{ "data": { "question": { "questionId": "1208", "questionFrontendId": "1111", "categoryTitle": "Algorithms", "boundTopicId": 12519, "title": "Maximum Nesting Depth of Two Valid Parentheses Strings", "titleSlug": "maximum-nesting-depth-of-two-valid-parentheses-strings", "content": "

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

\r\n\r\n\r\n\r\n

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

\r\n\r\n\r\n\r\n

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

\r\n\r\n

 

\r\n\r\n

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).

\r\n\r\n

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

\r\n\r\n

Return an answer array (of length seq.length) that encodes such a choice of A and Banswer[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.

\r\n\n

 

\n

Example 1:

\n\n
\nInput: seq = "(()())"\nOutput: [0,1,1,1,1,0]\n
\n\n

Example 2:

\n\n
\nInput: seq = "()(())()"\nOutput: [0,0,0,1,1,0,1,1]\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "有效括号的嵌套深度", "translatedContent": "

有效括号字符串 定义:对于每个左括号,都能找到与之对应的右括号,反之亦然。详情参见题末「有效括号字符串」部分。

\n\n

嵌套深度 depth 定义:即有效括号字符串嵌套的层数,depth(A) 表示有效括号字符串 A 的嵌套深度。详情参见题末「嵌套深度」部分。

\n\n

有效括号字符串类型与对应的嵌套深度计算方法如下图所示:

\n\n

\"\"

\n\n

 

\n\n

给你一个「有效括号字符串」 seq,请你将其分成两个不相交的有效括号字符串,A 和 B,并使这两个字符串的深度最小。

\n\n\n\n

划分方案用一个长度为 seq.length 的答案数组 answer 表示,编码规则如下:

\n\n\n\n

如果存在多个满足要求的答案,只需返回其中任意 一个 即可。

\n\n

 

\n\n

示例 1:

\n\n
输入:seq = "(()())"\n输出:[0,1,1,1,1,0]\n
\n\n

示例 2:

\n\n
输入:seq = "()(())()"\n输出:[0,0,0,1,1,0,1,1]\n解释:本示例答案不唯一。\n按此输出 A = "()()", B = "()()", max(depth(A), depth(B)) = 1,它们的深度最小。\n像 [1,1,1,0,0,1,1,1],也是正确结果,其中 A = "()()()", B = "()", max(depth(A), depth(B)) = 1 。 \n
\n\n

 

\n\n

提示:

\n\n\n\n

 

\n\n

有效括号字符串:

\n\n
仅由 "(" 和 ")" 构成的字符串,对于每个左括号,都能找到与之对应的右括号,反之亦然。\n下述几种情况同样属于有效括号字符串:\n\n  1. 空字符串\n  2. 连接,可以记作 ABAB 连接),其中 A 和 B 都是有效括号字符串\n  3. 嵌套,可以记作 (A),其中 A 是有效括号字符串\n
\n\n

嵌套深度:

\n\n
类似地,我们可以定义任意有效括号字符串 s嵌套深度 depth(S):\n\n  1. s 为空时,depth("") = 0\n  2. sAB 连接时,depth(A + B) = max(depth(A), depth(B)),其中 A 和 B 都是有效括号字符串\n  3. s 为嵌套情况,depth("(" + A + ")") = 1 + depth(A),其中 A 是有效括号字符串\n\n例如:"""()()",和 "()(()())" 都是有效括号字符串,嵌套深度分别为 0,1,2,而 ")(" 和 "(()" 都不是有效括号字符串。\n
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