Question

Given an array of N elements, A[0 .. N - 1], Produce an array B such that:

 B[i] = min (A[i], A[i+1], ..., A[i+K-1]). 

(The array B will have exactly (N-k+1) elements.

Time complexity should be better than O(N*k)

I was thinking of using minheap… but heapify will increase the complexity
Also brute force is O(n*k)

Also space complexity s’d be less than equal to O(k)

Here’s an example

Input: 
A={ 2,1,3,2,5,7,1}, N=7,k=3

Output:
B={1,1,2,2,1}

Answer 1

To solve the problem, you can use queue in which push_rear(), pop_front() and get_min() are all constant time operations.

Push first k elements from the array A to this queue. Then continue filling the queue from the array A, while popping elements from it and appending minimum values to the array B.

Time complexity is O(N). Space complexity is O(k).