Infer an Alien Alphabet from Sorted Words

Question

You are asked to infer the order of characters in an alien language based on a list of sorted words. The goal is to create a graph representation of the characters and determine their order.

Codemia · Accepted Answer

To solve the problem of inferring the order of characters, I will leverage a directed graph. Each character will be a node, and a directed edge will represent the order derived from the sorted words. By comparing adjacent words, we can identify the first differing character to establish a relationship.

1. Create a graph using a dictionary to represent edges and an in-degree count for each character.
2. Iterate through the list of words, comparing each word with the next.
3. For the first differing character between two words, add a directed edge from the first character to the second in the graph and update the in-degree counts accordingly. This ensures that we capture the correct order.

To determine the order of characters, we will perform a topological sort on the graph we constructed. We can use Kahn's algorithm, which involves:
- Initializing a queue with all nodes that have an in-degree of 0.
- Repeatedly removing nodes from the queue, appending them to the result list, and reducing the in-degree of their neighbors. If any neighbor's in-degree becomes 0, we add it to the queue.
- If we can process all nodes, we have a valid order; otherwise, a cycle exists.

The time complexity of this solution is O(N + E), where N is the number of characters and E is the number of edges (relationships between characters). The space complexity is O(N) for storing the graph and in-degree counts. This approach efficiently handles the constraints of the problem.

I will also consider edge cases, such as when the list of words is empty or contains only one word, which should directly return the characters in that word. Additionally, if two words are prefixes of each other, we need to ensure that the longer word comes after the shorter one in the sorted order.

Infer an Alien Alphabet from Sorted Words

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