<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>

class Solution {
private:
    int bfs(string &a, string &b) {
        set<string> used;
        queue<string> q;
        q.push(a);
        used.insert(a);
        
        int level = 0;
        while(!q.empty()) {
            level += 1;
            int qsize = q.size();
            // process all nodes at the same level
            while(qsize--) {
                string u = q.front();
                q.pop();
                
                // escape previously matched characters
                int i = 0;
                while(i < u.length() && u[i] == b[i])
                    i += 1;
                
                // make only possible swap to make i th char same
                // should not check all possibilities using two for loop(gives tle)
                for(int j = i + 1; j < u.length(); j++) {
                    if(b[i] == u[j]) {
                        swap(u[i], u[j]);
                        if(!used.count(u)) {
                            if(u == b)
                                return level;
                            used.insert(u);
                            q.push(u);
                        }
                        // previous state
                        swap(u[i], u[j]);
                    }
                }
            }
        }
        
        return level;
    }
    
    
public:
    int kSimilarity(string s1, string s2) {
        if(s1 == s2)
            return 0;
        
        return bfs(s1, s2);
    }
};
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