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3Sum and Parentheses Generation

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Problem

Licious may need one algorithmic service to process numeric combinations and construct valid packaging expression patterns. Implement both operations: find every unique triplet that sums to zero, and generate every valid sequence containing n pairs of parentheses.

Formal Specification

Implement solve_3sum_and_parentheses(nums, n):

  1. nums is a list of integers. Return all unique triplets [a, b, c] such that a + b + c == 0. Each triplet must be sorted in nondecreasing order, and the collection must not contain duplicates.
  2. n is a nonnegative integer. Return all strings containing exactly n opening and n closing parentheses that are balanced and properly nested.

Return a dictionary with keys triplets and parentheses. The triplets should be produced in lexicographic order, and parentheses should be generated with opening parentheses attempted before closing parentheses.

Constraints

  • 3 <= len(nums) <= 3000
  • -10^5 <= nums[i] <= 10^5
  • 0 <= n <= 8
  • Triplets must be unique and internally sorted
  • The parentheses output contains the Catalan number C(n) of strings

Function Signature

def solve_3sum_and_parentheses(nums, n):
Your solutionPython 3
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