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678. Valid Parenthesis String

Medium
String
Dynamic Programming
Stack
Greedy
Solve on LeetCode View Solutions

Description

Given a string s containing only three types of characters: '(', ')' and '*', return true if s is valid.

The following rules define a valid string:

  • Any left parenthesis '(' must have a corresponding right parenthesis ')'.
  • Any right parenthesis ')' must have a corresponding left parenthesis '('.
  • Left parenthesis '(' must go before the corresponding right parenthesis ')'.
  • '*' could be treated as a single right parenthesis ')' or a single left parenthesis '(' or an empty string "".

 

Example 1:

Input: s = "()"
Output: true

Example 2:

Input: s = "(*)"
Output: true

Example 3:

Input: s = "(*))"
Output: true

 

Constraints:

  • 1 <= s.length <= 100
  • s[i] is '(', ')' or '*'.

Hints

Hint 1
Use backtracking to explore all possible combinations of treating '*' as either '(', ')', or an empty string. If any combination leads to a valid string, return true.
Hint 2
DP[i][j] represents whether the substring s[i:j] is valid.
Hint 3
Keep track of the count of open parentheses encountered so far. If you encounter a close parenthesis, it should balance with an open parenthesis. Utilize a stack to handle this effectively.
Hint 4
How about using 2 stacks instead of 1? Think about it.

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