Leetcode 61. Alien Dictionary. Python

 

There is a new alien language which uses the latin alphabet. However, the order among letters are unknown to you. You receive a list of non-empty words from the dictionary, where words are sorted lexicographically by the rules of this new language. Derive the order of letters in this language.

1. You may assume all letters are in lowercase.
2. The dictionary is invalid, if string a is prefix of string b and b is appear before a.
3. If the order is invalid, return an empty string.
4. There may be multiple valid order of letters, return the smallest in normal lexicographical order.
5. The letters in one string are of the same rank by default and are sorted in Human dictionary order.

Example

Example 1:

Input：["wrt","wrf","er","ett","rftt"]
Output："wertf"
Explanation：
from "wrt"and"wrf" ,we can get 't'<'f'
from "wrt"and"er" ,we can get 'w'<'e'
from "er"and"ett" ,we can get 'r'<'t'
from "ett"and"rftt" ,we can get 'e'<'r'
So return "wertf"

Example 2:

Input：["z","x"]
Output："zx"
Explanation：
from "z" and "x"，we can get 'z' < 'x'
So return "zx"

Solution :

from typing import (
    List,
)
class Solution:
    def alien_order(self, words: List[str]) -> str:
        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]
            lmin = min(len(w1), len(w2))
            if len(w1) > len(w2) and w1[:lmin] == w2[:lmin] :
                return ""
            for j in range(lmin):
                if w1[j] != w2[j]:
                    adj[w1[j]].add(w2[j])
                    break
        
        ans = []
        vs = {}
        
        def dfs(c):
            if c in vs:
                return vs[c]
            vs[c] = True
            for n in adj[c]:
                if dfs(n):
                    return True
            vs[c] = False
            ans.append(c)
        
        for c in adj:
            if dfs(c) :
                return ""
                
        ans.reverse()
        return "".join(ans)

        

Explaination :