Given a string `s` containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid (Valid Parentheses).

Optimal Stack-Based Approach & Code:
- Use a Last-In-First-Out (LIFO) stack to match closing brackets with the most recently opened bracket.

def is_valid_parentheses(s: str) -> bool:
    stack = []
    bracket_map = {')': '(', '}': '{', ']': '['}
    for char in s:
        if char in bracket_map:
            top = stack.pop() if stack else '#'
            if bracket_map[char] != top:
                return False
        else:
            stack.append(char)
    return len(stack) == 0

Complexity & Key Logic:
- Time Complexity: O(N) scanning the string of length N once.
- Space Complexity: O(N) worst-case stack space when all characters are opening brackets.
- Algorithm Details:
- Opening brackets are pushed onto the stack.
- When encountering a closing bracket, verify that the stack is non-empty and that the popped opening bracket matches the expected pair.
- After processing the entire string, the stack must be completely empty for the string to be valid.