Valid Parentheses

Problem

Given a string containing only (, ), {, }, [ and ], decide if every opening bracket is closed by the same type of bracket and brackets close in the correct order.

Constraints

• 1 ≤ s.length ≤ 10⁴
• s consists of brackets only

Approach — Stack

This is a Stack problem. The idea: scan the input once, pushing work onto a stack and popping when the top can be resolved, so the stack always reflects what's still open. Work through the reference code below line by line, then re-derive it yourself in the editor — that's how the pattern sticks.

Complexity: O(n) time, O(n) space.

Solution code

Python

class Solution:
    def isValid(self, s):
        pairs = {')': '(', ']': '[', '}': '{'}
        st = []
        for c in s:
            if c in pairs:
                if not st or st.pop() != pairs[c]:
                    return False
            else:
                st.append(c)
        return not st

Java

import java.util.HashMap;
import java.util.Stack;

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<>();

    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.empty();
  }
}

Practice it

Reading a solution isn't the same as being able to write it under pressure. Open this problem in the in-browser editor, hide the solution, and solve it from scratch — your code runs against real test cases instantly.