Trie树(字典树)的C++实现

问题描述:

Trie树

又称单词查找树,是一种树形结构,是一种哈希树的变种。典型应用是用于统计,排序和保存大量的字符串(但不仅限于字符串),所以经常被搜索引擎系统用于文本词频统计。

举个例子:os,oh,old,char,chat这些关键词构成的trie树:

                               root

                             /         \

                          c            o

                         /               /  \

                       h              s     h

                     /  

                   a    

                 /  \

               r      t    

trie树特点:

①根节点不包含字符,其他节点均包含一个字符

②每个节点的最大分支数为字符可能取值的个数

③每个节点对应的单词为从根节点到该节点的路径上的字符的排列。

④两个单词的公共前缀为根节点到这两个点的路径的公共部分。


应用:

①词频统计:trie树中的公共前缀只由一条路径表示,因此相对于hash方法,节约了内存。

②前缀匹配:检索所有以某前缀开头的字符串。朴素做法的时间复杂度为O(n*N),n为前缀长度,N为单词个数,而使用trie树可以做到O(h)h为检索的单词的长度。

③串排序:N个字符串按字典序排序,只需trie树进行先序遍历

④串的快速检索:trie树的节点结构中可加入记录其他信息的变量,如某词在文章中第一次出现的位置编号等,问题例:给出N个单词组成的熟词表,以及一篇全用小写英文书写的文章,请你按最早出现的顺序写出所有不在熟词表中的生词。在这道题中,我们可以用字典树,先把熟词建一棵树,然后读入文章进行比较,这种方法效率是比较高的。

算法:

树种单词的存储策略有两种:

①每个节点存一个字符

②每个节点存从根节点到该节点的路径表示的字符串


后一种方式需要的空间可能较多,但是检索的时候不需要一个辅助栈来记录路径,效率较高,本着空间换时间的原则,本文采用第二种存储方式。

代码实现:

测试:对单词集word.txt构建trie树,并给每个单词置一个ID号(可以认为是单词在字符集中第一次出现的位置),并检索其中以‘fu’开头的单词。

//TrieTreeNode.h
#pragma once
#include<iostream>
using namespace std;


template<class T>
class TrieTreeNode
{
public:
<span style="white-space:pre">	</span>TrieTreeNode(int MaxBranch)//用于构造根节点
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>MaxBranchNum = MaxBranch;
<span style="white-space:pre">		</span>ChildNodes = new TrieTreeNode<T>*[MaxBranchNum];
<span style="white-space:pre">		</span>for (int i = 0; i < MaxBranchNum; i++)
<span style="white-space:pre">			</span>ChildNodes[i] = NULL;
<span style="white-space:pre">		</span>word = NULL;
<span style="white-space:pre">		</span>Freq = 0;
<span style="white-space:pre">		</span>ID = -1;
<span style="white-space:pre">	</span>}
public:
<span style="white-space:pre">	</span>int MaxBranchNum;//最大分支数;
<span style="white-space:pre">	</span>char* word;//单词字符串的指针
<span style="white-space:pre">	</span>TrieTreeNode<T> **ChildNodes;
<span style="white-space:pre">	</span>int Freq;//词频统计
<span style="white-space:pre">	</span>int ID;//构建TrieTree树时的插入顺序,可用来记录字符串第一次出现的位置
};

//TrieTree.h
#pragma once
#include<iostream>
#include"TrieTreeNode.h"
using namespace std;


template<class T>
class TrieTree
{
<span style="white-space:pre">	</span>//Insert时为节点代表的单词word分配内存,Delete时只修改Freq而不删除word,Search时以Freq的数值作为判断依据,而不是根据word是否为NULL
public:
<span style="white-space:pre">	</span>TrieTree(const int size);
<span style="white-space:pre">	</span>~TrieTree(){ Destroy(root); };
<span style="white-space:pre">	</span>void Insert(const T* str);//插入单词str
<span style="white-space:pre">	</span>void Insert(const T* str, const int num);//插入单词str,带有编号信息
<span style="white-space:pre">	</span>int Search(const T* str);//查找单词str,返回出现次数
<span style="white-space:pre">	</span>bool Delete(const T* str);//删除单词str
<span style="white-space:pre">	</span>void PrintALL();//打印trie树中所有节点对应的单词
<span style="white-space:pre">	</span>void PrintPre(const T* str);//打印以str为前缀的单词
private:
<span style="white-space:pre">	</span>void Print(const TrieTreeNode<T>* p);
<span style="white-space:pre">	</span>void Destroy(TrieTreeNode<T>* p);//由析构函数调用,释放以p为根节点的树的空间
private:
<span style="white-space:pre">	</span>TrieTreeNode<T>* root;
<span style="white-space:pre">	</span>int MaxBranchNum;//最大分支数
};


template<class T>
void TrieTree<T>::Destroy(TrieTreeNode<T>* p)
{
<span style="white-space:pre">	</span>if (!p)
<span style="white-space:pre">		</span>return;
<span style="white-space:pre">	</span>for (int i = 0; i < MaxBranchNum; i++)
<span style="white-space:pre">		</span>Destroy(p->ChildNodes[i]);
<span style="white-space:pre">	</span>if (!p->word)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>delete[] p->word;//只是释放了char数组word的空间,指针word本身的空间未释放,由后续的delete p释放
<span style="white-space:pre">		</span>p->word = NULL;
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>delete p;//释放节点空间
<span style="white-space:pre">	</span>p = NULL;//节点指针置为空
<span style="white-space:pre">	</span>//以上的置NULL的两句无太大意义,但是:编程习惯
}


template<class T>
bool TrieTree<T>::Delete(const T* str)
{
<span style="white-space:pre">	</span>TrieTreeNode<T>* p = root;
<span style="white-space:pre">	</span>if (!str)
<span style="white-space:pre">		</span>return false;
<span style="white-space:pre">	</span>for (int i = 0; str[i]; i++)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>int index = str[i] - 'a';
<span style="white-space:pre">		</span>if (p->ChildNodes[index])
<span style="white-space:pre">			</span>p = p->ChildNodes[index];
<span style="white-space:pre">		</span>else return false;
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>p->Freq = 0;
<span style="white-space:pre">	</span>p->ID = -1;
<span style="white-space:pre">	</span>return true;
}


template<class T>
void TrieTree<T>::PrintPre(const T* str)
{
<span style="white-space:pre">	</span>TrieTreeNode<T>* p = root;
<span style="white-space:pre">	</span>if (!str)
<span style="white-space:pre">		</span>return;
<span style="white-space:pre">	</span>for (int i = 0; str[i]; i++)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>int index = str[i] - 'a';
<span style="white-space:pre">		</span>if (p->ChildNodes[index])
<span style="white-space:pre">			</span>p = p->ChildNodes[index];
<span style="white-space:pre">		</span>else return;
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>cout << "以" << str << "为前缀的单词有:" << endl;
<span style="white-space:pre">	</span>Print(p);
}


template<class T>
int TrieTree<T>::Search(const T* str)
{
<span style="white-space:pre">	</span>TrieTreeNode<T>* p = root;
<span style="white-space:pre">	</span>if (!str)
<span style="white-space:pre">		</span>return -1;
<span style="white-space:pre">	</span>for (int i = 0; str[i]; i++)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>int index = str[i] - 'a';
<span style="white-space:pre">		</span>if (p->ChildNodes[index])
<span style="white-space:pre">			</span>p = p->ChildNodes[index];
<span style="white-space:pre">		</span>else return 0;
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>return p->Freq;
}


template<class T>
TrieTree<T>::TrieTree(const int size)
{
<span style="white-space:pre">	</span>MaxBranchNum = size;
<span style="white-space:pre">	</span>root = new TrieTreeNode<T>(MaxBranchNum);//根节点不储存字符
}


template<class T>
void TrieTree<T>::Insert(const T* str)
{
<span style="white-space:pre">	</span>TrieTreeNode<T>* p = root;
<span style="white-space:pre">	</span>for (int i = 0; str[i]; i++)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>if (str[i]<'a' || str[i]>'z')
<span style="white-space:pre">		</span>{
<span style="white-space:pre">			</span>cout << "格式错误!" << endl;
<span style="white-space:pre">			</span>return;
<span style="white-space:pre">		</span>}
<span style="white-space:pre">		</span>int index = str[i] - 'a';//下溯的分支编号
<span style="white-space:pre">		</span>if (!p->ChildNodes[index])
<span style="white-space:pre">			</span>p->ChildNodes[index] = new TrieTreeNode<T>(MaxBranchNum);
<span style="white-space:pre">		</span>p = p->ChildNodes[index];
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>if (!p->word)//该词以前没有出现过
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>p->word = new char[strlen(str) + 1];
<span style="white-space:pre">		</span>strcpy_s(p->word, strlen(str) + 1, str);
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>p->Freq++;
}


template<class T>
void TrieTree<T>::Insert(const T* str, const int num)
{
<span style="white-space:pre">	</span>TrieTreeNode<T>* p = root;
<span style="white-space:pre">	</span>for (int i = 0; str[i]; i++)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>if (str[i]<'a' || str[i]>'z')
<span style="white-space:pre">		</span>{
<span style="white-space:pre">			</span>cout << "格式错误!" << endl;
<span style="white-space:pre">			</span>return;
<span style="white-space:pre">		</span>}
<span style="white-space:pre">		</span>int index = str[i] - 'a';//下溯的分支编号
<span style="white-space:pre">		</span>if (!p->ChildNodes[index])
<span style="white-space:pre">			</span>p->ChildNodes[index] = new TrieTreeNode<T>(MaxBranchNum);
<span style="white-space:pre">		</span>p = p->ChildNodes[index];
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>if (!p->word)//该词以前没有出现过
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>p->word = new char[strlen(str) + 1];
<span style="white-space:pre">		</span>strcpy_s(p->word, strlen(str) + 1, str);
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>p->Freq++;
<span style="white-space:pre">	</span>if (num < p->ID || p->ID == -1)//取最小的num作为当前节点代表的单词的ID
<span style="white-space:pre">		</span>p->ID = num;
}


template<class T>
void TrieTree<T>::PrintALL()
{
<span style="white-space:pre">	</span>Print(root);
}


template<class T>
void TrieTree<T>::Print(const TrieTreeNode<T>* p)
{
<span style="white-space:pre">	</span>if (p == NULL)
<span style="white-space:pre">		</span>return;
<span style="white-space:pre">	</span>if (p->Freq > 0)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>cout << "单词:" << p->word << "<span style="white-space:pre">	</span>频数:" << p->Freq;
<span style="white-space:pre">		</span>if (p->ID >= 0)
<span style="white-space:pre">			</span>cout << "<span style="white-space:pre">		</span>ID:" << p->ID;
<span style="white-space:pre">		</span>cout << endl;
<span style="white-space:pre">	</span>}
<span style="white-space:pre">	</span>for (int i = 0; i < MaxBranchNum; i++)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>if (p->ChildNodes[i])
<span style="white-space:pre">		</span>{
<span style="white-space:pre">			</span>Print(p->ChildNodes[i]);
<span style="white-space:pre">		</span>}
<span style="white-space:pre">	</span>}


}

//main.cpp
#pragma once
#include<iostream>
#include<fstream>
#include"TrieTree.h"
using namespace std;

void test(TrieTree<char>* t)
{
	char* charbuffer = new char[50];
	char* cb = charbuffer;

	fstream fin("d:\\words.txt");
	if (!fin){
		cout << "File open error!\n";
		return;
	}
	char c;
	int num = 0;
	while ((c = fin.get()) != EOF)
	{
		if (c >= '0'&&c <= '9')
			num = num * 10 + c - '0';
		if (c >= 'a'&&c <= 'z')
			*cb++ = c;
		if (c == '\n')
		{
			*cb = NULL;
			t->Insert(charbuffer, num);
			cb = charbuffer;
			num = 0;
		}
	}
	fin.close();
}


void main()
{
	TrieTree<char>* t = new TrieTree<char>(26);
	char* pre = "fu";
	/*char* c1 = "fuck";
	char* c2 = "class";
	char* c3 = "name";
	char* c4 = NULL;
	char* c5 = "fucka";
	char* c6 = "fuckaa";
	char* c7 = "fuckaabc";
	t->Insert(c1);
	t->Delete(c1);
	t->Insert(c1);
	t->Insert(c2);
	t->Insert(c5);
	t->Insert(c6);
	t->Insert(c7);*/
	test(t);
	t->PrintALL();
	cout << endl;
	t->PrintPre(pre);
	//cout << t->Search(c1) << endl;
	system("pause");
}

检索结果:

《Trie树(字典树)的C++实现》

    原文作者:Trie树
    原文地址: https://blog.csdn.net/hgqqtql/article/details/42309049
    本文转自网络文章,转载此文章仅为分享知识,如有侵权,请联系博主进行删除。
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