N Pairs Parentheses

Introduction

In computer science, the problem of generating all valid combinations of n-pairs of parentheses is a classic problem. It is often used as an example problem in computer science courses and coding interviews.

Skills Graph

N Pairs Parentheses

Problem

The problem is to find all valid combinations of n-pairs of parentheses. A valid combination is one in which each opening parenthesis has a corresponding closing parenthesis and the pairs of parentheses are properly nested. For example, the following are valid combinations of 3-pairs of parentheses:

• ((()))
• (()())
• (())()
• ()(())
• ()()()

The following are not valid combinations of 3-pairs of parentheses:

• )()(
• ((()
• ))((
• ()()()

Requirements

To solve this problem, we need to answer the following questions:

• Is the input an integer representing the number of pairs?
  • Yes, the input is an integer representing the number of pairs.
• Can we assume the inputs are valid?
  • No, we cannot assume the inputs are valid.
• Is the output a list of valid combinations?
  • Yes, the output is a list of valid combinations.
• Should the output have duplicates?
  • No, the output should not have duplicates.
• Can we assume this fits memory?
  • Yes, we can assume this fits memory.

Example Usage

The following are example usages of the function:

• None -> Exception
• Negative -> Exception
• 0 -> []
• 1 -> ['()']
• 2 -> ['(())', '()()']
• 3 -> ['((()))', '(()())', '(())()', '()(())', '()()()']

Summary

In summary, the problem of generating all valid combinations of n-pairs of parentheses is a classic problem in computer science. To solve this problem, we need to find all valid combinations of n-pairs of parentheses, where each opening parenthesis has a corresponding closing parenthesis and the pairs of parentheses are properly nested. The output should be a list of valid combinations without duplicates.