Alien Dictionary
Detailed guide and Python implementation for the 'Alien Dictionary' problem.
1. Concept Overview
The 'Alien Dictionary' problem is a key challenge in the Advanced Graphs section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Alien Dictionary.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Alien Dictionary carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
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.
- •1 <= len(words) <= 100
- •1 <= len(words[i]) <= 100
- •words[i] consists of lowercase English letters
Examples
words = ["wrt","wrf","er","ett","rftt"]
"wertf"
From the sorted words, we can derive the relationships: 'w' -> 'e', 'r' -> 't', 't' -> 'f', etc.
words = ["z","x"]
"zx"
From "z" and "x", we know 'z' comes before 'x'.
words = ["z","x","z"]
""
The order is invalid because 'z' comes before 'x' and 'x' comes before 'z'.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def alien_order_opt(words):
return alien_order_brute(words)Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def alien_order_brute(words):
adj = {c: set() for w in words for c in w}
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
visit = {} # False: visiting, True: visited
res = []
def dfs(c):
if c in visit: return visit[c]
visit[c] = False
for nei in adj[c]:
if not dfs(nei): return True
visit[c] = True; res.append(c)
return False
for c in adj:
if dfs(c): return ""
return "".join(res[::-1])Algorithm Pattern Checklist
When dealing with Advanced Graphs data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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