<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 {
public:
    int kSimilarity(string s1, string s2) {
        int n = s1.size();
        queue<string> q;
        unordered_set<string> visited; 
        q.push(s1);
        visited.insert(s1);
        int cnt = 0;

        while (!q.empty()) {
            int sz = q.size();
            while (sz--) {
                string t = q.front();
                q.pop();
                if (t == s2) return cnt;

                int i = 0;
                while (i < n && t[i] == s2[i]) i++;  // Skip already matched characters

                for (int j = i + 1; j < n; j++) {
                    if (t[j] == s2[i]) {  // Only swap if it brings t closer to s2
                        swap(t[i], t[j]);
                        if (visited.find(t) == visited.end()) {  // Check if this state was visited
                            q.push(t);
                            visited.insert(t);
                        }
                        swap(t[i], t[j]);  // Swap back to explore other options
                    }
                }
            }
            cnt++;
        }
        return cnt;
    }
};

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