591

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

// OJ: https://leetcode.com/problems/tag-validator
// Author: github.com/lzl124631x
// 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();
  }
};