<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:
    def numSimilarGroups(self, strs: List[str]) -> int:
        union = UnionFind(len(strs))
        for i,str1 in enumerate(strs):
            for j,str2 in enumerate(strs[i+1:],i+1):
                if self.areSimilar(str1,str2):
                    union.union(i,j)
        return sum(idx==parent for idx,parent in enumerate(union.parents))

    def areSimilar(self,word1,word2):
        swapped = 0
        for i,j in zip(word1,word2):
            if i!=j:
                swapped+=1
                if swapped>2:
                    return False
        return True

class UnionFind:
    def __init__(self,size):
        self.parents = list(range(size))
        self.rank = [0]*size
    
    def find_parent(self,idx):
        if idx==self.parents[idx]:
            return idx
        self.parents[idx]=self.find_parent(self.parents[idx])
        return self.parents[idx]
    
    def union(self,set1,set2):
        parent_1,parent_2 = self.find_parent(set1), self.find_parent(set2)
        if parent_1!=parent_2:
            if self.rank[parent_1]<self.rank[parent_2]:
                parent_1,parent_2=parent_2,parent_1
            self.parents[parent_2]=parent_1
            if self.rank[parent_1]==self.rank[parent_2]:
                self.rank[parent_1]+=1
        
17100