GeekforGeeks Trie - 键树简单介绍 - 构造 插入 和 搜索

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https://blog.csdn.net/kenden23/article/details/24453639

Trie是非常高效的信息检索数据结构， 时间效率会是O(m)，当中m是须要搜索的keyword的长度。

缺点就是须要的存储空间大。

Trie的特点：

1. 每一个Trie的节点都由多个分支构成

2. 每一个分支代表可能的keyword的一个字符

3. 须要mark（标志）每一个keyword的最后一个字符为leaf node（叶子节点）

英文字母的节点数据结构能够表演示样例如以下：

struct TrieNode
{
	int value; /* Used to mark leaf nodes */
	TrieNode *children[ALPHABET_SIZE];
};

插入keyword：

1. keyword的每一个字符都作为独立的trie节点， 注意每一个子节点都是一组指针，指向下一个trie节点。

2 假设输入的keyword是新的，或者是比原有keyword长， 就须要构造新的节点， 并且须要标志它的结束点为叶子节点。 

3. 假设keyword比原有的某个keyword短，那么就能够仅仅标志新的叶子节点。

4. keyword的长度决定了trie的深度

搜索keyword：

1. 比較keyword的字符。然后往下一层移动

2. 假设keyword结束，或者没有这个字符在trie中，那么搜索结束。 前者比較最后一个节点是否是叶子节点，假设是表示搜索成功，否则不成功。后者表示搜索不成功。

參考原文：

http://www.geeksforgeeks.org/trie-insert-and-search/

实现程序：

#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <string>

#define ARRAY_SIZE(a) sizeof(a)/sizeof(a[0])
#define ALPHABET_SIZE (26)
#define CHAR_TO_INDEX(c) ((int)c - (int)'a')

struct TrieNode
{
	int value; /* Used to mark leaf nodes */
	TrieNode *children[ALPHABET_SIZE];
};

struct TrieT
{
	TrieNode *root;
	int count;
};

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

	if( pNode )
	{
		int i;
		pNode->value = 0;
		for(i = 0; i < ALPHABET_SIZE; i++)
		{
			pNode->children[i] = NULL;
		}
	}
	return pNode;
}

// Initializes trie (root is dummy node)
void initialize(TrieT *pTrie)
{
	pTrie->root = getNode();
	pTrie->count = 0;
}

// If not present, inserts key into trie
// If the key is prefix of trie node, just marks leaf node
void insert(TrieT *pTrie, char key[])
{
	int level = 0;
	int length = strlen(key);
	int index = 0;
	TrieNode *pCrawl;

	pTrie->count++;
	pCrawl = pTrie->root;

	for( level = 0; level < length; level++ )
	{
		index = CHAR_TO_INDEX(key[level]);
		if( !pCrawl->children[index] )
		{
			pCrawl->children[index] = getNode();
		}
		pCrawl = pCrawl->children[index];
	}
	// mark last node as leaf
	pCrawl->value = pTrie->count;
}

// Returns non zero, if key presents in trie
int search(TrieT *pTrie, char key[])
{
	int level;
	int length = strlen(key);
	int index;
	TrieNode *pCrawl;

	pCrawl = pTrie->root;
	for( level = 0; level < length; level++ )
	{
		index = CHAR_TO_INDEX(key[level]);
		if( !pCrawl->children[index] )
		{
			return 0;
		}
		pCrawl = pCrawl->children[index];
	}
	return (0 != pCrawl && pCrawl->value);
}

// Driver
int main()
{
	// Input keys (use only 'a' through 'z' and lower case)
	char keys[][8] = {"the", "a", "there", "answer", "any", "by", "bye", "their"};
	TrieT trie;

	char output[][32] = {"Not present in trie", "Present in trie"};

	initialize(&trie);

	// Construct trie
	for(int i = 0; i < ARRAY_SIZE(keys); i++)
	{
		insert(&trie, keys[i]);
	}

	// Search for different keys
	printf("%s --- %s\n", "the", output[search(&trie, "the")] );
	printf("%s --- %s\n", "these", output[search(&trie, "these")] );
	printf("%s --- %s\n", "their", output[search(&trie, "their")] );
	printf("%s --- %s\n", "thaw", output[search(&trie, "thaw")] );

	return 0;
}

更新 2014 5 -16

C++写的类，主要是带构造函数和析构函数。能够非常好管理内存，甚至不须要递归地手动释放内存了，析构函数能够自己主动递归调用释放全部Node，这个是C++比C强大的地方之中的一个：

class TrieInsertAndSearch
{
	const static int ALPH_SIZE = 26;

	struct Node
	{
		int val;
		Node *children[ALPH_SIZE];
		explicit Node(int v = 0) : val(v)
		{
			for (int i = 0; i < ALPH_SIZE; i++)
			{
				children[i] = nullptr;
			}
		}
		~Node()
		{
			for (int i = 0; i < ALPH_SIZE; i++)
			{
				if (children[i]) delete children[i];
				children[i] = nullptr;
			}
		}
	};
	struct Tree
	{
		Node *root;
		int count;
		explicit Tree(int c = 0, Node *r = nullptr) : count(c), root(r){}
		~Tree()
		{
			if (root) delete root;
			root = nullptr;
		}
	};

	Tree *pT;
	void insert(char key[])
	{
		int len = strlen(key);
		Node *pCrawl = pT->root;
		pT->count++;
		for (int lv = 0; lv < len; lv++)
		{
			int id = key[lv] - 'a';
			if (!pCrawl->children[id])
			{
				pCrawl->children[id] = new Node;
			}
			pCrawl = pCrawl->children[id];
		}
		pCrawl->val = pT->count;
	}
	bool search(char key[])
	{
		int len = strlen(key);
		Node *pCrawl = pT->root;
		for (int lv = 0; lv < len; lv++)
		{
			int id = key[lv] - 'a';
			if (!pCrawl->children[id]) return false;
			pCrawl = pCrawl->children[id];
		}
		return (pCrawl && pCrawl->val);
	}
public:
	TrieInsertAndSearch()
	{
		char keys[][8] = {"the", "a", "there", "answer", "any", "by", "bye", "their"};
		pT = new Tree(0, new Node);
		int n = sizeof(keys) / sizeof(keys[0]);
		for (int i = 0; i < n; i++)
		{
			insert(keys[i]);
		}

		// Search for different keys
		if (search("the")) printf("the is in Trie\n");
		else printf("the is not in Trie\n");
		if (search("these")) printf("these is in Trie\n");
		else printf("these is not in Trie\n");
		if (search("their")) printf("their is in Trie\n");
		else printf("their is not in Trie\n");
		if (search("thaw")) printf("thaw is in Trie\n");
		else printf("thaw is not in Trie\n");
	}
	~TrieInsertAndSearch()
	{
		if (pT) delete pT;
		pT = nullptr;
	}
};