<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 minSwaps = std::numeric_limits<int>::max();
        Rec(s1, s2, 0, 0, minSwaps);
        return minSwaps;
    }
    
private:
    void Rec(std::string& s1, const std::string& s2,
             int i, int swapsSoFar, int& minSwaps) const {
        if (i == s1.size()) {
            minSwaps = std::min(minSwaps, swapsSoFar);
            return;
        }
        
        // pruning
        if (swapsSoFar >= minSwaps) {
            return;
        }
        
        if (s1[i] == s2[i]) {
            Rec(s1, s2, i+1, swapsSoFar, minSwaps);
            return;
        }
        
        // Best option: perfect swap (s1[i] == s2[i] && s1[j] == s2[j])
        auto j = FindPerfectSwap(s1, s2, i);
        if (j != -1) {
            std::swap(s1[i], s1[j]);
            Rec(s1, s2, i+1, swapsSoFar + 1, minSwaps);
            std::swap(s1[i], s1[j]);
            return;
        }

        // Alternative: try any other swap that makes s1[i] == s2[j]
        for (int j = i + 1; j < s1.size(); ++j) {
            if (s1[j] != s2[i]) {
                continue;
            }
            std::swap(s1[i], s1[j]);
            Rec(s1, s2, i+1, swapsSoFar + 1, minSwaps);
            std::swap(s1[i], s1[j]);
        }
    }
    
    int FindPerfectSwap(const std::string& s1, const std::string& s2, int i) const {
        for (int j = i+1; j < s1.size(); ++j) {
            if (s1[j] == s2[i] && s1[i] == s2[j]) {
                return j;
            }
        }
        return -1;
    }
};
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