Trie 的原理和實現 (python 實現）

原理：（from wiki）

In computer science, a trie, or prefix tree, is an ordered tree data structure that is used to store an associative array where the keys are usually strings.

Unlike a binary search tree, no node in the tree stores the key associated with that node; instead, its position in the tree defines the key with which it is associated.

Values are normally not associated with every node, only with leaves and some inner nodes that correspond to keys of interest. (consider a dictionary)

Looking up keys is faster. Looking up a key of length m takes worst case O(m) time. BST takes O(m log n) time.

• Tries facilitate longest-prefix matching.

 

Tries facilitate longest-prefix matching, but hashing does not, as a consequence of the above.

 

1.       A common application of a trie is storing a dictionary, such as one found on a mobile telephone.

2.       Tries are also well suited for implementing approximate matching algorithms.

3.       Lexicographic sorting of a set of keys can be accomplished with a simple trie-based algorithm as follows. (e.g. radix sort using trie)

4.       A trie forms the fundamental data structure of Burstsort, currently (2007) the fastest known, memory/cache-based, string sorting algorithm.[6]

 

實現實例：

 

#!/usr/bin/python                                                                                                                                                      
print '================ A Trie Demo =============='

class Node:
    def __init__(self):
        self.value = None
        self.children = {}    # children is of type {char, Node}                                                                                                       

class Trie:
    def __init__(self):
        self.root = Node()

    def insert(self, key):      # key is of type string                                                                                                                
        # key should be a low-case string, this must be checked here!                                                                                                  
        node = self.root
        for char in key:
            if char not in node.children:
                child = Node()
                node.children[char] = child
                node = child
            else:
                node = node.children[char]
        node.value = key

    def search(self, key):
        node = self.root
        for char in key:
            if char not in node.children:
                return None
            else:
                node = node.children[char]
        return node.value

    def display_node(self, node):
        if (node.value != None):
            print node.value
        for char in 'abcdefghijklmnopqrstuvwxyz':
            if char in node.children:
                self.display_node(node.children[char])
        return

    def display(self):
        self.display_node(self.root)

trie = Trie()
trie.insert('hello')
trie.insert('nice')
trie.insert('to')
trie.insert('meet')
trie.insert('you')
trie.display()
print
print trie.search('hello')
print trie.search('HELLO')
print

print '================= END ====================='

 

示例結果：

root@localhost :/home/James/mypro/Python# ./trie.py
================ A Trie Demo ==============
hello
meet
nice
to
you

hello
None

================= END =====================
root@localhost :/home/James/mypro/Python#