<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 DisjointSet {
    public:
    vector<int> size, parent;
    DisjointSet(int n) {
        size.resize(n+1, 1);
        parent.resize(n+1);
        for (int i = 0; i <= n; i++) {
            parent[i] = i;
        }
    }
    
    int findUParent(int u) {
        if (parent[u] == u)
            return u;
        return parent[u] = findUParent(parent[u]);
    }
    
    void unionBySize(int u, int v) {
        int pu = findUParent(u);
        int pv = findUParent(v);
        
        if (pu == pv) return;
        
        if (size[pu] < size[pv]) {
            parent[pu] = pv;
            size[pv] += size[pu];
        } else {
            parent[pv] = pu;
            size[pu] += size[pv];
        }
    }
};

class Solution {
public:
    bool isEquivalent(string& str1, string& str2) {
        int len = str1.size();

        // for (int i = 0; i < len; i++) {
        //     for (int j = i+1; j < len; j++) {
        //         if (str1 == str2) return true;
        //         swap(str1[i], str1[j]);
        //         if (str1 == str2) return true;
        //         swap(str1[i], str1[j]);
        //     }
        // }
        int diff = 0;
        for (int i = 0; i < len; i++) {
            if (str1[i] != str2[i]) {
                diff++;
            }
        }

        return diff == 0 || diff == 2;
    }

    int numSimilarGroups(vector<string>& strs) {
        int n = strs.size();

        DisjointSet ds(n);
        for (int i = 0; i < n; i++) {
            for (int j = i+1; j < n; j++) {
                string str1 = strs[i];
                string str2 = strs[j];

                if (isEquivalent(str1, str2)) {
                    ds.unionBySize(i, j);
                }
            }
        }

        int result = 0;
        for (int i = 0; i < n; i++) {
            if (ds.parent[i] == i) {
                result++;
            }
        }

        return result;
    }
};
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