Count the Number of Consistent Strings LeetCode solution in C++

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class Solution {
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 public:
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  int countConsistentStrings(string allowed, vector<string> &words) {
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    // support variable
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    int res = words.size();
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    bool alpha[26] = {};
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    // populating alpha
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    for (char c : allowed) alpha[c - 'a'] = true;
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    // parsing all the words to see if each character is in alpha
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    for (string word : words) {
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      // in case we find an unallowed character, we decrease res and break
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      for (char c : word)
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        if (!alpha[c - 'a']) {
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          res--;
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          break;
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        }
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    }
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    return res;
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  }
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};