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. --- ### 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.