<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:
    # DFS
    def kSimilarity(self, A: str, B: str) -> int:
        N = len(A)
        def dfs(A, B, pos):
            if A == B:
                return 0
            
            while A[pos] == B[pos]:
                pos += 1
                
            minCnt = float('inf')
            for i in range(pos + 1, N):
                if B[i] == A[pos] and B[i] != A[i]:
                    B[i], B[pos] = B[pos], B[i]
                    tmp = dfs(A, B, pos + 1) + 1
                    minCnt = min(tmp, minCnt)
                    B[i], B[pos] = B[pos], B[i]
                    
            return minCnt
        
        return dfs(list(A), list(B), 0)

    # DFS with memorization
    def kSimilarity1(self, A: str, B: str) -> int:
        N = len(A)
        def dfs(A, B, pos):
            sB = ''.join(B)
            if sB in map:
                return map[sB]
            
            if A == B:
                return 0
            
            while A[pos] == B[pos]:
                pos += 1
                
            minCnt = float('inf')
            for i in range(pos + 1, N):
                if B[i] == A[pos] and B[i] != A[i]:
                    B[i], B[pos] = B[pos], B[i]
                    tmp = dfs(A, B, pos + 1) + 1
                    minCnt = min(tmp, minCnt)
                    B[i], B[pos] = B[pos], B[i]
                    
            map[sB] = minCnt
            return minCnt
                    
        map = collections.defaultdict()
        return dfs(list(A), list(B), 0)
    
    # BFS
    def kSimilarity2(self, A: str, B: str) -> int:
        N = len(B)
        q = collections.deque([B])
        visited = set(B)
        
        cnt = 0
        pos = 0
        while q:
            qSize = len(q)
            
            for _ in range(qSize):
                cur = q.popleft()
                if cur == A:
                    return cnt
                
                pos = 0
                while cur[pos] == A[pos]:
                    pos += 1
                
                lCur = list(cur)
                for i in range(pos + 1, N):
                    if lCur[i] == A[pos] and lCur[i] != A[i]:
                        lCur[i], lCur[pos] = lCur[pos], lCur[i]
                        
                        sCur = ''.join(lCur)
                        if sCur not in visited:
                            q.append(sCur)
                            
                        visited.add(sCur)
                        lCur[i], lCur[pos] = lCur[pos], lCur[i]
            cnt += 1
            
        return cnt
16600