What is the optimal time complexity of solving Alien Dictionary?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Alien Dictionary?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Alien Dictionary?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Alien Dictionary?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Alien Dictionary

Learn how to solve the 'Alien Dictionary' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

There is a new alien language that uses the English alphabet. However, the order of the letters is unknown to you.

You are given a list of strings words from the alien language's dictionary, where the strings in words are sorted lexicographically according to the rules of this new language.

Return a string of the unique letters in the new alien language sorted in lexicographically increasing order by the new language's rules. If there is no solution, return "". If there are multiple solutions, return any of them.

Write a function alienOrder(words: List[str]) -> str.

Constraints

•1 <= len(words) <= 100
•1 <= len(words[i]) <= 100
•words[i] consists of lowercase English letters

Examples

Example 1

Input

words = ["wrt","wrf","er","ett","rftt"]

Output

"wertf"

Explanation

From the sorted words, we can derive the relationships: 'w' -> 'e', 'r' -> 't', 't' -> 'f', etc.

Example 2

Input

words = ["z","x"]

Output

"zx"

Explanation

From "z" and "x", we know 'z' comes before 'x'.

Example 3

Input

words = ["z","x","z"]

Output

""

Explanation

The order is invalid because 'z' comes before 'x' and 'x' comes before 'z'.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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