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Sliding Window Maximum using Deque

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 15

Write a Java program to find the maximum element in each sliding window of size k in an array. Given an array of integers nums and a window size k, return an array of maximum values for each window as it slides from left to right.

Example 1
    
  
  • Input: nums = [1, 3, -1, -3, 5, 3, 6, 7], k = 3
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  • Output: [3, 3, 5, 5, 6, 7]
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  • Explanation: 
    
    Step 1: The sliding window has size k = 3
    
    Step 2: Window 1: [1, 3, -1] → max = 3
    
    Step 3: Window 2: [3, -1, -3] → max = 3
    
    Step 4: Window 3: [-1, -3, 5] → max = 5
    
    Step 5: Window 4: [-3, 5, 3] → max = 5
    
    Step 6: Window 5: [5, 3, 6] → max = 6
    
    Step 7: Window 6: [3, 6, 7] → max = 7
  
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Example 2
    
  
  • Input: nums = [1, -1], k = 1
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  • Output: [1, -1]
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  • Explanation: 
    
    Step 1: The sliding window has size k = 1
    
    Step 2: Window 1: [1] → max = 1
    
    Step 3: Window 2: [-1] → max = -1
  
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Constraints
    
  
  • 1 <= nums.length <= 10^5
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  • -10^4 <= nums[i] <= 10^4
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  • 1 <= k <= nums.length
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  • Time Complexity: O(n) where n is the length of the array
    • 
  
  • Space Complexity: O(k)
    •
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Hint
Solution

Solution Hints

    
  
  • Use a deque (double-ended queue) to maintain potential maximum elements.
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  • Keep the deque in decreasing order of values.
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  • The front of the deque will always contain the maximum element of the current window.
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  • When sliding the window, remove elements from the front if they are outside the window.
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  • Before adding a new element, remove elements from the back that are smaller than the new element.
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  • This ensures that the deque is always in decreasing order and contains only elements from the current window.
    •

Steps to solve by this approach:

 Step 1: Initialize a deque to store indices of array elements in decreasing order of their values.

 Step 2: Process the first k elements separately to initialize the deque.

 Step 3: For each element, remove all elements smaller than the current element from the back of the deque.

 Step 4: Add the current element's index to the back of the deque.

 Step 5: For each subsequent element, first remove elements from the front of the deque that are outside the current window.

 Step 6: Remove elements smaller than the current one from the back of the deque, then add the current element's index.

 Step 7: After processing each element, the front of the deque contains the index of the maximum element for the current window.

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