Solve two array and string problems

You will solve two independent coding tasks.

Problem 1: Generate All Subsets of a Set

You are given an integer array nums containing n distinct elements.

Return all possible subsets (the power set) of nums.

• A subset can be of any size from 0 to n.
• The order of subsets in the output does not matter.
• The order of elements inside a subset also does not matter.

Example

Input:

• nums = [1, 2, 3]

One valid output (order may differ):

• [
  [],
  [1],
  [2],
  [3],
  [1, 2],
  [1, 3],
  [2, 3],
  [1, 2, 3]
  ]
  

Constraints

• 1 <= n <= 20
• -10^9 <= nums[i] <= 10^9
• All nums[i] are distinct.

You may return the result in any order.

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Problem 2: Validate Parentheses in a Noisy String

You are given a string s that may contain:

• the characters '(' and ')', and
• any other characters (letters, digits, punctuation, etc.).

A string is considered parentheses-valid if, after ignoring all non-parenthesis characters, the remaining sequence of '(' and ')' is a valid parentheses sequence:

• Every opening parenthesis '(' has a corresponding closing parenthesis ')'.
• Parentheses are properly nested.

Implement a function that returns true if s is parentheses-valid, and false otherwise.

Examples

1. Input: s = "a(b)c"

   • Ignoring non-parenthesis characters, we get "()" which is valid.
   • Output: true.

2. Input: s = "(a(b)c"

   • Ignoring non-parenthesis characters, we get "(()" which is not valid.
   • Output: false.

3. Input: s = "ab)c(d)e"

   • Ignoring non-parenthesis characters, we get ")()" which is not valid.
   • Output: false.

Constraints

• 1 <= len(s) <= 10^5
• s may contain any printable ASCII characters.