<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 {
    unordered_map<string, string> parent;
    unordered_map<string, int> rank;
public:
    string find(string word) {
        if (parent.find(word) == parent.end() || parent[word] == word) {
            return parent[word] = word;
        } else {
            return parent[word] = find(parent[word]);
        }
    }

    void Union(string word1, string word2) {
        string word1Parent = find(word1);
        string word2Parent = find(word2);
        if (word1Parent == word2Parent) {
            return;
        }
        if (rank[word1Parent] < rank[word2Parent]) {
            parent[word2Parent] = word1Parent;
            rank[word1Parent]++;
        } else {
            parent[word1Parent] = word2Parent;
            rank[word2Parent]++;
        }
    }

    bool isValid(string word1, string word2) {
        int diff = 0;
        if (word1.size() != word2.size()) {
            return false;
        }
        for (int i = 0; i < word1.size(); i++) {
            if (word1[i] != word2[i]) {
                diff++;
            }
            if (diff > 2) {
                return false;
            }
        }
        return true;
    }

    int numSimilarGroups(vector<string>& strs) {
        for(int i = 0; i < strs.size() - 1; i++) {
            for(int j = i + 1; j < strs.size(); j++) {
                if (isValid(strs[i], strs[j])) {
                    Union(strs[i], strs[j]);
                }
            }
        }
        unordered_set<string> ans;
        for(auto it: strs) {
            ans.insert(find(it));
        }
        return ans.size();
    }
};
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