This is a very poorly worded problem in my opinion, and the given test cases are unclear / incomplete.

There are two things that you need to check for as you iterate through the list of original input words:

1. Is the current input word a prefix of any of the previously checked words? If yes, print "BAD SET" and print the current word (which is a prefix, this is what I think is very unclear from the description)

2. Is a prefix of the current word one of the words I've previously processed? If yes, print "BAD SET" and print the current word (not the prefix).

To check these two conditions I used a std::multiset to keep track of the input words (to be able to detect duplicate words), and a std::set to keep track of all previous prefixes to check input words against (I don't care about duplicates here, so a normal set will work just fine).

See my solution in C++14:

void noPrefix(vector<string> words) {

    multiset<string> words_to_check; // set of words to add to as we process the original list, this must be a multiset so we can detect duplicate words

    set<string> all_prefixes; // set of all prefixes of words we've already checked, this allows us to see if a new word in the list is a prefix to a word we've already checked

    // cycle through all the words
    for(auto w : words)
    {
        // check if current word is a prefix of other words
        if(all_prefixes.find(w) != all_prefixes.end())
        {
            // we found the prefix in the original word set
            cout << "BAD SET" << endl;
            cout << w << endl;
            return;
        }

        // check all 'prefixes' of current word in words_to_check set
        string prefix = w;
        while (!prefix.empty()) {
            // insert each prefix in list of prefixes to check future words against
            all_prefixes.insert(prefix);

            // check to see if the current prefix matches a word we've seen before
            if(words_to_check.find(prefix) != words_to_check.end();
            {
                // we found the prefix in the original word set
                cout << "BAD SET" << endl;
                cout << w << endl;
                return;
            } else {
                // remove one character from back of prefix, creating a new prefix
                prefix.pop_back();
            }
        }
        // append the most recently checked word to my list of full words to check on future prefixes
        words_to_check.insert(w);
    }
    // if we've checked every word in the original list and not found any prefixes, we must have a good set
    cout << "GOOD SET" << endl;
}