<p>Given a string <code>licensePlate</code> and an array of strings <code>words</code>, find the <strong>shortest completing</strong> word in <code>words</code>.</p>

<p>A <strong>completing</strong> word is a word that <strong>contains all the letters</strong> in <code>licensePlate</code>. <strong>Ignore numbers and spaces</strong> in <code>licensePlate</code>, and treat letters as <strong>case insensitive</strong>. If a letter appears more than once in <code>licensePlate</code>, then it must appear in the word the same number of times or more.</p>

<p>For example, if <code>licensePlate</code><code> = &quot;aBc 12c&quot;</code>, then it contains letters <code>&#39;a&#39;</code>, <code>&#39;b&#39;</code> (ignoring case), and <code>&#39;c&#39;</code> twice. Possible <strong>completing</strong> words are <code>&quot;abccdef&quot;</code>, <code>&quot;caaacab&quot;</code>, and <code>&quot;cbca&quot;</code>.</p>

<p>Return <em>the shortest <strong>completing</strong> word in </em><code>words</code><em>.</em> It is guaranteed an answer exists. If there are multiple shortest <strong>completing</strong> words, return the <strong>first</strong> one that occurs in <code>words</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> licensePlate = &quot;1s3 PSt&quot;, words = [&quot;step&quot;,&quot;steps&quot;,&quot;stripe&quot;,&quot;stepple&quot;]
<strong>Output:</strong> &quot;steps&quot;
<strong>Explanation:</strong> licensePlate contains letters &#39;s&#39;, &#39;p&#39;, &#39;s&#39; (ignoring case), and &#39;t&#39;.
&quot;step&quot; contains &#39;t&#39; and &#39;p&#39;, but only contains 1 &#39;s&#39;.
&quot;steps&quot; contains &#39;t&#39;, &#39;p&#39;, and both &#39;s&#39; characters.
&quot;stripe&quot; is missing an &#39;s&#39;.
&quot;stepple&quot; is missing an &#39;s&#39;.
Since &quot;steps&quot; is the only word containing all the letters, that is the answer.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> licensePlate = &quot;1s3 456&quot;, words = [&quot;looks&quot;,&quot;pest&quot;,&quot;stew&quot;,&quot;show&quot;]
<strong>Output:</strong> &quot;pest&quot;
<strong>Explanation:</strong> licensePlate only contains the letter &#39;s&#39;. All the words contain &#39;s&#39;, but among these &quot;pest&quot;, &quot;stew&quot;, and &quot;show&quot; are shortest. The answer is &quot;pest&quot; because it is the word that appears earliest of the 3.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= licensePlate.length &lt;= 7</code></li>
	<li><code>licensePlate</code> contains digits, letters (uppercase or lowercase), or space <code>&#39; &#39;</code>.</li>
	<li><code>1 &lt;= words.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 15</code></li>
	<li><code>words[i]</code> consists of lower case English letters.</li>
</ul>

class Solution {
 public:
  string shortestCompletingWord(string licensePlate, vector<string>& words) {
    string ans(16, '.');
    vector<int> count(26);

    for (const char c : licensePlate)
      if (isalpha(c))
        ++count[tolower(c) - 'a'];

    for (const string& word : words)
      if (word.length() < ans.length() && isComplete(count, getCount(word)))
        ans = word;

    return ans;
  }

 private:
  // Returns true if c1 is a subset of c2.
  bool isComplete(const vector<int>& c1, const vector<int> c2) {
    for (int i = 0; i < 26; ++i)
      if (c1[i] > c2[i])
        return false;
    return true;
  }

  vector<int> getCount(const string& word) {
    vector<int> count(26);
    for (const char c : word)
      ++count[c - 'a'];
    return count;
  }
};
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