<p>Given an array of strings <code>words</code>, return <em>the smallest string that contains each string in</em> <code>words</code> <em>as a substring</em>. If there are multiple valid strings of the smallest length, return <strong>any of them</strong>.</p>

<p>You may assume that no string in <code>words</code> is a substring of another string in <code>words</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;alex&quot;,&quot;loves&quot;,&quot;leetcode&quot;]
<strong>Output:</strong> &quot;alexlovesleetcode&quot;
<strong>Explanation:</strong> All permutations of &quot;alex&quot;,&quot;loves&quot;,&quot;leetcode&quot; would also be accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;catg&quot;,&quot;ctaagt&quot;,&quot;gcta&quot;,&quot;ttca&quot;,&quot;atgcatc&quot;]
<strong>Output:</strong> &quot;gctaagttcatgcatc&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= words.length &lt;= 12</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 20</code></li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>words</code> are <strong>unique</strong>.</li>
</ul>

class Solution:
    def shortestSuperstring(self, words: List[str]) -> str:
        N = len(words)
        lookup = {}
        def merge(cur, next):
            if cur == "":
                return next
            key = cur + ":" + next
            if key in lookup:
                return lookup[key]

            M, N = len(cur), len(next)
            for i in range(M):
                if M-i > N:
                    continue
                found = True
                for j in range(M-i):
                    if cur[i+j] != next[j]:
                        found = False
                        break
                if found:
                    lookup[key] = cur + next[M-i:]
                    return cur + next[M-i:]
            lookup[key] = cur + next
            return cur + next

        memo = {}
        def dp(k, left):
            if left == 0:
                return words[k]
            index = k | left << 10
            if index in memo:
                return memo[index]

            res = ""
            for i in range(N):
                if (1<<i) & left:
                    tmp = dp(i, left & (~(1<<i)))
                    #next = merge(words[k], tmp)
                    next2 = merge(words[k], words[i]) + tmp[len(words[i]):]
                    #print("next: ", next, ", next2:", next2)
                    #if next != next2:
                    #    print("next != next2")
                    if res == "" or len(next2) < len(res):
                        res = next2
            memo[index] = res
            return res

        words.append("")
        return dp(N, (1<<N) - 1)

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