<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:
    def kSimilarity(self, s1: str, s2: str) -> int:
        self.memo = {} 
        return self.get_swaps(list(s1), list(s2), 0)

    def get_swaps(self, a1, a2, i):
        # we have a match, no more steps needed
        if str(a1) == str(a2):
            return 0

        # increment until we get a mismatch
        while a1[i] == a2[i]:
            i += 1

        # get all swap candidates
        candidates = [j for j in range(i, len(a1)) if a2[j] == a1[i]]

        min_swaps = None
        for c in candidates:
            # do the swap and recursive call the next
            arr = a2.copy()
            arr[c], arr[i] = arr[i], arr[c]

            arr_str = "".join(arr)
            if mem := self.memo.get(arr_str):
                swaps = mem
            else:
                swaps = self.get_swaps(a1, arr, i+1) + 1
                self.memo[arr_str] = swaps

            min_swaps = swaps if min_swaps is None else min(min_swaps, swaps)
        
        return min_swaps
18700