3Sum and Parentheses Generation

HardPython

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):

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.
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):

Formal Specification

Implement solve_3sum_and_parentheses(nums, n):

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.
n is a nonnegative integer. Return all strings containing exactly n opening and n closing parentheses that are balanced and properly nested.