Problem URL: Maximum nesting depth of two valid parentheses strings

We will keep on iterating over the string and we will keep on pushing the current character into the stack. If the current character is (, we will increment the current depth. If the current character is ), we will decrement the current depth. If the current depth is greater than the maximum depth, we will update the maximum depth to be the current depth. We will keep on doing this until we have processed all the characters. At the end, we will return the maximum depth.

class Solution:
    def maxDepthAfterSplit(self, seq: str) -> List[int]:
        A = B = 0
        res = [0] * len(seq)
        for i, c in enumerate(seq):
            v = 1 if c == '(' else -1
            if (v > 0) == (A < B):
                A += v
            else:
                B += v
                res[i] = 1
        return res

Time complexity: O(n)
Space complexity: O(1)