Formatted question description: https://leetcode.ca/all/591.html

591. Tag Validator (Hard)

Given a string representing a code snippet, you need to implement a tag validator to parse the code and return whether it is valid. A code snippet is valid if all the following rules hold:

  1. The code must be wrapped in a valid closed tag. Otherwise, the code is invalid.
  2. A closed tag (not necessarily valid) has exactly the following format : <TAG_NAME>TAG_CONTENT</TAG_NAME>. Among them, <TAG_NAME> is the start tag, and </TAG_NAME> is the end tag. The TAG_NAME in start and end tags should be the same. A closed tag is valid if and only if the TAG_NAME and TAG_CONTENT are valid.
  3. A valid TAG_NAME only contain upper-case letters, and has length in range [1,9]. Otherwise, the TAG_NAME is invalid.
  4. A valid TAG_CONTENT may contain other valid closed tags, cdata and any characters (see note1) EXCEPT unmatched <, unmatched start and end tag, and unmatched or closed tags with invalid TAG_NAME. Otherwise, the TAG_CONTENT is invalid.
  5. A start tag is unmatched if no end tag exists with the same TAG_NAME, and vice versa. However, you also need to consider the issue of unbalanced when tags are nested.
  6. A < is unmatched if you cannot find a subsequent >. And when you find a < or </, all the subsequent characters until the next > should be parsed as TAG_NAME (not necessarily valid).
  7. The cdata has the following format : <![CDATA[CDATA_CONTENT]]>. The range of CDATA_CONTENT is defined as the characters between <![CDATA[ and the first subsequent ]]>.
  8. CDATA_CONTENT may contain any characters. The function of cdata is to forbid the validator to parse CDATA_CONTENT, so even it has some characters that can be parsed as tag (no matter valid or invalid), you should treat it as regular characters.

Valid Code Examples:

Input: "<DIV>This is the first line <![CDATA[<div>]]></DIV>"

Output: True

Explanation: 

The code is wrapped in a closed tag : <DIV> and </DIV>. 

The TAG_NAME is valid, the TAG_CONTENT consists of some characters and cdata. 

Although CDATA_CONTENT has unmatched start tag with invalid TAG_NAME, it should be considered as plain text, not parsed as tag.

So TAG_CONTENT is valid, and then the code is valid. Thus return true.


Input: "<DIV>>>  ![cdata[]] <![CDATA[<div>]>]]>]]>>]</DIV>"

Output: True

Explanation:

We first separate the code into : start_tag|tag_content|end_tag.

start_tag -> "<DIV>"

end_tag -> "</DIV>"

tag_content could also be separated into : text1|cdata|text2.

text1 -> ">>  ![cdata[]] "

cdata -> "<![CDATA[<div>]>]]>", where the CDATA_CONTENT is "<div>]>"

text2 -> "]]>>]"


The reason why start_tag is NOT "<DIV>>>" is because of the rule 6.
The reason why cdata is NOT "<![CDATA[<div>]>]]>]]>" is because of the rule 7.

Invalid Code Examples:

Input: "<A>  <B> </A>   </B>"
Output: False
Explanation: Unbalanced. If "<A>" is closed, then "<B>" must be unmatched, and vice versa.

Input: "<DIV>  div tag is not closed  <DIV>"
Output: False

Input: "<DIV>  unmatched <  </DIV>"
Output: False

Input: "<DIV> closed tags with invalid tag name  <b>123</b> </DIV>"
Output: False

Input: "<DIV> unmatched tags with invalid tag name  </1234567890> and <CDATA[[]]>  </DIV>"
Output: False

Input: "<DIV>  unmatched start tag <B>  and unmatched end tag </C>  </DIV>"
Output: False

Note:

  1. For simplicity, you could assume the input code (including the any characters mentioned above) only contain letters, digits, '<','>','/','!','[',']' and ' '.

Solution 1. Automaton

I did similar job before, so the first thing came into my mind is automaton. Maybe it’s not neat, but the tasks in each state is quite clear.

// OJ: https://leetcode.com/problems/tag-validator
// Time: O(N)
// Space: O(H)
class Solution {
private:
  enum State {
    INIT,
    START_TAG,
    TAG_CONTENT,
    END_TAG,
    CDATA
  };
public:
  bool isValid(string code) {
    stack<string> s;
    State state = INIT;
    string startTag, endTag;
    int i = 0;
    while (i < code.size()) {
      switch(state) {
        case INIT: {
          if (code[i] != '<') return false;
          ++i; // <
          state = START_TAG;
          break;
        }
        case START_TAG: {
          while (i < code.size() && isupper(code[i])) {
            startTag += code[i++];
          }
          if (i >= code.size() || code[i] != '>' || startTag.empty() || startTag.size() > 9) return false;
          s.push(startTag);
          ++i; // >
          state = TAG_CONTENT;
          break;
        }
        case TAG_CONTENT: {
          while (i < code.size() && code[i] != '<') ++i;
          if (i >= code.size() || code[i] != '<') return false;
          ++i; // <
          if (i < code.size() && code[i] == '/') {
              ++i; // /
              state = END_TAG;
              endTag.clear();
          } else if (i < code.size() && code[i] == '!') {// <![CDATA[
            string mark = "![CDATA[";
            int j = 0;
            while (i < code.size() && j < mark.size() && code[i] == mark[j]) ++i, ++j;
            if (j < mark.size()) return false;
            state = CDATA;
          } else {
            state = START_TAG;
            startTag.clear();
          }
          break;
        }
        case END_TAG: {
          while (i < code.size() && isupper(code[i])) {
            endTag += code[i++];
          }
          if (i >= code.size() || code[i] != '>' || endTag.empty() || s.empty() || s.top() != endTag) return false;
          s.pop();
          ++i; // >
          if (s.empty() && i < code.size()) return false;
          state = TAG_CONTENT;
          break;
        }
        case CDATA: {
          int end = code.find("]]>", i);
          if (end == string::npos) return false;
          i = end + 3;
          state = TAG_CONTENT;
          break;
        }
      }
    }
    return s.empty();
  }
};

Java

  • public class Solution {
        public boolean isValid(String code) {
            if (code == null || code.length() == 0)
                return false;
            Stack<String> stack = new Stack<String>();
            int length = code.length();
            int index = 0;
            while (index < length) {
                if (index > 0 && stack.isEmpty())
                    return false;
                if (index + 9 <= length && code.substring(index, index + 9).equals("<![CDATA[")) {
                    index += 9;
                    while (index <= length - 3 && !code.substring(index, index + 3).equals("]]>"))
                        index++;
                    if (index > length - 3)
                        return false;
                    else
                        index += 2;
                } else if (code.substring(index, index + 2).equals("</")) {
                    index += 2;
                    int start = index;
                    while (index < length && code.charAt(index) != '>')
                        index++;
                    if (index >= length)
                        return false;
                    String tag = code.substring(start, index);
                    if (stack.isEmpty() || !stack.peek().equals(tag))
                        return false;
                    stack.pop();
                } else if (code.charAt(index) == '<') {
                    index++;
                    int start = index;
                    while (index < length && code.charAt(index) != '>')
                        index++;
                    if (index >= length || index == start || index - start > 9)
                        return false;
                    for (int i = start; i < index; i++) {
                        char c = code.charAt(i);
                        if (c < 'A' || c > 'Z')
                            return false;
                    }
                    String tag = code.substring(start, index);
                    stack.push(tag);
                }
                index++;
            }
            return stack.isEmpty();
        }
    }
    
  • // OJ: https://leetcode.com/problems/tag-validator
    // Time: O(N)
    // Space: O(H)
    class Solution {
    private:
      enum State {
        INIT,
        START_TAG,
        TAG_CONTENT,
        END_TAG,
        CDATA
      };
    public:
      bool isValid(string code) {
        stack<string> s;
        State state = INIT;
        string startTag, endTag;
        int i = 0;
        while (i < code.size()) {
          switch(state) {
            case INIT: {
              if (code[i] != '<') return false;
              ++i; // <
              state = START_TAG;
              break;
            }
            case START_TAG: {
              while (i < code.size() && isupper(code[i])) {
                startTag += code[i++];
              }
              if (i >= code.size() || code[i] != '>' || startTag.empty() || startTag.size() > 9) return false;
              s.push(startTag);
              ++i; // >
              state = TAG_CONTENT;
              break;
            }
            case TAG_CONTENT: {
              while (i < code.size() && code[i] != '<') ++i;
              if (i >= code.size() || code[i] != '<') return false;
              ++i; // <
              if (i < code.size() && code[i] == '/') {
                  ++i; // /
                  state = END_TAG;
                  endTag.clear();
              } else if (i < code.size() && code[i] == '!') {// <![CDATA[
                string mark = "![CDATA[";
                int j = 0;
                while (i < code.size() && j < mark.size() && code[i] == mark[j]) ++i, ++j;
                if (j < mark.size()) return false;
                state = CDATA;
              } else {
                state = START_TAG;
                startTag.clear();
              }
              break;
            }
            case END_TAG: {
              while (i < code.size() && isupper(code[i])) {
                endTag += code[i++];
              }
              if (i >= code.size() || code[i] != '>' || endTag.empty() || s.empty() || s.top() != endTag) return false;
              s.pop();
              ++i; // >
              if (s.empty() && i < code.size()) return false;
              state = TAG_CONTENT;
              break;
            }
            case CDATA: {
              int end = code.find("]]>", i);
              if (end == string::npos) return false;
              i = end + 3;
              state = TAG_CONTENT;
              break;
            }
          }
        }
        return s.empty();
      }
    };
    
  • import string
    
    
    class Solution(object):
      def isValid(self, code):
        """
        :type code: str
        :rtype: bool
        """
    
        def getTokenStartsAt(start):
          for i in range(start, len(code)):
            if code[i] == ">":
              break
          return code[start:i + 1]
    
        def isTagsMatched(left, right):
          return len(left) + 1 == len(right) and left[1:] == right[2:]
    
        def isClosedTag(tag):
          return tag[1] == "/"
    
        def isCDATATag(i):
          return code.startswith("<![CDATA[", i)
    
        def isTag(tag):
          if len(tag) < 3:
            return False
          if tag[-1] != ">":
            return False
    
          tag = tag[1:-1]
          if tag[0] == "/":
            tag = tag[1:]
          if not 1 <= len(tag) <= 9:
            return False
          for c in tag:
            if c not in string.ascii_uppercase:
              return False
          return True
    
        if code[0] != "<":
          return False
        tagLen = 0
        stack = []
        i = 0
        while i < len(code):
          if code[i] == "<":
            if isCDATATag(i):
              if not stack:
                return False
              while i < len(code) - 7 and not code.startswith("]]>", i):
                i += 1
              if code.startswith("]]>", i):
                i += 3
                continue
              else:
                return False
            else:
              token = getTokenStartsAt(i)
              if not isTag(token):
                return False
              if not isClosedTag(token):
                stack.append(token)
              else:
                if not stack:
                  return False
                if isTagsMatched(stack[-1], token):
                  stack.pop()
                  if not stack and i + len(token) < len(code):
                    return False
                else:
                  return False
              i += len(token)
          else:
            i += 1
        return not stack
    
    

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