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Sliding Window Maximum

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

Write a C++ program to solve the Sliding Window Maximum problem. You are given an array of integers `nums` and an integer `k`, there is a sliding window of size `k` which is moving from the very left of the array to the very right. You can only see the `k` numbers in the window. Each time the sliding window moves right by one position, return the maximum element in the sliding window.

Example 1
    

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

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

    • Step 1: Create a data structure to track the maximum element in the current window.
      • 

    • Step 2: Slide the window through the array, one position at a time.
      • 

    • Step 3: For each window position, record the maximum element:
   [1, 3, -1] → max = 3
   [3, -1, -3] → max = 3
   [-1, -3, 5] → max = 5
   [-3, 5, 3] → max = 5
   [5, 3, 6] → max = 6
   [3, 6, 7] → max = 7
      • 

    • Step 4: Return the array of maximum values [3, 3, 5, 5, 6, 7].
      • 

    •
Example 2
    

  • Input: nums = [1], k = 1
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  • Output: [1]
    • 

  • Explanation: 
      

    • Step 1: Create a data structure to track the maximum element in the current window.
      • 

    • Step 2: There is only one element and one window of size 1.
      • 

    • Step 3: The maximum in this window is 1.
      • 

    • Step 4: Return the array with the single maximum value [1].
      • 

    •
Constraints
    

  • 1 ≤ nums.length ≤ 10^5
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  • -10^4 ≤ nums[i] ≤ 10^4
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  • 1 ≤ k ≤ nums.length
    • 

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

  • Space Complexity: O(k) where k is the window size
    •
DequeIBMGoldman Sachs
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Hint
Solution

Solution Hints

    
  
  • Consider using a deque (double-ended queue) to track potential maximum values
    • 
  
  • Maintain elements in the deque in decreasing order
    • 
  
  • Remove elements that are outside the current window
    • 
  
  • Remove smaller elements that won't be maximum in current or future windows
    • 
  
  • The front of the deque will always contain the current window's maximum
    •

Steps to solve by this approach:

 Step 1: Create a deque to store indices of elements in the current window.
 Step 2: For each element in the array, remove indices that are outside the current window.
 Step 3: Remove indices of all elements smaller than the current element from the back of the deque.
 Step 4: Add the current element's index to the deque.
 Step 5: Once we've processed k elements, add the maximum (front of deque) to the result.
 Step 6: Continue this process for each element, sliding the window to the right.
 Step 7: Return the result array containing maximum values for each window position.

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