class Solution {

  // Hash table that takes care of the mappings.

  private HashMap<Character, Character> mappings;

  // Initialize hash map with mappings. This simply makes the code easier to read.

  public Solution() {

    this.mappings = new HashMap<Character, Character>();

    this.mappings.put(')', '(');

    this.mappings.put('}', '{');

    this.mappings.put(']', '[');

  }

  public boolean isValid(String s) {

    // Initialize a stack to be used in the algorithm.

    Stack<Character> stack = new Stack<Character>();

    for (int i = 0; i < s.length(); i++) {

      char c = s.charAt(i);

      // If the current character is a closing bracket.

      if (this.mappings.containsKey(c)) {

        // Get the top element of the stack. If the stack is empty, set a dummy value of '#'

        char topElement = stack.empty() ? '#' : stack.pop();

        // If the mapping for this bracket doesn't match the stack's top element, return false.

        if (topElement != this.mappings.get(c)) {

          return false;

        }

      } else {

        // If it was an opening bracket, push to the stack.

        stack.push(c);

      }

    }

    // If the stack still contains elements, then it is an invalid expression.

    return stack.isEmpty();

  }

}