Trie树及Java实现

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引言

Trie树，又称为前缀树或字典树，是一种有序树，用于保存关联数组，其中的键通常是字符串。与二叉查找树不同，键不是直接保存在节点中，而是由节点在树中的位置决定。一个节点的所有子孙都有相同的前缀，也就是这个节点对应的字符串，而根节点对应空字符串。

如下是一棵典型的Trie树:

Trie的来源是Retrieval,它常用于前缀匹配和词频统计。可能有人要说了，词频统计简单啊，一个hash或者一个堆就可以搞定，但问题来了，如果内存有限呢？还能这么
玩吗？所以这里我们就可以用trie树来压缩下空间，因为公共前缀都是用一个节点保存的。

1.定义

这里为了简化，只考虑了26个小写字母。

首先是节点的定义:

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public class TrieNode {
    
    public TrieNode[] children;
    public char data;
    public int freq;
    public TrieNode() {
        //因为有26个字母
        children = new TrieNode[26];
        freq = 0;
    }
}

然后是Trie树的定义: 

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public class TrieTree {
    private TrieNode root;
    public TrieTree(){
        root=new TrieNode();
    }
    ...
}

2.插入

由于是26叉树，故可通过charArray[index]-‘a’;来得知字符应该放在哪个孩子中。 

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public void insert(String word){
      if(TextUtils.isEmpty(word)){
          return;
      }
      insertNode(root,word.toCharArray(),0);
  }
  private static void insertNode(TrieNode rootNode,char[]charArray,int index){
      int k=charArray[index]-'a';
      if(k<0||k>25){
          throw new RuntimeException("charArray[index] is not a alphabet!");
      }
      if(rootNode.children[k]==null){
          rootNode.children[k]=new TrieNode();
          rootNode.children[k].data=charArray[index];
      }
      if(index==charArray.length-1){
          rootNode.children[k].freq++;
          return;
      }else{
          insertNode(rootNode.children[k],charArray,index+1);
      }
  }

3.移除节点

移除操作中，需要对词频进行减一操作。 

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public void remove(String word){
       if(TextUtils.isEmpty(word)){
           return;
       }
       remove(root,word.toCharArray(),0);
   }
   private static void remove(TrieNode rootNode,char[]charArray,int index){
       int k=charArray[index]-'a';
       if(k<0||k>25){
           throw new RuntimeException("charArray[index] is not a alphabet!");
       }
       if(rootNode.children[k]==null){
           //it means we cannot find the word in this tree
           return;
       }
       if(index==charArray.length-1&&rootNode.children[k].freq >0){
           rootNode.children[k].freq--;
       }
       remove(rootNode.children[k],charArray,index+1);
   }

4.查找频率

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public int getFreq(String word){
     if(TextUtils.isEmpty(word)){
         return 0;
     }
     return getFreq(root,word.toCharArray(),0);
 }
 private static int getFreq(TrieNode rootNode,char[]charArray,int index){
     int k=charArray[index]-'a';
      if(k<0||k>25){
         throw new RuntimeException("charArray[index] is not a alphabet!");
     }
     //it means the word is not in the tree
     if(rootNode.children[k]==null){
         return 0;
     }
     if(index==charArray.length-1){
         return rootNode.children[k].freq;
     }
     return getFreq(rootNode.children[k],charArray,index+1);
 }

5.测试

测试代码如下: 

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public static void test(){
       TrieTree trieTree=new TrieTree();
       String sourceStr="Democratic presumptive nominee Hillary Clintons campaign posed pounced on Trumps assertion that British term monetary turmoil might benefit his business venture in Scotland";
       //String sourceStr="the that";
       sourceStr=sourceStr.toLowerCase();
       String[]strArray=sourceStr.split(" ");
       for(String str:strArray){
           trieTree.insert(str);
       }
       String sourceStr2="Every president is tested by world events But Donald Trump thinks about how is his golf resort can profit from that";
       sourceStr2=sourceStr2.toLowerCase();
       String[]strArray2=sourceStr2.split(" ");
       for(String str:strArray2){
           trieTree.insert(str);
       }
       BinaryTree.print("frequence of 'that':"+trieTree.getFreq("that"));
       BinaryTree.print("\nfrequence of 'donald':"+trieTree.getFreq("donald"));
       trieTree.remove("that");
       BinaryTree.print("\nafter remove 'that' once,freq of 'that':"+trieTree.getFreq("that"));
       trieTree.remove("that");
       BinaryTree.print("\nafter remove 'that' twice,freq of 'that':"+trieTree.getFreq("that"));
       trieTree.remove("donald");
       BinaryTree.print("\nafter remove 'donald' once,freq of 'donald':"+trieTree.getFreq("donald"));
       BinaryTree.reallyStartPrint();
   }

测试结果如下: