How to Efficiently Implement a Sliding Window Maximum Algorithm in Python?
I'm attempting to set up I've been banging my head against this for hours... I'm trying to implement a sliding window maximum algorithm in Python that can efficiently find the maximum value in every subarray of size `k`. I need this to work with large arrays, and I'm worried about performance since I'm dealing with an array that can be up to 10^6 elements long. I've tried a straightforward approach using nested loops, but it's too slow for large inputs. Here's what I have so far: ```python def sliding_window_max(nums, k): result = [] for i in range(len(nums) - k + 1): max_value = max(nums[i:i + k]) result.append(max_value) return result ``` This works, but for large arrays, I get a timeout behavior as my algorithm runs in O(n * k) time. I also explored using a deque to maintain the maximum values but Iām not quite sure how to implement it correctly. The following is my attempt using a deque: ```python from collections import deque def sliding_window_max(nums, k): d = deque() result = [] for i in range(len(nums)): while d and d[0] < i - k + 1: d.popleft() while d and nums[d[-1]] < nums[i]: d.pop() d.append(i) if i >= k - 1: result.append(nums[d[0]]) return result ``` When I run this modified function, it works for small inputs, but when I try to use it with an array of size 10^6, I encounter an `IndexError` which says `deque index out of range`. Could someone guide to identify what I'm doing wrong here? Also, are there any other optimizations or best practices I can implement to enhance performance even further? My development environment is macOS. I'd really appreciate any guidance on this.