在指定长度的O（n ^ 2）下的正整数列表中找到子列表的最大和数Python 3.5

Question

For one of my programming questions, I am required to define a function that accepts two variables, a list of length l and an integer w. I then have to find the maximum sum of a sublist with length w within the list.

Conditions:

1<=w<=l<=100000

Each element in the list ranges from [1, 100]

Currently, my solution works in O(n^2) (correct me if I'm wrong, code attached below), which the autograder does not accept, since we are required to find an even simpler solution.

My code:

def find_best_location(w, lst):
    best = 0
    n = 0
    while n <= len(lst) - w:
        lists = lst[n: n + w]
        cur = sum(lists)
        best = cur if cur>best else best
        n+=1

    return best

If anyone is able to find a more efficient solution, please do let me know! Also if I computed my big-O notation wrongly do let me know as well!

Thanks in advance!

Answer 1

1) Find sum current of first w elements, assign it to best .
2) Starting from i = w : current = current + lst[i]-lst[iw] , best = max(best, current) .
3) Done.

Answer 2

Your solution is indeed O(n^2) (or O(n*W) if you want a tighter bound)

You can do it in O(n) by creating an aux array sums , where:

sums[0] = l[0]
sums[i] = sums[i-1] + l[i]

Then, by iterating it and checking sums[i] - sums[iW] you can find your solution in linear time

You can even calculate sums array on the fly to reduce space complexity, but if I were you, I'd start with it, and see if I can upgrade my solution next.