<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 DSU {
private:
    vector<int> parent, size;
public:
    explicit DSU(int n) {
        parent.resize(n + 1);
        size.resize(n + 1, 1);
        for (int i = 0; i < n + 1; i++) {
            parent[i] = i;
        }
    }

    int findPar(int node) {
        if (parent[node] == node) return node;
        return parent[node] = findPar(parent[node]);
    }

    void unionBySize(int u, int v) {
        int par_u = findPar(u);
        int par_v = findPar(v);
        if (par_u == par_v) return;
        if (size[par_u] < size[par_v]) {
            parent[par_u] = par_v;
            size[par_v] += size[par_u];
        } else {
            parent[par_v] = par_u;
            size[par_u] += size[par_v];
        }
    }

    int countGroups() {
        int count = 0;
        for (int i=0;i<parent.size();i++) {
            count += (i == parent[i]);
        }
        return count;
    }

};

class Solution {
public:
    vector<vector<int>> isSimilar;
    enum SIM_STATUS {
        UNVISITED, NO, YES
    };

    static bool checkSimilar(const string &s1, const string &s2) {
        vector<int> diff;
        for (int i = 0; i < s1.size(); i++) {
            if (s1[i] != s2[i]) {
                diff.push_back(i);
                if (diff.size() > 2) return false;
            }
        }
        if (
                diff.empty() ||
                (
                        diff.size() == 2 &&
                        s1[diff[0]] == s2[diff[1]] &&
                        s2[diff[0]] == s1[diff[1]]
                )
                )
            return true;
        return false;
    }

    int numSimilarGroups(vector<string> &strs) {
        int n = strs.size();
        isSimilar.resize(n, vector<int>(n, SIM_STATUS::UNVISITED));
        for (int i = 0; i < n; i++) isSimilar[i][i] = SIM_STATUS::YES;

        DSU dsu(n-1);

        for (int i=0;i<n;i++) {
            for (int j=i;j<n;j++) {
                bool similar;
                if (isSimilar[i][j] != SIM_STATUS::UNVISITED) similar = (isSimilar[i][j] == SIM_STATUS::YES);
                else {
                    similar = checkSimilar(strs[i], strs[j]);
                    if (similar) isSimilar[i][j] = SIM_STATUS::YES;
                    else isSimilar[i][j] = SIM_STATUS::NO;
                }
                if (similar) dsu.unionBySize(i, j);
            }
        }
        return dsu.countGroups();

    }
};

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