<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 {
    vector<string> nextWords(string word, string& s2, int i){
        // we have to prune the unnecessary branches in the BFS tree
        int n = word.size();
        vector<string> result;
        
        // skip the characters that are equal
        while(word[i] == s2[i]){
            i++;
        }
        
        // perform swap with the characters that are equal to s2[i]
        for(int j=i+1; j<n; j++){
            if(word[j] == s2[i]){
                swap(word[i], word[j]);
                result.push_back(word);
                swap(word[i], word[j]);
            }
        }
        
        return result;
    }
public:
    int kSimilarity(string s1, string s2) {
        
        queue<string> q;
        q.push(s1);

        set<string> st;
        st.insert(s1);

        int moves = 0;
        while(!q.empty()){
            int sz = q.size();
            while(sz--) {
                string frontNode = q.front();
                q.pop();

                if(frontNode == s2) return moves;
                for(auto next:nextWords(frontNode,s2,moves)){
                    if(st.find(next)==st.end()){
                        q.push(next);
                        st.insert(next);
                    }
                }
            }
            moves++;
        }
        return -1;
    }
};
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