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1111. Maximum Nesting Depth of Two Valid Parentheses Strings

Difficulty Topics

Description

A string is a valid parentheses string (denoted VPS) if and only if it consists of "(" and ")" characters only, and:

  • It is the empty string, or
  • It can be written as AB (A concatenated with B), where A and B are VPS's, or
  • It can be written as (A), where A is a VPS.

We can similarly define the nesting depth depth(S) of any VPS S as follows:

  • depth("") = 0
  • depth(A + B) = max(depth(A), depth(B)), where A and B are VPS's
  • depth("(" + A + ")") = 1 + depth(A), where A is a VPS.

For example,  "", "()()", and "()(()())" are VPS's (with nesting depths 0, 1, and 2), and ")(" and "(()" are not VPS's.

 

Given a VPS seq, split it into two disjoint subsequences A and B, such that A and B are VPS's (and A.length + B.length = seq.length).

Now choose any such A and B such that max(depth(A), depth(B)) is the minimum possible value.

Return an answer array (of length seq.length) that encodes such a choice of A and B:  answer[i] = 0 if seq[i] is part of A, else answer[i] = 1.  Note that even though multiple answers may exist, you may return any of them.

 

Example 1:

Input: seq = "(()())"
Output: [0,1,1,1,1,0]

Example 2:

Input: seq = "()(())()"
Output: [0,0,0,1,1,0,1,1]

 

Constraints:

  • 1 <= seq.size <= 10000

Solution

maximum-nesting-depth-of-two-valid-parentheses-strings.py
class Solution:
    def maxDepthAfterSplit(self, seq):
        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