1249. Minimum Remove to Make Valid Parentheses

https://leetcode.com/problems/minimum-remove-to-make-valid-parentheses/

Given a string s of '(' , ')' and lowercase English characters. 
Your task is to remove the minimum number of parentheses ( '(' or ')', in any positions ) so that the resulting parentheses string is valid and return any valid string.
Formally, a parentheses string is valid if and only if:
  • It is the empty string, contains only lowercase characters, or
  • It can be written as AB (A concatenated with B), where A and B are valid strings, or
  • It can be written as (A), where A is a valid string.

Example 1:
Input: s = "lee(t(c)o)de)"
Output: "lee(t(c)o)de"
Explanation: "lee(t(co)de)" , "lee(t(c)ode)" would also be accepted.
Example 2:
Input: s = "a)b(c)d"
Output: "ab(c)d"
Example 3:
Input: s = "))(("
Output: ""
Explanation: An empty string is also valid.
Example 4:
Input: s = "(a(b(c)d)"
Output: "a(b(c)d)"

Constraints:
  • 1 <= s.length <= 10^5
  • s[i] is one of  '(' , ')' and lowercase English letters.
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Intuition
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Can be solved with one stack tracking the unbalanced parenthesis index
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Also possible with two data structures
Track the mismatched open and closed parenthesis separately.
Extra open can be tracked with a stack of open parenthesis
Extra closed can be tracked in a set

Work through the string backwards since stack is LIFO
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Time - O(n)
Space - O(n)
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Related problems
1021-remove-outermost-parentheses
301-remove-invalid-parentheses
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