Valid Parenthese

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

The brackets must close in the correct order, "()" and "()[]{}" are all valid but "(]" and "([)]" are not.

Method 1: Stack

Analysis

We can use a stack to push the left parentheses into stack and pop the top element from the stack if the new character is right parentheses.

There is a small optimization. If the element in the stack is more than the number of left characters, we can directly return false, since it is impossible to be valid.

Corner Case

1. more right parenthese than left parentheses, stack may become empty and poping elemenet can cause exception.
2. less right parenthese, at last, stack may not be empty

Complexity

Time: O(N)

Space: O(N)

Code

Java

public class Solution {
  /**
   * @param s A string
   * @return whether the string is a valid parentheses
   */
  public boolean isValidParentheses(String s) {
    Stack<Character> stack = new Stack<>();
    for (char c : s.toCharArray()) {
      if (c == '(' || c == '[' || c == '{') {
        stack.push(c);
      } else if (stack.isEmpty() || !isMatch(stack.pop(), c)) {
        return false;
      }
    }
    return stack.isEmpty();
  }

  private boolean isMatch(char c1, char c2) {
    if ((c1 == '(' && c2 == ')') || (c1 == '[' && c2 == ']') 
        || (c1 == '{' && c2 == '}')) {
      return true;
    } 
    return false;
  }
}

2. Extension

This is an interview question I had with BloomReach. The string can contains other characters in addition to braces. For example "if main() {}" is valid.

In addition, there are many different types of braces.

Analysis

Since there are many different types of braces, it is important to make the code easy to change. We can put all possible mapping of braces in a CSV file and read it into a map.

Complexity

Time: O(N)

Space: O(N), there are some additional costs to store vaild types of parentheses.

Code

Java

public class Solution {
  private static final Map<Character, Character> leftToRightBraces = new HashMap<>();
  private static final Set<Character> leftBracesSet = new HashSet<>();
  private static final Set<Character> rightBracesSet = new HashSet<>();

  static {
    // It is possible to change this to read from, for example a CSV file, to get 
    // more kinds of braces. The benefit of this is that you don't need to change 
    // other code. Simply changes the CSV file, and anything else remains the same. 
    leftToRightBraces.put('(', ')');
    leftToRightBraces.put('[', ']');
    leftToRightBraces.put('{', '}');
    for (char c : new char[] {'(', '[', '{'}) {
      leftBracesSet.add(c);
    }
    for (char c : new char[] {')', ']', '}'}) {
      rightBracesSet.add(c);
    }
  }

  public boolean isValidParentheses(String s) {
    Stack<Character> stack = new Stack<>();
    for (char c : s.toCharArray()) {
      if (isLeftBrace(c)) {
        stack.push(c);
      } else if (isRightBrace(c)) {
        if (stack.isEmpty() || !isMatch(stack.pop(), c)) {
          return false;
        }
      }
    }
    return stack.isEmpty();
  }

  private boolean isLeftBrace(char c) {
    return leftBracesSet.contains(c);
  }

  private boolean isRightBrace(char c) {
    return rightBracesSet.contains(c);
  }

  private boolean isMatch(char c1, char c2) {
    if (leftToRightBraces.containsKey(c1)) {
      return leftToRightBraces.get(c1) == c2;
    }
    return false;
  }
}