leetcode/1111.Maximum-Nesting-Depth-of-Two-Valid-Parentheses-Strings/README.md
A string is a valid parentheses string (denoted VPS) if and only if it consists of "(" and ")" characters only, and:
AB (A concatenated with B), where A and B are VPS's, or(A), where A is a VPS.We can similarly define the nesting depth depth(S) of any VPS S as follows:
depth("") = 0depth(A + B) = max(depth(A), depth(B)), where A and B are VPS'sdepth("(" + 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有效括号字符串 仅由 "(" 和 ")" 构成，并符合下述几个条件之一：
类似地，我们可以定义任意有效括号字符串 s 的 嵌套深度 depth(S)：
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。
给你一个有效括号字符串 seq，将其分成两个不相交的子序列 A 和 B，且 A 和 B 满足有效括号字符串的定义（注意：A.length + B.length = seq.length）。
现在，你需要从中选出 任意 一组有效括号字符串 A 和 B，使 max(depth(A), depth(B)) 的可能取值最小。
返回长度为 seq.length 答案数组 answer ，选择 A 还是 B 的编码规则是：如果 seq[i] 是 A 的一部分，那么 answer[i] = 0。否则，answer[i] = 1。即便有多个满足要求的答案存在，你也只需返回 一个。
max(depth(A), depth(B)) 值最小。在最终的数组中输出 0 和 1，0 标识是 A 部分，1 标识是 B 部分。max(depth(A), depth(B)) 值最小，可以使用贪心思想。如果 A 部分和 B 部分都尽快括号匹配，不深层次嵌套，那么总的层次就会变小。只要让嵌套的括号中属于 A 的和属于 B 的间隔排列即可。例如：“(((())))”，上面的字符串的嵌套深度是 4，按照上述的贪心思想，则标记为 0101 1010。