<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 Trie:
    def __init__(self):
        self.childs = {}
        self.owners = set()
    
    def add(self, word, owner):
        node = self
        for c in word:
            next = node.childs.get(c, None)
            if next is None:
                next = Trie()
                node.childs[c] = next
            node = next
        node.owners.add(owner)

class Solution:
    def shortestSubstrings(self, arr: List[str]) -> List[str]:
        def get_all_substrings(word):
            N = len(word)
            ans = []
            for size in range(1, N+1):
                for i in range(0, N-size+1):
                    ans.append(word[i:i+size])
            return ans
        def add_strings_to_trie(root, substrings, owner):
            for word in substrings:
                root.add(word, owner)
        
        def find_shortest_unique_substring(root, substrings):
            # assume substrings are sorted ascendingly in length
            substrings = sorted(substrings, key=lambda x: (len(x), x))
            for word in substrings:
                node = root
                for c in word:
                    node = node.childs[c]
                if len(node.owners) == 1:
                    return word
            return ""
        
        root = Trie()
        for owner, word in enumerate(arr):
            substrings = get_all_substrings(word)
            print(substrings)
            add_strings_to_trie(root, substrings, owner)
        
        answer = []
        for word in arr:
            substrings = get_all_substrings(word)
            shortest_unique_substring = find_shortest_unique_substring(root, substrings)
            answer.append(shortest_unique_substring)
        return answer
                
        
        
        
                
                            


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