<p>Two strings, <code>X</code> and <code>Y</code>, are considered similar if either they are identical or we can make them equivalent by swapping at most two letters (in distinct positions) within the string <code>X</code>.</p>

<p>For example, <code>&quot;tars&quot;</code>&nbsp;and <code>&quot;rats&quot;</code>&nbsp;are similar (swapping at positions <code>0</code> and <code>2</code>), and <code>&quot;rats&quot;</code> and <code>&quot;arts&quot;</code> are similar, but <code>&quot;star&quot;</code> is not similar to <code>&quot;tars&quot;</code>, <code>&quot;rats&quot;</code>, or <code>&quot;arts&quot;</code>.</p>

<p>Together, these form two connected groups by similarity: <code>{&quot;tars&quot;, &quot;rats&quot;, &quot;arts&quot;}</code> and <code>{&quot;star&quot;}</code>.&nbsp; Notice that <code>&quot;tars&quot;</code> and <code>&quot;arts&quot;</code> are in the same group even though they are not similar.&nbsp; Formally, each group is such that a word is in the group if and only if it is similar to at least one other word in the group.</p>

<p>We are given a list <code>strs</code> of strings where every string in <code>strs</code> is an anagram of every other string in <code>strs</code>. How many groups are there?</p>

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

<pre>
<strong>Input:</strong> strs = [&quot;tars&quot;,&quot;rats&quot;,&quot;arts&quot;,&quot;star&quot;]
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> strs = [&quot;omv&quot;,&quot;ovm&quot;]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= strs.length &lt;= 300</code></li>
	<li><code>1 &lt;= strs[i].length &lt;= 300</code></li>
	<li><code>strs[i]</code> consists of lowercase letters only.</li>
	<li>All words in <code>strs</code> have the same length and are anagrams of each other.</li>
</ul>

class Solution {
public:
    int numSimilarGroups(vector<string>& strs) {
        unordered_set<string> set(strs.begin(), strs.end());
        int count = 0;
        while (!set.empty()) {
            string s(*set.begin());
            set.erase(set.begin());
            bfs(set, s);
            ++count;
        }
        return count;
    }

    bool similar(const string& a, const string& b) {
        int counts[26] = {}, mismatches = 0;
        for (size_t i = 0; i < a.size(); ++i) {
            if (a[i] != b[i]) ++mismatches;
            counts[a[i] - 'a']++;
            counts[b[i] - 'a']--;
        }
        
        for (int count : counts)
            if (count != 0)
                return false;

        return mismatches <= 2;
    }

    void bfs(unordered_set<string>& set, const string& s) {
        queue<string> q({s});
        while (!q.empty()) {
            string s = q.front();
            q.pop();
            for (auto it = set.begin(); it != set.end(); ) {
                if (similar(*it, s)) {
                    q.push(*it);
                    it = set.erase(it);
                } else {
                    ++it;
                }
            }
        }
    }
};
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