Sliding Window Maximum @LeetCode

PROBLEM :

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?

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SIMPLE c++ IMPLEMENTATION :
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class Solution {
public:
    vector<int> maxSlidingWindow(vector<int>& nums, int k) {
        vector<int> ans ;
        if(nums.size()==0)
            return ans ;
           
        vector<int> left(nums.size()) ;
        left[0]=nums[0] ;
       
        for(int i=1;i<nums.size();i++)
            left[i]=(i%k==0) ? nums[i] : (nums[i] > left[i-1] ? nums[i] : left[i-1]) ;
           
        vector<int> right(nums.size()) ;
        right[nums.size()-1]=nums[nums.size()-1] ;
       
        for(int i=nums.size()-2;i>=0;i--)
            right[i]=(i%k==0) ? nums[i] : (nums[i] > right[i+1] ? nums[i] : right[i+1]) ;
       
        for(int i=0;i<nums.size()-k+1;i++)
            ans.push_back( right[i]>left[i+k-1] ? right[i] : left[i+k-1] ) ;
           
        return ans ;
    }
};

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