Question

剑指 Offer II 062. 实现前缀树

题目描述

Trie（发音类似 "try"）或者说 前缀树 是一种树形数据结构，用于高效地存储和检索字符串数据集中的键。这一数据结构有相当多的应用情景，例如自动补完和拼写检查。

请你实现 Trie 类：

• Trie() 初始化前缀树对象。
• void insert(String word) 向前缀树中插入字符串 word 。
• boolean search(String word) 如果字符串 word 在前缀树中，返回 true（即，在检索之前已经插入）；否则，返回 false 。
• boolean startsWith(String prefix) 如果之前已经插入的字符串 word 的前缀之一为 prefix ，返回 true ；否则，返回 false 。

 

示例：

输入
inputs = ["Trie", "insert", "search", "search", "startsWith", "insert", "search"]
inputs = [[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
输出
[null, null, true, false, true, null, true]

解释
Trie trie = new Trie();
trie.insert("apple");
trie.search("apple");   // 返回 True
trie.search("app");   // 返回 False
trie.startsWith("app"); // 返回 True
trie.insert("app");
trie.search("app");   // 返回 True

 

提示：

• 1 <= word.length, prefix.length <= 2000
• word 和 prefix 仅由小写英文字母组成
• insert、search 和 startsWith 调用次数 总计 不超过 3 * 104 次

 

 

注意：本题与主站 208 题相同：https://leetcode.cn/problems/implement-trie-prefix-tree/ 

解法

方法一：前缀树

前缀树每个节点包括两部分：

1. 指向子节点的指针数组 $children$，对于本题而言，数组长度为 $26$，即小写英文字母的数量。$children[0]$ 对应小写字母 $a$，…，$children[25]$ 对应小写字母 $z$。
2. 布尔字段 $isEnd$，表示该节点是否为字符串的结尾。

1. 插入字符串

我们从字典树的根开始，插入字符串。对于当前字符对应的子节点，有两种情况：

• 子节点存在。沿着指针移动到子节点，继续处理下一个字符。
• 子节点不存在。创建一个新的子节点，记录在 $children$ 数组的对应位置上，然后沿着指针移动到子节点，继续搜索下一个字符。

重复以上步骤，直到处理字符串的最后一个字符，然后将当前节点标记为字符串的结尾。

2. 查找前缀

我们从字典树的根开始，查找前缀。对于当前字符对应的子节点，有两种情况：

• 子节点存在。沿着指针移动到子节点，继续搜索下一个字符。
• 子节点不存在。说明字典树中不包含该前缀，返回空指针。

重复以上步骤，直到返回空指针或搜索完前缀的最后一个字符。

若搜索到了前缀的末尾，就说明字典树中存在该前缀。此外，若前缀末尾对应节点的 $isEnd$ 为真，则说明字典树中存在该字符串。

class Trie:
  def __init__(self):
    self.children = [None] * 26
    self.is_end = False

  def insert(self, word: str) -> None:
    node = self
    for c in word:
      idx = ord(c) - ord('a')
      if node.children[idx] is None:
        node.children[idx] = Trie()
      node = node.children[idx]
    node.is_end = True

  def search(self, word: str) -> bool:
    node = self._search_prefix(word)
    return node is not None and node.is_end

  def startsWith(self, prefix: str) -> bool:
    node = self._search_prefix(prefix)
    return node is not None

  def _search_prefix(self, prefix: str):
    node = self
    for c in prefix:
      idx = ord(c) - ord('a')
      if node.children[idx] is None:
        return None
      node = node.children[idx]
    return node


# Your Trie object will be instantiated and called as such:
# obj = Trie()
# obj.insert(word)
# param_2 = obj.search(word)
# param_3 = obj.startsWith(prefix)

class Trie {
  private Trie[] children;
  private boolean isEnd;

  public Trie() {
    children = new Trie[26];
  }

  public void insert(String word) {
    Trie node = this;
    for (char c : word.toCharArray()) {
      int idx = c - 'a';
      if (node.children[idx] == null) {
        node.children[idx] = new Trie();
      }
      node = node.children[idx];
    }
    node.isEnd = true;
  }

  public boolean search(String word) {
    Trie node = searchPrefix(word);
    return node != null && node.isEnd;
  }

  public boolean startsWith(String prefix) {
    Trie node = searchPrefix(prefix);
    return node != null;
  }

  private Trie searchPrefix(String s) {
    Trie node = this;
    for (char c : s.toCharArray()) {
      int idx = c - 'a';
      if (node.children[idx] == null) {
        return null;
      }
      node = node.children[idx];
    }
    return node;
  }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.insert(word);
 * boolean param_2 = obj.search(word);
 * boolean param_3 = obj.startsWith(prefix);
 */

class Trie {
private:
  vector<Trie*> children;
  bool isEnd;

  Trie* searchPrefix(string s) {
    Trie* node = this;
    for (char c : s) {
      int idx = c - 'a';
      if (!node->children[idx]) return nullptr;
      node = node->children[idx];
    }
    return node;
  }

public:
  Trie()
    : children(26)
    , isEnd(false) {}

  void insert(string word) {
    Trie* node = this;
    for (char c : word) {
      int idx = c - 'a';
      if (!node->children[idx]) node->children[idx] = new Trie();
      node = node->children[idx];
    }
    node->isEnd = true;
  }

  bool search(string word) {
    Trie* node = searchPrefix(word);
    return node != nullptr && node->isEnd;
  }

  bool startsWith(string prefix) {
    Trie* node = searchPrefix(prefix);
    return node != nullptr;
  }
};

/**
 * Your Trie object will be instantiated and called as such:
 * Trie* obj = new Trie();
 * obj->insert(word);
 * bool param_2 = obj->search(word);
 * bool param_3 = obj->startsWith(prefix);
 */

type Trie struct {
  children [26]*Trie
  isEnd  bool
}

func Constructor() Trie {
  return Trie{}
}

func (this *Trie) Insert(word string) {
  node := this
  for _, c := range word {
    idx := c - 'a'
    if node.children[idx] == nil {
      node.children[idx] = &Trie{}
    }
    node = node.children[idx]
  }
  node.isEnd = true
}

func (this *Trie) Search(word string) bool {
  node := this.SearchPrefix(word)
  return node != nil && node.isEnd
}

func (this *Trie) StartsWith(prefix string) bool {
  node := this.SearchPrefix(prefix)
  return node != nil
}

func (this *Trie) SearchPrefix(s string) *Trie {
  node := this
  for _, c := range s {
    idx := c - 'a'
    if node.children[idx] == nil {
      return nil
    }
    node = node.children[idx]
  }
  return node
}

/**
 * Your Trie object will be instantiated and called as such:
 * obj := Constructor();
 * obj.Insert(word);
 * param_2 := obj.Search(word);
 * param_3 := obj.StartsWith(prefix);
 */

/**
 * Initialize your data structure here.
 */
var Trie = function () {
  this.children = {};
};

/**
 * Inserts a word into the trie.
 * @param {string} word
 * @return {void}
 */
Trie.prototype.insert = function (word) {
  let node = this.children;
  for (let char of word) {
    if (!node[char]) {
      node[char] = {};
    }
    node = node[char];
  }
  node.isEnd = true;
};

/**
 * Returns if the word is in the trie.
 * @param {string} word
 * @return {boolean}
 */
Trie.prototype.search = function (word) {
  let node = this.searchPrefix(word);
  return node != undefined && node.isEnd != undefined;
};

Trie.prototype.searchPrefix = function (prefix) {
  let node = this.children;
  for (let char of prefix) {
    if (!node[char]) return false;
    node = node[char];
  }
  return node;
};

/**
 * Returns if there is any word in the trie that starts with the given prefix.
 * @param {string} prefix
 * @return {boolean}
 */
Trie.prototype.startsWith = function (prefix) {
  return this.searchPrefix(prefix);
};

/**
 * Your Trie object will be instantiated and called as such:
 * var obj = new Trie()
 * obj.insert(word)
 * var param_2 = obj.search(word)
 * var param_3 = obj.startsWith(prefix)
 */

public class Trie {
  bool isEnd;
  Trie[] children = new Trie[26];

  public Trie() {

  }

  public void Insert(string word) {
    Trie node = this;
    foreach (var c in word)
    {
      var idx = c - 'a';
      node.children[idx] ??= new Trie();
      node = node.children[idx];
    }
    node.isEnd = true;
  }

  public bool Search(string word) {
    Trie node = SearchPrefix(word);
    return node != null && node.isEnd;
  }

  public bool StartsWith(string prefix) {
    Trie node = SearchPrefix(prefix);
    return node != null;
  }

  private Trie SearchPrefix(string s) {
    Trie node = this;
    foreach (var c in s)
    {
      var idx = c - 'a';
      if (node.children[idx] == null)
      {
        return null;
      }
      node = node.children[idx];
    }
    return node;
  }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.Insert(word);
 * bool param_2 = obj.Search(word);
 * bool param_3 = obj.StartsWith(prefix);
 */