Trie樹，也叫字典樹、前綴樹。可用於”predictive text”和”autocompletion”。亦可用於統計詞頻（邊插入Trie樹邊更新或加入詞頻）。

在計算機科學中。trie，又稱前綴樹或字典樹。是一種有序樹，用於保存關聯數組，當中的鍵一般是字符串。與二叉查找樹不同。鍵不是直接保存在節點中，而是由節點在樹中的位置決定。一個節點的全部子孫都有同樣的前綴，也就是這個節點相應的字符串，而根節點相應空字符串。

普通情況下，不是全部的節點都有相應的值，僅僅有葉子節點和部分內部節點所相應的鍵才有相關的值。

參考資料：http://zh.wikipedia.org/wiki/Trie

#!/usr/bin/python
# -*- coding:utf-8 -*-
# * trie, prefix tree, can be used as a dict
# * author: [email protected]
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 站臺', 1)
  trie.insert('happy 站臺 xx', 10)
  trie.insert('happy 站臺 xx yy', 11)
  trie.insert('happy 站臺 美食 購物 廣場', 2)
  trie.insert('sm')
  trie.insert('sm 國際', 22)
  trie.insert('sm 國際 廣場', 2)
  trie.insert('sm 城市廣場', 3)
  trie.insert('sm 廣場', 4)
  trie.insert('sm 新生活 廣場', 5)
  trie.insert('sm 購物 廣場', 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 站臺')
  print trie.shortest_prefix('happy 站臺 xx')
  print trie.shortest_prefix('sm')
  print trie.longest_prefix('sm xx', sep = '&', default = None)
  print 'sm 廣場 --> ', trie.get('sm 廣場')
  print trie.get('sm 廣場'.split(' '))
  print trie.get('神馬')
  print trie.get('happy 站臺')
  print trie.get('happy 站臺 美食 購物 廣場')
  print trie.longest_prefix('soho 廣場', 'default')
  print trie.longest_prefix('soho 尚都 廣場')
  print trie.longest_prefix_value('soho 尚都 廣場')
  print trie.longest_prefix_value('xx 尚都 廣場', 90)
  print trie.longest_prefix_value('xx 尚都 廣場', 'no prefix')
  print trie.longest_prefix_item('soho 尚都 廣場')

  print '============== keys ================='
  print 'prefix "sm": ', ' | '.join(trie.keys('sm'))
  print '============== items ================='
  print 'prefix "sm": ', trie.items('sm')

  print '================= delete ====================='
  print trie.delete('sm 廣場')
  print trie.get('sm 廣場')
  print trie.delete('sm 國際')
  print trie.get('sm 國際')
  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')

None
empty list
sm
happy 站臺
happy 站臺
sm
None
sm 廣場 --> 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 廣場 | sm 城市廣場 | sm 廣場 | sm 購物 廣場 | sm 國際 | sm 國際 廣場
============== 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!

支持中文的基於詞為基本粒度的前綴樹（prefix trie）python實現