Sliding Window Maximum
Given an array and sliding window of size k, return the maximum in each window position.
Output space-separated.
Example:
1,3,-1,-3,5,3,6,7 3
3 3 5 5 6 7
- The array is processed with a sliding window of size k=3, starting from the first element.
- For each window position, the maximum value is found:
- Window 1: max(1,3,−1)=3
- Window 2: max(3,−1,−3)=3
- Window 3: max(−1,−3,5)=5
- Window 4: max(−3,5,3)=5
- Window 5: max(5,3,6)=6
- Window 6: max(3,6,7)=7
- The maximum values from each window are collected and output as space-separated values.
- The final output is therefore: 335567
Constraints:
- 1 <= len(nums) <= 10^5
- -10^4 <= nums[i] <= 10^4
- 1 <= k <= len(nums)
Background Knowledge
The Sliding Window Maximum problem involves finding the maximum element in each window of a given size k as it slides over an array. This problem is a classic example of a window-based problem, where we need to process a subset of the data at a time. To solve this problem, we need to understand the concept of queues and deques (double-ended queues), which are data structures that allow efficient insertion and removal of elements from both ends. We also need to understand the concept of priority queues, which are data structures that allow efficient insertion and removal of elements based on their priority.
The key concept in this problem is the use of a deque to keep track of the indices of the elements in the current window. We can use the deque to efficiently remove elements that are out of the current window and add new elements that enter the window. We also need to understand the concept of maximum and how to find it in a window of elements. This can be done using a priority queue, which can keep track of the maximum element in the window.
The Sliding Window Maximum problem is a variation of the Maximum Subarray problem, which involves finding the maximum sum of a subarray of a given size. However, in this problem, we need to find the maximum element in each window, rather than the maximum sum. This requires a different approach, using a deque to keep track of the indices of the elements in the current window, and a priority queue to keep track of the maximum element in the window.
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