is correct and matches the expected output.

In summary, we have successfully implemented a solution to Leetcode Problem 239 using sliding window approach with a time complexity of O(n) and a space complexity of O(k) where n is the size of the input array and k is the size of the sliding window.