https://leetcode.com/problems/alien-dictionary/
Alien Dictionary
Total Accepted: 1390 Total Submissions: 8315 Difficulty: Hard
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 words from the dictionary, where words are sorted lexicographically by the rules of this new language. Derive the order of letters in this language.
For example,
Given the following words in dictionary,
[ "wrt", "wrf", "er", "ett", "rftt" ]
The correct order is: "wertf".
Note:
- You may assume all letters are in lowercase.
- If the order is invalid, return an empty string.
- There may be multiple valid order of letters, return any one of them is fine.
Code
from sets import Set
class Solution(object):
def alienOrder(self, words):
"""
:type words: List[str]
:rtype: str
"""
if not words:
return ""
if len(words) == 1:
return "".join([s for s in Set(words[0])])
# len(words) >=2
adj_dict = self.build_graph(words)
visit_dict = dict([(k,0) for k in adj_dict.keys()])
res = []
self.valid = True
for c in adj_dict.keys():
self.topo_sort(c, visit_dict, adj_dict, res)
return "".join([s for s in res]) if self.valid else ""
def build_graph(self, words):
adj_dict = {}
def add_node(c):
if adj_dict.get(c, None) == None:
adj_dict = {}
def add_link(src, des):
adj_dict[src][des] = None
for i in xrange(len(words)-1):
w1 = words[i]
w2 = words[i+1]
start2 = 0
for j in xrange(min(len(w1), len(w2))):
if w1[j] == w2[j]:
add_node(w1[j])
else:
add_node(w1[j])
add_node(w2[j])
add_link(w2[j], w1[j])
start2 = j+1
break
for j in xrange(start2, len(w1)):
add_node(w1[j])
for j in xrange(start2, len(w2)):
add_node(w2[j])
return adj_dict
def topo_sort(self, c, visit_dict, adj_dict, res):
if self.valid and not visit_dict:
visit_dict = 1
for adj_c in adj_dict.keys():
if visit_dict[adj_c] == 1:
self.valid = False
return
if not visit_dict[adj_c] and self.valid:
self.topo_sort(adj_c, visit_dict, adj_dict, res)
visit_dict = 2
res.append(c)
Idea
Build a graph first, in which nodes are letters and a link from letter A to letter B means A should be latter than B in the final order. Then use topological sort to output nodes in order. https://en.wikipedia.org/wiki/Topological_sorting