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Solution 4: Peak Element Tracking (Sliding Window Maximum)

Approach Explanation

We use a Monotonic Deque to store indices of potential maxima. The deque will maintain indices in decreasing order of their corresponding values in nums.

Step-by-Step Logic

  1. Initialize q = deque(), output = [].
  2. Iterate r from 0 to len(nums)-1:
    • While q is not empty and nums[q[-1]] < nums[r], q.pop().
    • q.append(r).
    • If l > q[0], q.popleft() (out of window).
    • If r + 1 >= k, output.append(nums[q[0]]), increment l.
  3. Return output.

Complexity

  • Time Complexity: O(N).
  • Space Complexity: O(K).

Code

from collections import deque

def max_sliding_window(nums, k):
    output = []
    q = deque() # indices
    l = r = 0
    
    while r < len(nums):
        # pop smaller values from q
        while q and nums[q[-1]] < nums[r]:
            q.pop()
        q.append(r)
        
        # remove left val from window
        if l > q[0]:
            q.popleft()
            
        if (r + 1) >= k:
            output.append(nums[q[0]])
            l += 1
        r += 1
        
    return output