<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) {
        return Rec(s1, s2, 0);
    }

private:
    struct Swaps {
        std::vector<int> swaps;
        std::optional<int> perfectSwap;
    };

    int Rec(std::string& s1, std::string& s2, int i) const {
        if (i == s1.size()) {
            return 0;
        }

        if (s1[i] == s2[i]) {
            return Rec(s1, s2, i+1);
        }

        auto [swaps, perfectSwap] = FindSwaps(s1, s2, i);

        if (perfectSwap) {
            std::swap(s1[i], s1[*perfectSwap]);
            auto count = 1 + Rec(s1, s2, i+1);
            std::swap(s1[i], s1[*perfectSwap]);
            return count;
        }

        int minCount = std::numeric_limits<int>::max();

        for (auto j : swaps) {
            std::swap(s1[i], s1[j]);
            auto count = 1 + Rec(s1, s2, i+1);
            minCount = std::min(minCount, count);
            std::swap(s1[i], s1[j]);
        }

        return minCount;
    }

    Swaps FindSwaps(const std::string& s1, const std::string& s2, int i) const {
        auto swaps = std::vector<int>{};

        assert(s1[i] != s2[i]);

        for (int j = i+1; j<s1.size(); ++j) {
            if (s1[j] != s2[i]) {
                continue;
            }

            if (s1[i] == s2[j]) {
                // perfect swap!
                return {{}, j};
            }
            
            swaps.push_back(j);
        }

        return {swaps, std::nullopt};
    }
};
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