Alien Dictionary Leetcode Problem 269 [Python Solution]

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def alienOrder(self, words: List[str]) -> str:
    # Create an adjacency list for characters
    adj = {char: set() for word in words for char in word}

    for i in range(len(words) - 1):
        w1, w2 = words[i], words[i + 1]
        minLen = min(len(w1), len(w2))
        if len(w1) > len(w2) and w1[:minLen] == w2[:minLen]:
            return ""
        for j in range(minLen):
            if w1[j] != w2[j]:
                adj[w1[j]].add(w2[j])
                break

    visited = {}  # {char: bool} False visited, True in the current path
    res = []

    def dfs(char):
        if char in visited:
            return visited[char]

        visited[char] = True

        for neighChar in adj[char]:
            if dfs(neighChar):
                return True

        visited[char] = False
        res.append(char)

    for char in adj:
        if dfs(char):
            return ""

    res.reverse()
    return "".join(res)

Now, let’s break down this problem and its solution in detail.

Problem Overview

The Alien Dictionary problem is a fascinating challenge that requires determining the order of letters in an unknown alien language.

This language uses the Latin alphabet, but the order of the letters is not provided.

You are given a list of words from the dictionary, and these words are sorted according to the rules of the alien language.

Your task is to derive the correct order of letters in this alien language.

However, there are some rules and constraints to consider:

• All letters are in lowercase.
• The dictionary is considered invalid if one word is a prefix of another word, and the latter appears before the former.
• If there is no valid order for the letters, you should return an empty string.
• Multiple valid orders may exist, but you should return the smallest one in normal lexicographical order.

Understanding Constraints

Before diving into the solution, let’s clarify the constraints and challenges presented by this problem:

• The order of letters in the alien language is unknown.
• The dictionary provides words sorted based on the alien language’s rules.
• We need to extract the order of letters from the given words.

Alien Dictionary LeetCode Problem Solution

Now that we have a clear understanding of the problem, let’s explore the Python solution to the Alien Dictionary problem.

1. Bruteforce Approach

The solution starts by creating an adjacency list for characters.

This list represents the relationships between characters based on their order in the given words.

The dictionary adj is used to store each character as a key, and the corresponding value is an empty set.

This set will be used to keep track of characters that come after the current character.

adj = {char: set() for word in words for char in word}

2. An Efficient Approach to Build Relationships

The algorithm proceeds to examine each pair of adjacent words to build the relationships between characters.

It takes the minimum length of the current and next words and compares their characters character by character.

If it finds a differing character, it adds a relationship in the adjacency list and stops comparing.

If the length of the current word is greater than the next word and their prefixes match, the dictionary is considered invalid, and the function returns an empty string.

for i in range(len(words) - 1):
    w1, w2 = words[i], words[i + 1]
    minLen = min(len(w1), len(w2))
    if len(w1) > len(w2) and w1[:minLen] == w2[:minLen]:
        return ""
    for j in range(minLen):
        if w1[j] != w2[j]:
            adj[w1[j]].add(w2[j])
            break

Time and Space Complexity

The time complexity of this solution depends on the number of characters present in the input words, as we need to traverse all the characters to build the relationships.

The space complexity is determined by the size of the adjacency list, which is also related to the number of characters.

Reasoning Behind Our Approach

This solution efficiently builds a graph that represents the relationships between characters based on the given words.

It accounts for various constraints, such as word prefixes and multiple valid orders.

By using a depth-first search (DFS) approach, it ensures that the result is derived in the correct order while detecting any loops or contradictions.

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Conclusion

In this blog post, we’ve explored the Alien Dictionary problem, a challenging graph problem from the Blind 75 list.

We’ve provided an efficient Python solution that takes into account various constraints and efficiently derives the correct order of letters in an unknown alien language.

This solution uses an adjacency list and DFS traversal to ensure accuracy and handles potential loop detection.

We hope this guide has been helpful in understanding and solving this complex problem.

If you have any questions, suggestions, or comments, please feel free to share them.

We encourage discussion and engagement with the content.

Thank you for reading!

*Note: The code provided is part of the solution for educational purposes and to help you understand the problem better