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Sliding Window Maximum

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C# program to implement the MaxSlidingWindow(int[] nums, int k) function, which takes an array of integers nums and an integer k as input. The function should find the maximum element in each sliding window of size k and return an array of these maximums.

Example 1
    

  • Input: nums = [1, 3, -1, -3, 5, 3, 6, 7], k = 3
    • 

  • Output: [3, 3, 5, 5, 6, 7]
    • 

  • Explanation:

      

    • Step 1: Create a sliding window of size k and move it through the array.
      • 

    • Step 2: For each window position, find the maximum element.

        

      • Window [1, 3, -1] → maximum is 3
        • 

      • Window [3, -1, -3] → maximum is 3
        • 

      • Window [-1, -3, 5] → maximum is 5
        • 

      • Window [-3, 5, 3] → maximum is 5
        • 

      • Window [5, 3, 6] → maximum is 6
        • 

      • Window [3, 6, 7] → maximum is 7
        • 

      

      • 

    • Step 3: Return the array of maximum values [3, 3, 5, 5, 6, 7].
      • 

    •
Example 2
    

  • Input: nums = [9, 11, 8, 7, 6, 5], k = 3
    • 

  • Output: [11, 11, 8, 7]
    • 

  • Explanation:

      

    • Step 1: Create a sliding window of size k and move it through the array.
      • 

    • Step 2: For each window position, find the maximum element.

        

      • Window [9, 11, 8] → maximum is 11
        • 

      • Window [11, 8, 7] → maximum is 11
        • 

      • Window [8, 7, 6] → maximum is 8
        • 

      • Window [7, 6, 5] → maximum is 7
        • 

      

      • 

    • Step 3: Return the array of maximum values [11, 11, 8, 7].
      • 

    •
Constraints
    

  • 1 ≤ nums.length ≤ 10^5
    • 

  • -10^4 ≤ nums[i] ≤ 10^4
    • 

  • 1 ≤ k ≤ nums.length
    • 

  • Time Complexity: O(n) where n is the length of the input array
    • 

  • Space Complexity: O(k) for storing the deque of size k
    •
DequeGoldman SachsD. E. Shaw
Editorial

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Hint
Solution

Solution Hints

    
  
  • Use a deque (double-ended queue) to maintain a window of potential maximum values
    • 
  
  • Keep the deque in descending order to quickly find the maximum
    • 
  
  • As you slide the window, remove elements that are outside the current window
    • 
  
  • Also remove smaller elements from the back as they won't be needed
    • 
  
  • The front of the deque always contains the maximum element of the current window
    •

Steps to solve by this approach:

 Step 1: Create a deque (we use LinkedList in C#) to store indices of array elements.
 Step 2: Process each element in the array one by one.
 Step 3: Remove elements from the front of the deque that are outside the current window.
 Step 4: Remove all elements smaller than the current element from the back of the deque.
 Step 5: Add the current element's index to the deque.
 Step 6: Once we've processed k elements, start adding the maximum (front of deque) to the result array.
 Step 7: Return the array of maximum values for each window.

Submitted Code :