Sliding Window Maximum

Given an array nums, 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.

For example, Given nums = [1,3,-1,-3,5,3,6,7], and k = 3.

Window position                Max
---------------               -----
[1  3  -1] -3  5  3  6  7       3
 1 [3  -1  -3] 5  3  6  7       3
 1  3 [-1  -3  5] 3  6  7       5
 1  3  -1 [-3  5  3] 6  7       5
 1  3  -1  -3 [5  3  6] 7       6
 1  3  -1  -3  5 [3  6  7]      7

Therefore, return the max sliding window as [3,3,5,5,6,7].

Note: You may assume k is always valid, ie: 1 ≤ k ≤ input array’s size for non-empty array.

Follow up: Could you solve it in linear time?

Hint:

How about using a data structure such as deque (double-ended queue)?
The queue size need not be the same as the window’s size.
Remove redundant elements and the queue should store only elements that need to be considered.

Solution 1:

public class Solution {
    public int[] maxSlidingWindow(int[] nums, int k) {
        if(nums.length==0) return new int[0];
        int[] ans = new int[nums.length-k+1];
        int left = 0, right = 0;
        PriorityQueue<Integer> pq = new PriorityQueue<>(k, (a,b)->(b-a));
        while(right<k) pq.offer(nums[right++]);
        while(right<=nums.length){
            ans[left] = pq.peek();
            pq.remove(nums[left++]);
            if(right!=nums.length) pq.offer(nums[right]);
            right++;
        }
        return ans;
    }
}

Solution 2:

public class Solution {
    public int[] maxSlidingWindow(int[] nums, int k) {
        if(nums.length==0) return new int[0];
        int[] ans = new int[nums.length-k+1];
        Deque<Integer> dq = new ArrayDeque<>();
        for(int i=0; i<nums.length; i++){
            while(!dq.isEmpty() && dq.peek()<i-k+1) dq.poll();
            while(!dq.isEmpty() && nums[dq.peekLast()]<=nums[i]) dq.pollLast();
            dq.offer(i);
            if(i>=k-1) ans[i-k+1] = nums[dq.peek()];
        }
        return ans;
    }
}
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