Trie树，也叫字典树、前缀树。可用于”predictive text”和”autocompletion”。亦可用于统计词频（边插入Trie树边更新或加入词频）。
在计算机科学中。trie，又称前缀树或字典树。是一种有序树，用于保存关联数组，当中的键一般是字符串。与二叉查找树不同。键不是直接保存在节点中，而是由节点在树中的位置决定。一个节点的全部子孙都有同样的前缀，也就是这个节点相应的字符串，而根节点相应空字符串。
普通情况下，不是全部的节点都有相应的值，仅仅有叶子节点和部分内部节点所相应的键才有相关的值。
參考资料：http://zh.wikipedia.org/wiki/Trie
#!/usr/bin/python
# -*- coding:utf-8 -*-
# * trie, prefix tree, can be used as a dict
# * author: yangxudongsuda@gmail.com
import sys
reload(sys)
sys.setdefaultencoding("utf-8")
# Singleton sentinel - works with pickling
class NULL(object):
pass
class Node:
def __init__(self, value = NULL):
self.value = value
self.children = {}
class Trie(object):
def __init__(self):
self.root = Node()
def insert(self, key, value = None, sep = ' '): # key is a word sequence separated by 'sep'
elements = key if isinstance(key, list) else key.split(sep)
node = self.root
for e in elements:
if not e: continue
if e not in node.children:
child = Node()
node.children[e] = child
node = child
else:
node = node.children[e]
node.value = value
def get(self, key, default = None, sep = ' '):
elements = key if isinstance(key, list) else key.split(sep)
node = self.root
for e in elements:
if e not in node.children:
return default
node = node.children[e]
return default if node.value is NULL else node.value
def delete(self, key, sep = ' '):
elements = key if isinstance(key, list) else key.split(sep)
return self.__delete(elements)
def __delete(self, elements, node = None, i = 0):
node = node if node else self.root
e = elements[i]
if e in node.children:
child_node = node.children[e]
if len(elements) == (i+1):
if child_node.value is NULL: return False # not in dict
if len(child_node.children) == 0:
node.children.pop(e)
else:
child_node.value = NULL
return True
elif self.__delete(elements, child_node, i+1):
if len(child_node.children) == 0:
return node.children.pop(e)
return True
return False
def shortest_prefix(self, key, default = NULL, sep = ' '):
elements = key if isinstance(key, list) else key.split(sep)
results = []
node = self.root
value = node.value
for e in elements:
if e in node.children:
results.append(e)
node = node.children[e]
value = node.value
if value is not NULL:
return sep.join(results)
else:
break
if value is NULL:
if default is not NULL:
return default
else:
raise Exception("no item matches any prefix of the given key!")
return sep.join(results)
def longest_prefix(self, key, default = NULL, sep = ' '):
elements = key if isinstance(key, list) else key.split(sep)
results = []
node = self.root
value = node.value
for e in elements:
if e not in node.children:
if value is not NULL:
return sep.join(results)
elif default is not NULL:
return default
else:
raise Exception("no item matches any prefix of the given key!")
results.append(e)
node = node.children[e]
value = node.value
if value is NULL:
if default is not NULL:
return default
else:
raise Exception("no item matches any prefix of the given key!")
return sep.join(results)
def longest_prefix_value(self, key, default = NULL, sep = ' '):
elements = key if isinstance(key, list) else key.split(sep)
node = self.root
value = node.value
for e in elements:
if e not in node.children:
if value is not NULL:
return value
elif default is not NULL:
return default
else:
raise Exception("no item matches any prefix of the given key!")
node = node.children[e]
value = node.value
if value is not NULL:
return value
if default is not NULL:
return default
raise Exception("no item matches any prefix of the given key!")
def longest_prefix_item(self, key, default = NULL, sep = ' '):
elements = key if isinstance(key, list) else key.split(sep)
node = self.root
value = node.value
results = []
for e in elements:
if e not in node.children:
if value is not NULL:
return (sep.join(results), value)
elif default is not NULL:
return default
else:
raise Exception("no item matches any prefix of the given key!")
results.append(e)
node = node.children[e]
value = node.value
if value is not NULL:
return (sep.join(results), value)
if default is not NULL:
return (sep.join(results), default)
raise Exception("no item matches any prefix of the given key!")
def __collect_items(self, node, path, results, sep):
if node.value is not NULL:
results.append((sep.join(path), node.value))
for k, v in node.children.iteritems():
path.append(k)
self.__collect_items(v, path, results, sep)
path.pop()
return results
def items(self, prefix, sep = ' '):
elements = prefix if isinstance(prefix, list) else prefix.split(sep)
node = self.root
for e in elements:
if e not in node.children:
return []
node = node.children[e]
results = []
path = [prefix]
self.__collect_items(node, path, results, sep)
return results
def keys(self, prefix, sep = ' '):
items = self.items(prefix, sep)
return [key for key,value in items]
if __name__ == '__main__':
trie = Trie()
trie.insert('happy 站台', 1)
trie.insert('happy 站台 xx', 10)
trie.insert('happy 站台 xx yy', 11)
trie.insert('happy 站台 美食 购物 广场', 2)
trie.insert('sm')
trie.insert('sm 国际', 22)
trie.insert('sm 国际 广场', 2)
trie.insert('sm 城市广场', 3)
trie.insert('sm 广场', 4)
trie.insert('sm 新生活 广场', 5)
trie.insert('sm 购物 广场', 6)
trie.insert('soho 尚都', 3)
print trie.get('sm')
print trie.longest_prefix([], default="empty list")
print trie.longest_prefix('sm')
print trie.shortest_prefix('happy 站台')
print trie.shortest_prefix('happy 站台 xx')
print trie.shortest_prefix('sm')
print trie.longest_prefix('sm xx', sep = '&', default = None)
print 'sm 广场 --> ', trie.get('sm 广场')
print trie.get('sm 广场'.split(' '))
print trie.get('神马')
print trie.get('happy 站台')
print trie.get('happy 站台 美食 购物 广场')
print trie.longest_prefix('soho 广场', 'default')
print trie.longest_prefix('soho 尚都 广场')
print trie.longest_prefix_value('soho 尚都 广场')
print trie.longest_prefix_value('xx 尚都 广场', 90)
print trie.longest_prefix_value('xx 尚都 广场', 'no prefix')
print trie.longest_prefix_item('soho 尚都 广场')
print '============== keys ================='
print 'prefix "sm": ', ' | '.join(trie.keys('sm'))
print '============== items ================='
print 'prefix "sm": ', trie.items('sm')
print '================= delete ====================='
print trie.delete('sm 广场')
print trie.get('sm 广场')
print trie.delete('sm 国际')
print trie.get('sm 国际')
print trie.delete('sm xx')
print trie.delete('xx')
print '====== no item matches any prefix of given key ========'
print trie.longest_prefix_value('happy')
print trie.longest_prefix_value('soho xx')
执行结果：
None
empty list
sm
happy 站台
happy 站台
sm
None
sm 广场 --> 4
4
None
1
2
default
soho 尚都
3
90
no prefix
('soho \xe5\xb0\x9a\xe9\x83\xbd', 3)
============== keys =================
prefix "sm": sm | sm 新生活 广场 | sm 城市广场 | sm 广场 | sm 购物 广场 | sm 国际 | sm 国际 广场
============== items =================
prefix "sm": [('sm', None), ('sm \xe6\x96\xb0\xe7\x94\x9f\xe6\xb4\xbb \xe5\xb9\xbf\xe5\x9c\xba', 5), ('sm \xe5\x9f\x8e\xe5\xb8\x82\xe5\xb9\xbf\xe5\x9c\xba', 3), ('sm \xe5\xb9\xbf\xe5\x9c\xba', 4), ('sm \xe8\xb4\xad\xe7\x89\xa9 \xe5\xb9\xbf\xe5\x9c\xba', 6),
('sm \xe5\x9b\xbd\xe9\x99\x85', 22), ('sm \xe5\x9b\xbd\xe9\x99\x85 \xe5\xb9\xbf\xe5\x9c\xba', 2)]
================= delete =====================
True
None
True
None
False
False
====== no item matches any prefix of given key ========
Traceback (most recent call last):
File "./word_based_trie.py", line 225, in <module>
print trie.longest_prefix_value('happy')
File "./word_based_trie.py", line 128, in longest_prefix_value
raise Exception("no item matches any prefix of the given key!")
Exception: no item matches any prefix of the given key!
