1614. Maximum Nesting Depth of the Parentheses

题目

A string is a valid parentheses string (denoted VPS) if it meets one of the following:

It is an empty string "", or a single character not equal to "(" 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(C) = 0, where C is a string with a single character not equal to "(" or ")".
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 represented as string s, return the nesting depth of s.

Example 1:

Input: s = "(1+(2*3)+((8)/4))+1"
Output: 3
Explanation: Digit 8 is inside of 3 nested parentheses in the string.

Example 2:

Input: s = "(1)+((2))+(((3)))"
Output: 3

Example 3:

Input: s = "1+(2*3)/(2-1)"
Output: 1

Example 4:

Input: s = "1"
Output: 0

Constraints:

1 <= s.length <= 100
s consists of digits 0-9 and characters '+', '-', '*', '/', '(', and ')'.
It is guaranteed that parentheses expression s is a VPS.

题目大意

如果字符串满足以下条件之一，则可以称之为有效括号字符串（valid parentheses string，可以简写为 VPS）：

字符串是一个空字符串 ""，或者是一个不为 "(" 或 ")" 的单字符。
字符串可以写为 AB（A 与 B 字符串连接），其中 A 和 B 都是有效括号字符串。
字符串可以写为 (A)，其中 A 是一个有效括号字符串。

类似地，可以定义任何有效括号字符串 S 的嵌套深度 depth(S)：

depth("") = 0
depth(C) = 0，其中 C 是单个字符的字符串，且该字符不是 "(" 或者 ")"
depth(A + B) = max(depth(A), depth(B))，其中 A 和 B 都是有效括号字符串
depth("(" + A + ")") = 1 + depth(A)，其中 A 是一个有效括号字符串

例如：""、"()()"、"()(()())" 都是有效括号字符串（嵌套深度分别为 0、1、2），而 ")(" 、"(()" 都不是有效括号字符串。给你一个有效括号字符串 s，返回该字符串的 s 嵌套深度。

解题思路

简单题。求一个括号字符串的嵌套深度。题目给的括号字符串都是有效的，所以不需要考虑非法的情况。扫描一遍括号字符串，遇到 ( 可以无脑 ++，并动态维护最大值，遇到 ) 可以无脑 - - 。最后输出最大值即可。

代码

package leetcode

func maxDepth(s string) int {
	res, cur := 0, 0
	for _, c := range s {
		if c == '(' {
			cur++
			res = max(res, cur)
		} else if c == ')' {
			cur--
		}
	}
	return res
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}