How to find maximum of each subarray of some fixed given length in a given array

Question

We are given an array of n elements and an integer k. Suppose that we want to slide a window of length k across the array, reporting the largest value contained in each window.

Answer 1

You could proceed like a tabu search :

Loop through the list and get the max of the 4 first ith element. Then on the next step just check if the i+1th element is superior to the max of the previous elements

• if i+1>=previous max then new max = i+1 reinialise tabu
• if i+1< previous max then if the previous max was found less than N step ago keep the previous (here is the tabu )
• if i+1< preivous max and the previous max is tabu then take the new max of the 4 i+1th elements.

I'm not sure it's clear but tell me if you have any question. below is a code in python to test it.

l=[15,10,9,16,20,14,13,11,12]
N=4
res=[-1] #initialise res
tabu=1  #initialise tabu
for k in range(0,len(l)):
#if the previous element res[-1] is higher than l[k] and not tabu then keep it
#if the previous is tabu and higher than l[k] make a new search without it
#if the previous is smaller than l[k] take the new max =l[k]

    if l[k]= res[-1]:
        tabu=1
        res.append(l[k])

print res[N:] #take of the N first element

Complexity:

I updated the code thx to flolo and the complexity. it's not anymore O(N) but O(M*N)

The worst case is when you need to recalculate a maximum at each step of the loop. i e a strictly decreasing list for example.

at each step of the loop you need to recalculate the max of M elements

then the overall complexity is O(M*N)