Trie

Trie又叫字典树，前缀树等，是一个高效的信息检索数据结构，专门处理字符串匹配。查找和插入字符串的时间复杂都为O(M)，M为字符串的长度，空间复杂度为O(ALPHABET_SIZE * key_length * N)，N为keys的个数。Trie用空间换时间，利用共同前缀来提高查找效率。

Trie的三个特点:

• 根节点不包含字符，除根节点外每一个节点都只包含一个字符
• 从根节点到某一节点，路径上经过的字符连接起来，为该节点对应的字符串
• 每个节点的所有子节点包含的字符都不相同

Trie的应用：

• 字符串检索
• 词频统计
• 字符串排序
• 前缀匹配

C++实现：

// C++ implementation of search and insert 
// operations on Trie 
#include <bits/stdc++.h> 
using namespace std; 

const int ALPHABET_SIZE = 26; 

// trie node 
struct TrieNode 
{ 
    struct TrieNode *children[ALPHABET_SIZE]; 

    // isEndOfWord is true if the node represents 
    // end of a word 
    bool isEndOfWord; 
}; 

// Returns new trie node (initialized to NULLs) 
struct TrieNode *getNode(void) 
{ 
    struct TrieNode *pNode = new TrieNode; 

    pNode->isEndOfWord = false; 

    for (int i = 0; i < ALPHABET_SIZE; i++) 
        pNode->children[i] = NULL; 

    return pNode; 
} 

// If not present, inserts key into trie 
// If the key is prefix of trie node, just 
// marks leaf node 
void insert(struct TrieNode *root, string key) 
{ 
    struct TrieNode *pCrawl = root; 

    for (int i = 0; i < key.length(); i++) 
    { 
        int index = key[i] - 'a'; 
        if (!pCrawl->children[index]) 
            pCrawl->children[index] = getNode(); 

        pCrawl = pCrawl->children[index]; 
    } 

    // mark last node as leaf 
    pCrawl->isEndOfWord = true; 
} 

// Returns true if key presents in trie, else 
// false 
bool search(struct TrieNode *root, string key) 
{ 
    struct TrieNode *pCrawl = root; 

    for (int i = 0; i < key.length(); i++) 
    { 
        int index = key[i] - 'a'; 
        if (!pCrawl->children[index]) 
            return false; 

        pCrawl = pCrawl->children[index]; 
    } 

    return (pCrawl != NULL && pCrawl->isEndOfWord); 
} 

// Driver 
int main() 
{ 
    // Input keys (use only 'a' through 'z' 
    // and lower case) 
    string keys[] = {"the", "a", "there", 
                    "answer", "any", "by", 
                    "bye", "their" }; 
    int n = sizeof(keys)/sizeof(keys[0]); 

    struct TrieNode *root = getNode(); 

    // Construct trie 
    for (int i = 0; i < n; i++) 
        insert(root, keys[i]); 

    // Search for different keys 
    search(root, "the")? cout << "Yes\n" : 
                        cout << "No\n"; 
    search(root, "these")? cout << "Yes\n" : 
                        cout << "No\n"; 
    return 0; 
}