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 withB
), whereA
andB
are VPS's, or - It can be written as
(A)
, whereA
is a VPS.
We can similarly define the nesting depth depth(S)
of any VPS S
as follows:
-
depth("") = 0
-
depth(C) = 0
, whereC
is a string with a single character not equal to"("
or")"
. -
depth(A + B) = max(depth(A), depth(B))
, whereA
andB
are VPS's. -
depth("(" + A + ")") = 1 + depth(A)
, whereA
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
Constraints:
-
1 <= s.length <= 100
-
s
consists of digits0-9
and characters'+'
,'-'
,'*'
,'/'
,'('
, and')'
. - It is guaranteed that parentheses expression
s
is a VPS.
SOLUTION:
class Solution:
def maxDepth(self, s: str) -> int:
depth = 0
mdepth = 0
for c in s:
if c == "(":
depth += 1
if c == ")":
depth -= 1
mdepth = max(mdepth, depth)
return mdepth
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