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Given an array of integers A[1...n-1] where N is the length of array A. Construct an array B such that B[i] = min(A[i], A[i+1], ..., A[i+K-1]), where K will be given. Array B will have N-K+1 elements.
We can solve the problem using min-heaps Construct min-heap for k elements – O(k). For every next element delete the first element and insert the new element and heapify.
Hence Worst Case Time – O( (n-k+1)*k ) + O(k) Space – O(k)
Can we do it better?
We can do better if in the algorithm from OP we change expensive “heapify” procedure to much cheaper “upheap” or “downheap”. This gives O(n * log(k)) time complexity.
Or, if we iterate through input array and put each element to the min-queue of size ‘k’, we can do it in O(n) time. Min-queue is a queue that can perform find-min in O(1) time. It may be implemented as a pair of min-stacks. See this answer for details.