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A valid parentheses string is either empty ("")
, "(" + A + ")"
, or A + B
, where A
and B
are valid parentheses strings, and +
represents string concatenation. For example, ""
, "()"
, "(())()"
, and "(()(()))"
are all valid parentheses strings.
A valid parentheses string S
is primitive if it is nonempty, and there does not exist a way to split it into S = A+B
, with A
and B
nonempty valid parentheses strings.
Given a valid parentheses string S
, consider its primitive decomposition: S = P_1 + P_2 + ... + P_k
, where P_i
are primitive valid parentheses strings.
Return S
after removing the outermost parentheses of every primitive string in the primitive decomposition of S
.
Example 1:
Input: "(()())(())"
Output: "()()()"
Explanation:
The input string is "(()())(())", with primitive decomposition "(()())" + "(())".
After removing outer parentheses of each part, this is "()()" + "()" = "()()()".
Example 2:
Input: "(()())(())(()(()))"
Output: "()()()()(())"
Explanation:
The input string is "(()())(())(()(()))", with primitive decomposition "(()())" + "(())" + "(()(()))".
After removing outer parentheses of each part, this is "()()" + "()" + "()(())" = "()()()()(())".
Example 3:
Input: "()()"
Output: ""
Explanation:
The input string is "()()", with primitive decomposition "()" + "()".
After removing outer parentheses of each part, this is "" + "" = "".
Note:
S.length <= 10000
S[i]
is "("
or ")"
S
is a valid parentheses string
[Stack]
Hints
Hint 1
Can you find the primitive decomposition? The number of ( and ) characters must be equal.