<p>Strings <code>s1</code> and <code>s2</code> are <code>k</code><strong>-similar</strong> (for some non-negative integer <code>k</code>) if we can swap the positions of two letters in <code>s1</code> exactly <code>k</code> times so that the resulting string equals <code>s2</code>.</p>

<p>Given two anagrams <code>s1</code> and <code>s2</code>, return the smallest <code>k</code> for which <code>s1</code> and <code>s2</code> are <code>k</code><strong>-similar</strong>.</p>

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

<pre>
<strong>Input:</strong> s1 = &quot;ab&quot;, s2 = &quot;ba&quot;
<strong>Output:</strong> 1
<strong>Explanation:</strong> The two string are 1-similar because we can use one swap to change s1 to s2: &quot;ab&quot; --&gt; &quot;ba&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s1 = &quot;abc&quot;, s2 = &quot;bca&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> The two strings are 2-similar because we can use two swaps to change s1 to s2: &quot;abc&quot; --&gt; &quot;bac&quot; --&gt; &quot;bca&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= s1.length &lt;= 20</code></li>
	<li><code>s2.length == s1.length</code></li>
	<li><code>s1</code> and <code>s2</code> contain only lowercase letters from the set <code>{&#39;a&#39;, &#39;b&#39;, &#39;c&#39;, &#39;d&#39;, &#39;e&#39;, &#39;f&#39;}</code>.</li>
	<li><code>s2</code> is an anagram of <code>s1</code>.</li>
</ul>

template <typename T> struct DSU {
    int Size;
    map<T,T> parent;
    map<T, int> Rank;
    DSU() : Size(0){}

    int size(){ return Size; }
    
    void init(int u){
        if(parent.count(u)) return;
        parent[u] = u;
        Rank[u] = 0; 
        Size++;
    }
    
    T find(T u){
        if(u == parent[u]) return u;
        return parent[u] = find(parent[u]) ;
    }
    
    void merge(T u , T v){
        init(u); init(v);
        u = find(u);
        v = find(v);
        if(u != v){
            if(Rank[u] < Rank[v]){
                swap(u, v);
            }
            parent[u] = v;
            if(Rank[u] == Rank[v]) Rank[u]++;
            Size--;
        }
    }
    
    map<T, vector<T>> get_comp(){
        map<T, vector<T>> comp;
        for(auto &[f, s] : parent){
            parent[f] = find(f);
            comp[parent[f]].push_back(f);
        }
        return comp;
    }
};
class Solution {
public:
    int kSimilarity(string a, string b){
        // Approach - 2, Not working
        // s1 - "bccaba" s2 - "abacbc"
        // DSU<char> dsu;
        // for(int i = 0; i < a.size(); i++) {
        //     if(a[i] != b[i]) {
        //         dsu.merge(a[i], b[i]);
        //     }
        // } 
        // map<char, vector<char>> comps = dsu.get_comp();
        // int res = 0;
        // for(auto &[c, v]: comps) {
        //     res += v.size() - 1;
        // }
        // return res;

        // Approach - 1
        queue<string> q;
        q.push(a);
        int res = 0;
        set<string> vis;
        vis.insert(a);
        while(q.size()){
            int sz = q.size();
            for(int rep = 0; rep < sz; rep++) {
                string s = q.front();
                q.pop();
                if(s == b) return res;
                int idx = 0;
                while(s[idx] == b[idx]) idx++;
                for(int i = idx + 1; i < s.size(); i++){
                    if(s[i] == b[idx]){
                        string temp = s;
                        swap(temp[i], temp[idx]);
                        if(vis.find(temp) == vis.end()){
                            q.push(temp);
                            vis.insert(temp);
                        }
                    }
                }
            }
            res += 1;
        }
        return 0;
    }
};
106008