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Invalid Parentheses

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to remove the minimum number of invalid parentheses to make the input string valid. Return all possible valid expressions. A valid expression should have properly matched parentheses with each opening parenthesis '(' having a corresponding closing parenthesis ')' and they should be in correct order.

Example 1
    
      
  • Input: s = "()())"
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  • Output: ["()()", "(())"]
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  • Explanation: 
        Step 1: Input has 3 opening and 3 closing parentheses, but one extra closing
        Step 2: Remove one closing parenthesis to make it valid
        Step 3: Two possibilities: remove 3rd ')' → "()()" or remove 5th ')' → "(())"
        Step 4: Both results are valid expressions
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Example 2
    
      
  • Input: s = "((("
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  • Output: [""]
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  • Explanation: 
        Step 1: Input has 3 opening parentheses with no closing ones
        Step 2: All opening parentheses must be removed to make it valid
        Step 3: Only empty string remains as valid expression
        Step 4: Therefore, output is [""]
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Constraints
    
      
  • 1 <= s.length <= 25
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  • s consists of lowercase English letters and parentheses '(' and ')'
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  • There will be at most 20 parentheses in s
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  • Time Complexity: O(2^n) where n is number of parentheses
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  • Space Complexity: O(n) for recursion stack
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Hint
Solution

Solution Hints

    
      
  • Count the number of invalid opening and closing parentheses
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  • Use backtracking to try removing different combinations of parentheses
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  • For each position, decide whether to keep or remove the parenthesis
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  • Check validity of expression by counting balanced parentheses
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  • Use a set or duplicate checking to avoid returning duplicate results
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  • Prune branches early if removing more parentheses than needed
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Steps to solve by this approach:

 Step 1: Count the number of invalid opening and closing parentheses that need to be removed
 Step 2: Use backtracking to explore all possible combinations of removing parentheses
 Step 3: At each position, decide whether to keep or remove the current character
 Step 4: Track the count of opening and closing parentheses to ensure balance
 Step 5: When reaching the end of string, check if all invalid parentheses are removed and expression is balanced
 Step 6: Store valid expressions while avoiding duplicates
 Step 7: Return all unique valid expressions found through backtracking

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