<p>You are given an array <code>arr</code> of size <code>n</code> consisting of <strong>non-empty</strong> strings.</p>

<p>Find a string array <code>answer</code> of size <code>n</code> such that:</p>

<ul>
	<li><code>answer[i]</code> is the <strong>shortest</strong> <span data-keyword="substring">substring</span> of <code>arr[i]</code> that does <strong>not</strong> occur as a substring in any other string in <code>arr</code>. If multiple such substrings exist, <code>answer[i]</code> should be the <span data-keyword="lexicographically-smaller-string">lexicographically smallest</span>. And if no such substring exists, <code>answer[i]</code> should be an empty string.</li>
</ul>

<p>Return <em>the array </em><code>answer</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [&quot;cab&quot;,&quot;ad&quot;,&quot;bad&quot;,&quot;c&quot;]
<strong>Output:</strong> [&quot;ab&quot;,&quot;&quot;,&quot;ba&quot;,&quot;&quot;]
<strong>Explanation:</strong> We have the following:
- For the string &quot;cab&quot;, the shortest substring that does not occur in any other string is either &quot;ca&quot; or &quot;ab&quot;, we choose the lexicographically smaller substring, which is &quot;ab&quot;.
- For the string &quot;ad&quot;, there is no substring that does not occur in any other string.
- For the string &quot;bad&quot;, the shortest substring that does not occur in any other string is &quot;ba&quot;.
- For the string &quot;c&quot;, there is no substring that does not occur in any other string.
</pre>

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

<pre>
<strong>Input:</strong> arr = [&quot;abc&quot;,&quot;bcd&quot;,&quot;abcd&quot;]
<strong>Output:</strong> [&quot;&quot;,&quot;&quot;,&quot;abcd&quot;]
<strong>Explanation:</strong> We have the following:
- For the string &quot;abc&quot;, there is no substring that does not occur in any other string.
- For the string &quot;bcd&quot;, there is no substring that does not occur in any other string.
- For the string &quot;abcd&quot;, the shortest substring that does not occur in any other string is &quot;abcd&quot;.
</pre>

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

<ul>
	<li><code>n == arr.length</code></li>
	<li><code>2 &lt;= n &lt;= 100</code></li>
	<li><code>1 &lt;= arr[i].length &lt;= 20</code></li>
	<li><code>arr[i]</code> consists only of lowercase English letters.</li>
</ul>

class Solution:
    def shortestSubstrings(self, arr: List[str]) -> List[str]:

        res = []
        substrings = defaultdict(set)
        # Let n be number of words and m be max length of a word
        # Loop complexity: O(n * m ^2) both space and time
        for i in range(len(arr)):
            word = arr[i]
            for j in range(len(word)):
                for k in range(j + 1, len(word) + 1):
                    substring = word[j : k]
                    substrings[i].add(substring)
        
        # Complexity: O(n * (m ^ 2) * n)
        for i in range(len(arr)):
            curr_substrings = substrings[i]
            curr_best_match = ""
            for substring in curr_substrings:
                is_uncommon = True
                for j in range(len(arr)):
                    if j == i:
                        continue
                    if substring in substrings[j]:
                        is_uncommon = False
                        break
                if is_uncommon:
                    if curr_best_match == "" or len(substring) < len(curr_best_match) or (len(substring) == len(curr_best_match) and substring < curr_best_match):
                        curr_best_match = substring
            res.append(curr_best_match)

        # Time O((n ^ 2) * (m ^ 2)), Space O(n * (m ^ 2))
        return res

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