Problem Statement

Determine if an input string containing only the characters '(', ')', '{', '}', '[', and ']' is valid. A string is considered valid if:

1. Open brackets must be closed by the same type of brackets.
2. Open brackets must be closed in the correct order.
3. Each close bracket has a corresponding open bracket of the same type.

Examples

1. • Input: "(]"
   • Expected Output: false
   • Justification: The opening parenthesis '(' is not closed by its corresponding closing parenthesis.
2. • Input: "{[]}"
   • Expected Output: true
   • Justification: The string contains pairs of opening and closing brackets in the correct order.
3. • Input: "[{]}"
   • Expected Output: false
   • Justification: The opening square bracket '[' is closed by a curly brace '}', which is incorrect.

Constraints:

• 1 <= s.length <= 10⁴
• s consists of parentheses only '()[]{}'.

Solution

• Initialization:
  • Start with an empty stack.
  • For every bracket in the input string:
    • If the bracket is an opening bracket ('(', '{', '['), push it onto the stack.
    • If the bracket is a closing bracket (')', '}', ']'):
      • If the stack is empty, return false.
      • Pop the top of the stack and check if it matches the corresponding opening bracket.
• Validation:
  • If the current closing bracket doesn't match the top of the stack, return false.
  • If the stack is not empty after processing all brackets in the string, return false.
• Final Output:
  • If the stack is empty at the end, return true, indicating that the string has valid parentheses.

Algorithm Walkthrough

Using the input "{[]}":

• Start with an empty stack.
• Encounter '{', push onto the stack.
• Encounter '[', push onto the stack.
• Encounter ']', pop from the stack and check if the popped character is '['. It matches, so continue.
• Encounter '}', pop from the stack and check if the popped character is '{'. It matches.
• The string is processed and the stack is empty, so return true.

Complexity Analysis

• Time Complexity: O(n) where n is the length of the string. Each character is processed once.
• Space Complexity: O(n) in the worst case when all characters are opening brackets.