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Valid Parentheses Combinations

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 10

Write a C# program to generate all combinations of well-formed parentheses for a given number of pairs n. Implement the GenerateParenthesis(int n) function that returns a list of all possible valid parenthesis combinations.

Example 1
    
  
  • Input: n = 3
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  • Output: ["((()))", "(()())", "(())()", "()(())", "()()()"]
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  • Explanation:
    
      
      
    • These are all the valid combinations of 3 pairs of parentheses.
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    •
Example 2
    
  
  • Input: n = 2
    • 
  
  • Output: ["(())", "()()"]
    • 
  
  • Explanation:
    
      
      
    • These are all the valid combinations of 2 pairs of parentheses.
      • 
    
    
  
    •
Constraints
    
  
  • 1 <= n <= 8
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  • Each generated string should have exactly 2*n characters
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  • Each string will only contain '(' and ')' characters
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  • All generated strings must be valid (properly closed) parentheses combinations
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  • Time Complexity: O(4^n / sqrt(n))
    • 
  
  • Space Complexity: O(n)
    •
RecursionBacktracking FacebookDropbox
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Hint
Solution

Solution Hints

    
  
  • Use backtracking/recursion to generate all possibilities
    • 
  
  • Keep track of open and closed parentheses counts
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  • Only add an opening parenthesis if you haven't used all n
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  • Only add a closing parenthesis if it won't create an invalid combination
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  • When both open and closed counts reach n, add the current string to the result list
    •

Steps to solve by this approach:

 Step 1: Create a recursive backtracking function that builds strings character by character

 Step 2: Track the number of open and closed parentheses already used

 Step 3: Only add an opening parenthesis if we haven't used all n of them yet

 Step 4: Only add a closing parenthesis if there are more open than closed parentheses

 Step 5: When the string reaches length 2*n, add it to our result list

 Step 6: Start with an empty string and backtrack to generate all valid combinations

 Step 7: Return the final list of all valid parentheses strings

Submitted Code :