14前缀树
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前缀树的性质
1、单个字符串中，字符串从前到后的加到一颗多叉树上
2、字符放在路上，节点上有专属的数据项(常见的是pass和end值)
3、所有样本都这样添加，如果没有路就新建，如有路就复用
4、沿途节点的pass值增加1，每个字符串结束时来到的节点end值增加1。
//所有字符串都是a~z小写
public static class Node1
private int pass;
private int end;
private Node1[] nexts;
public Node1()
pass=0;
end=0;
//本程序假设数组字符串全都是小写的字母，所以初始化每个节点下面都有26个节点
nexts =new Node1[26];
//方法1
public static class Trie1
private Node1 root;
public Trie1()
root=new Node1();
//在数组中新增一个字符串
public void insert(String word)
if (word == null)
return;
//将字符串转化成字符
char[] chars = word.toCharArray();
//一个引用(相当于一个箭头)，从头结点出发
Node1 node= root;
//新加字符串，头节点的pass值+1
node.pass++;
int path=0;
//从左到右遍历字符
for (int i = 0; i < chars.length; i++)
//由字符决定走哪条路，对应的ASCII相减：a-a=0 b-a=1
path=chars[i] - a;
//如果下一个节点为空，证明没有出现过，则新建节点
if(node.nexts[path]==null)
node.nexts[path]=new Node1();
//node跳到新建的节点上
node =node.nexts[path];
node.pass++;
//一个字符串走到终点时，end+1
node.end++;
//查询word这个单词之前加入过几次
public int search(String word)
if(word==null)
return 0;
char[] chars = word.toCharArray();
//将箭头初始化为头节点
Node1 node=root;
int path=0;
for (int i=0;i<chars.length;i++)
path = chars[i] -a;
if(node.nexts[path]==null)
return 0;
node=node.nexts[path];
return node.end;
//所有加入的字符串中，有几个是以pre这个这个字符串作为前缀的
public int prefixNumber(String word)
if (word==null)
return 0;
char[] chars = word.toCharArray();
Node1 node=root;
int path =0;
for(int i=0;i<chars.length;i++)
path = chars[i] - a;
if(node.nexts[path]==null)
return 0;
node=node.nexts[path];
return node.pass;
//删除一个字符串
public void delete(String word)
//先去查询一下看是否有word字符串，如果有，再进行删除，没有就直接跳出
if(search(word)!=0)
char[] chars = word.toCharArray();
//指针指向头节点
Node1 node=root;
//头节点的pass值减1
node.pass--;
int path=0;
for (int i=0;i<chars.length;i++)
path = chars[i] -a;
//如果当前节点的下一个节点的pass值为0，则当前节点的下一个节点指向空，之后的节点都没有意义了，没必要走下去
if (--node.nexts[path].pass==0)
node.nexts[path]=node;
return;
node=node.nexts[path];
node.end--;
//方法2：支持多种类字符
public static class Node2
public int pass;
public int end;
public HashMap<Integer, Node2> nexts;
public Node2()
pass = 0;
end = 0;
nexts = new HashMap<>();
public static class Trie2
private Node2 root;
public Trie2()
root=new Node2();
//加入一个字符串
public void insert(String word)
if(word==null)
return;
char[] chars = word.toCharArray();
Node2 node=root;
node.pass++;
int path =0;
for (int i=0;i<chars.length;i++)
path = (int)chars[i];
if (!node.nexts.containsKey(path))
node.nexts.put(path,new Node2());
node=node.nexts.get(path);
node.pass++;
node.end++;
public void delete(String word)
if (search(word) != 0)
char[] chs = word.toCharArray();
Node2 node = root;
node.pass--;
int index = 0;
for (int i = 0; i < chs.length; i++)
index = (int) chs[i];
if (--node.nexts.get(index).pass == 0)
node.nexts.remove(index);
return;
node = node.nexts.get(index);
node.end--;
// word这个单词之前加入过几次
public int search(String word)
if (word == null)
return 0;
char[] chs = word.toCharArray();
Node2 node = root;
int index = 0;
for (int i = 0; i < chs.length; i++)
index = (int) chs[i];
if (!node.nexts.containsKey(index))
return 0;
node = node.nexts.get(index);
return node.end;
// 所有加入的字符串中，有几个是以pre这个字符串作为前缀的
public int prefixNumber(String pre)
if (pre == null)
return 0;
char[] chs = pre.toCharArray();
Node2 node = root;
int index = 0;
for (int i = 0; i < chs.length; i++)
index = (int) chs[i];
if (!node.nexts.containsKey(index))
return 0;
node = node.nexts.get(index);
return node.pass;
//对数器
public static class Right
private HashMap<String, Integer> box;
public Right()
box = new HashMap<>();
public void insert(String word)
if (!box.containsKey(word))
box.put(word, 1);
else
box.put(word, box.get(word) + 1);
public void delete(String word)
if (box.containsKey(word))
if (box.get(word) == 1)
box.remove(word);
else
box.put(word, box.get(word) - 1);
public int search(String word)
if (!box.containsKey(word))
return 0;
else
return box.get(word);
public int prefixNumber(String pre)
int count = 0;
for (String cur : box.keySet())
if (cur.startsWith(pre))
count += box.get(cur);
return count;
// for test
public static String generateRandomString(int strLen)
char[] ans = new char[(int) (Math.random() * strLen) + 1];
for (int i = 0; i < ans.length; i++)
int value = (int) (Math.random() * 6);
ans[i] = (char) (97 + value);
return String.valueOf(ans);
// for test
public static String[] generateRandomStringArray(int arrLen, int strLen)
String[] ans = new String[(int) (Math.random() * arrLen) + 1];
for (int i = 0; i < ans.length; i++)
ans[i] = generateRandomString(strLen);
return ans;
public static void main(String[] args)
int arrLen = 100;
int strLen = 20;
int testTimes = 100000;
for (int i = 0; i < testTimes; i++)
String[] arr = generateRandomStringArray(arrLen, strLen);
Trie1 trie1 = new Trie1();
Trie2 trie2 = new Trie2();
Right right = new Right();
for (int j = 0; j < arr.length; j++)
double decide = Math.random();
if (decide < 0.25)
trie1.insert(arr[j]);
trie2.insert(arr[j]);
right.insert(arr[j]);
else if (decide < 0.5)
trie1.delete(arr[j]);
trie2.delete(arr[j]);
right.delete(arr[j]);
else if (decide < 0.75)
int ans1 = trie1.search(arr[j]);
int ans2 = trie2.search(arr[j]);
int ans3 = right.search(arr[j]);
if (ans1 != ans2 || ans2 != ans3)
System.out.println("Oops!");
else
int ans1 = trie1.prefixNumber(arr[j]);
int ans2 = trie2.prefixNumber(arr[j]);
int ans3 = right.prefixNumber(arr[j]);
if (ans1 != ans2 || ans2 != ans3)
System.out.println("Oops!");
System.out.println("finish!");
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