Implement palindrome check and valid parentheses

You have 20–25 minutes per problem. Implement the following two functions and be prepared to explain your approach and time/space complexity.

Problem 1 — Palindrome Check

Write a function that determines whether a given string is a palindrome.

• A string is a palindrome if it reads the same forward and backward.
• Compare characters exactly as they appear (no case folding and no ignoring punctuation/whitespace unless you explicitly state and implement it).

Function signature (example):

• bool is_palindrome(s: str)

Input:

• s : a string (may be empty)

Output:

• true if s is a palindrome, otherwise false

Examples:

• "abba" -> true
• "abc" -> false
• "" -> true

Problem 2 — Valid Parentheses Sequence

Write a function that checks whether a string containing only parentheses characters is valid.

A string is valid if:

1. Every opening bracket has a corresponding closing bracket of the same type.
2. Brackets close in the correct order.

Assume the allowed bracket types are: (), [], {}.

Function signature (example):

• bool is_valid_parentheses(s: str)

Input:

• s : a string consisting only of characters in ()[]{} (may be empty)

Output:

• true if s is valid, otherwise false

Examples:

• "()" -> true
• "([]){}" -> true
• "(]" -> false
• "([)]" -> false
• "" -> true

Documentation requirement

For each function, include a docstring with:

• Description
• Inputs/Outputs
• Callouts (assumptions, edge cases, complexity)