Alien Dictionary
There is a new alien language that uses the English alphabet. Given a list of words from the dictionary, return the order of characters in the new language. This is a Topological Sort problem.
Why Interviewers Ask This
Microsoft asks the Alien Dictionary problem to evaluate a candidate's ability to model real-world constraints as graph problems. They specifically test topological sorting skills, edge case handling like cycles and invalid orders, and logical reasoning under pressure. This assesses whether you can translate abstract rules into an efficient algorithmic solution.
How to Answer This Question
1. Clarify requirements: Ask if all characters appear in the input or if cycles are possible. 2. Model the graph: Treat each character as a node and derive directed edges by comparing adjacent words in the list. 3. Build adjacency lists: Iterate through word pairs, find the first differing character, and add a directed edge from the left char to the right char. 4. Handle edge cases: Immediately check for invalid inputs where a prefix is followed by a longer version of itself, indicating an impossible order. 5. Perform Topological Sort: Use Kahn's algorithm with a queue to process nodes with zero in-degree, ensuring deterministic ordering. 6. Validate result: If the final string length doesn't match unique characters, a cycle exists, meaning no valid order.
Key Points to Cover
- Explicitly identify the problem as a Topological Sort on a Directed Acyclic Graph
- Demonstrate clear logic for constructing edges by comparing adjacent characters in word pairs
- Address the critical edge case where a shorter word incorrectly follows a longer prefix
- Choose Kahn's Algorithm over DFS for better cycle detection and natural ordering
- Validate the final output length against unique characters to confirm cycle absence
Sample Answer
To solve the Alien Dictionary problem, I would first approach this as a graph traversal challenge. My goal is to determine the lexicographical order of characters based on the provided sorted dictionary. First, I need to build a directed graph where nodes represent characters and edges represent precedence relationships. I will iterate through the given list of words, comparing adjacent pairs. For each pair, I scan from left to right until I find the first index where the characters differ. The character in the first word at that index must come before the character in the second word, establishing a directed edge. I must also handle the specific edge case where one word is a prefix of another but appears after it; for example, if 'apple' comes after 'app', the order is invalid, and I should return an empty string immediately. Once the graph is constructed using an adjacency list and an in-degree map, I will apply Kahn's algorithm for topological sorting. I initialize a queue with all characters having zero in-degree. Then, I process the queue: remove a character, append it to my result string, and decrement the in-degree of its neighbors. If a neighbor's in-degree drops to zero, I add it to the queue. Finally, if the length of my result string equals the number of unique characters found, I have successfully returned the alien alphabet order. Otherwise, a cycle exists, indicating no valid solution. This approach runs in O(C) time, where C is the total number of characters across all words, which is optimal for this constraint.
Common Mistakes to Avoid
- Failing to detect invalid dictionary orders where a prefix appears after the full word
- Incorrectly building the graph by comparing non-adjacent words instead of consecutive pairs
- Ignoring cycle detection, leading to infinite loops or incorrect results in invalid inputs
- Not handling the case where multiple valid orderings exist without specifying a deterministic strategy
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