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Generate Parentheses

**Problem Statement:** Given the required input arguments, write an efficient algorithm to solve the **Generate Parentheses** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge. **Hint / Expected Approach:** DFS: open if open<n, close if close<open **Edge Cases to Consider:** - (1) n = 0 - (2) n = 1 - (3) Very large n (exponential output)

Examples

Example 1
Input: 1
Output: ["()"]
Explanation: One pair
Example 2
Input: 2
Output: ["(())","()()"]
Explanation: Two pairs
Example 3
Input: 3
Output: ["((()))","(()())","(())()","()(())","()()()"]
Explanation: 5 combos

Constraints

  • ▪Input arguments are within valid ranges
  • ▪Optimize for execution speed
  • ▪Handle null/empty inputs gracefully

Watch Out For Edge Cases

  • ▪n = 0
  • ▪n = 1
  • ▪Very large n (exponential output)
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