# LeetCode 1614. Maximum Nesting Depth of the Parentheses【String】簡單
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(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)+((<u>8</u>)/4))+1"
Output: 3
Explanation: Digit 8 is inside of 3 nested parentheses in the string.

**Example 2:**

Input:s = "(1)+((2))+(((<u>3</u>)))"
Output: 3

**解法**

**我們只需要知道VPS任一個字串的深度等於它之前的左括號個數 - 右括號個數 這樣即可。**

JAVA

class Solution {
    public int maxDepth(String s) {
        Stack<Character> stack = new Stack<>();
        char[] ch = s.toCharArray();
        int maxLevel = 0;
        for (char c: ch){
            if (c == '(') stack.add(c);
            else if (c == ')') stack.pop();
            int size = stack.size();
            maxLevel = Math.max(maxLevel, size);
        }
        return maxLevel;
    }
}