53 Maximum Subarray

So, at every new element in the array we make two choices A) either add the new element to the current running sum OR B) start a new current sum altogether. Now, starting a new current sum is equivalent to starting a new sub-array.

The solutions that seem the simplest are usually the hardest to grasp: because mainly they are abstracted over several complex concepts.

Code:

Python

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        cur_sum, sub_arr_max = -float('inf'), -float('inf')
        for n in nums:
            cur_sum = max(cur_sum + n, n)
            sub_arr_max = max(sub_arr_max, cur_sum)
        return sub_arr_max

Big O Analysis

• Runtime The runtime complexity here is O(N) as since we would be iterating the array once.
• Memory The memory usage is O(1)

— A

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