<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>

from collections import Counter
class Solution:
    #time complexity O(n * m^2 log m)
    def shortestSubstrings(self, arr: List[str]) -> List[str]:
        #O(m*2)
        def generateSubstring(strEle):
            subString = set()
            for i in range(len(strEle)):
                for j in range(i + 1, len(strEle) + 1):
                    subString.add(strEle[i:j])
            return subString        

        substringlist = []
        for elem in arr:
            subStrings = generateSubstring(elem)
            substringlist.append(subStrings)
        #count occurence of each substring
        elemCount = Counter(substring for substrings in substringlist for substring in substrings)
        #filter substrings only appear once, uniqueElem is a set contains all the unique substirngs
        uniqueElem = set(elem for elem, count in elemCount.items() if count == 1)
        #find the shortest substring
        ans = []
        for sub in substringlist:
            sub &= uniqueElem
            if not sub:
                ans.append("")
            else:    
                subList = list(sub)
                subList.sort(key=lambda s: (len(s), s))
                ans.append(subList[0])
        return ans

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