#3076

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Shortest Uncommon Substring in an Array

Find the shortest substring for each string in an array that does not appear in any other string efficiently using hashing and scanning.

array hash table string trie

Problem Statement

Given an array of non-empty strings, return an array of the same size where each element is the shortest substring of the corresponding string that does not appear in any other string in the array. If no such substring exists, return an empty string for that position.

Each string in the input array consists of lowercase English letters. Your task is to process the array efficiently to identify these minimal unique substrings using array scanning and hash lookup patterns, ensuring that each returned substring is lexicographically minimal when multiple options exist.

Examples

Example 1

Input: arr = ["cab","ad","bad","c"]

Output: ["ab","","ba",""]

We have the following:

For the string "cab", the shortest substring that does not occur in any other string is either "ca" or "ab", we choose the lexicographically smaller substring, which is "ab".
For the string "ad", there is no substring that does not occur in any other string.
For the string "bad", the shortest substring that does not occur in any other string is "ba".
For the string "c", there is no substring that does not occur in any other string.

Example 2

Input: arr = ["abc","bcd","abcd"]

Output: ["","","abcd"]

We have the following:

For the string "abc", there is no substring that does not occur in any other string.
For the string "bcd", there is no substring that does not occur in any other string.
For the string "abcd", the shortest substring that does not occur in any other string is "abcd".

Constraints

n == arr.length
2 <= n <= 100
1 <= arr[i].length <= 20
arr[i] consists only of lowercase English letters.

Solution Approach

Brute Force Substring Check

Generate all possible substrings for each string and check against all other strings using hash sets. Return the lexicographically smallest substring that is not present elsewhere, or an empty string if none exists.

Trie-Based Optimization

Build a trie containing all substrings of all strings. For each string, traverse the trie to find the shortest path that does not appear in other strings. This avoids redundant substring comparisons and speeds up detection.

Hash Map Frequency Counting

Use a hash map to store counts of all substrings across the array. For each string, scan its substrings in order of length and select the first substring with a count of one. This approach leverages array scanning plus hash lookup for efficient retrieval.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity depends on substring generation and checking; brute force can be O(n * l^3), trie optimization reduces repeated checks, and hash maps reduce to O(n * l^2) where l is string length. Space complexity ranges from O(n * l^2) for hash storage to potentially larger for trie structures.

What Interviewers Usually Probe

Looking for correct handling of overlapping substrings across multiple strings.
Checking for efficient substring uniqueness detection using hash tables or tries.
Expect candidate to consider lexicographical ordering when multiple minimal substrings exist.

Common Pitfalls or Variants

Common pitfalls

Failing to consider all possible substrings including single characters.
Not returning empty string when no unique substring exists.
Ignoring lexicographical order when multiple minimal substrings are valid.

Follow-up variants

Find the shortest uncommon prefix instead of any substring.
Return the longest unique substring instead of shortest.
Handle arrays with duplicate strings efficiently.

FAQ

What is the Shortest Uncommon Substring in an Array problem pattern?

It follows array scanning plus hash lookup, identifying minimal substrings unique to each string.

How do I handle strings with no unique substring?

Return an empty string for any string where every substring appears in another string.

Is lexicographical order important when multiple substrings qualify?

Yes, always return the lexicographically smallest substring to match problem requirements.

Can this problem be solved with a trie?

Yes, a trie can store all substrings and help find the shortest unique substring efficiently.

What is the expected complexity of a hash-based approach?

Using hash maps to count substrings reduces time complexity to O(n * l^2) and space complexity depends on total substring storage.

terminal

Solution

Solution 1: Enumeration

Given the small data scale, we can directly enumerate all substrings of each string and then determine whether it is a substring of other strings.

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class Solution:
    def shortestSubstrings(self, arr: List[str]) -> List[str]:
        ans = [""] * len(arr)
        for i, s in enumerate(arr):
            m = len(s)
            for j in range(1, m + 1):
                for l in range(m - j + 1):
                    sub = s[l : l + j]
                    if not ans[i] or ans[i] > sub:
                        if all(k == i or sub not in t for k, t in enumerate(arr)):
                            ans[i] = sub
                if ans[i]:
                    break
        return ans

Continue Practicing

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