Minimum value of maximum values in sub-segments … in O(n) complexity

Question

I interviewed with Amazon a few days ago. I could not answer one of the questions the asked me to their satisfaction. I have tried to get the answer after the interview but

Answer 1

I implemented (and commented) templatetypedef's answer in C#.

n is array length, k is window size.

    public static void printKMax(int[] arr, int n, int k)
    {
        Deque qi = new Deque(); 
        int i;

        for (i=0 ; i < k ; i++) // The first window of the array
        {
            while ((qi.Count > 0) && (arr[i] >= arr[qi.PeekBack()]))
            {
                qi.PopBack();
            }
            qi.PushBack(i);
        }

        for(i=k ; i < n ; ++i)
        {
            Console.WriteLine(arr[qi.PeekFront()]); // the first item is the largest element in previous window. The second item is its index.

            while (qi.Count > 0 && qi.PeekFront() <= i - k) 
            {
                qi.PopFront(); //When it's out of its window k 
            }
            while (qi.Count>0 && arr[i] >= arr[qi.PeekBack()]) 
            {
                qi.PopBack();
            }
            qi.PushBack(i);
        }
        Console.WriteLine(arr[qi.PeekFront()]);
    }