Trie
A trie or prefix tree is a tree data structure used to efficiently store and retrieve keys in a dataset of strings.
Overview
208. Implement Trie (Prefix Tree) will be used as an example.
A trie (pronounced as "try") or prefix tree is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. There are various applications of this data structure, such as autocomplete and spellchecker.
Implement the Trie class:
- Trie() Initializes the trie object.
- void insert(String word) Inserts the string word into the trie.
- boolean search(String word) Returns true if the string word is in the trie (i.e., was inserted before), and false otherwise.
- boolean startsWith(String prefix) Returns true if there is a previously inserted string word that has the prefix prefix, and false otherwise.
Example 1:
Input
["Trie", "insert", "search", "search", "startsWith", "insert", "search"]
[[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
Output
[null, null, true, false, true, null, true]
Explanation
Trie trie = new Trie();
trie.insert("apple");
trie.search("apple"); // return True
trie.search("app"); // return False
trie.startsWith("app"); // return True
trie.insert("app");
trie.search("app"); // return TrueConstraints:
- word and prefix consist only of lowercase English letters.
- At most 3 * 10^4 calls in total will be made to insert, search, and startsWith.
Trie
We can see Trie containing a number of Trie nodes. Each node contains a value and links to other nodes. We start from the root, we traverse till so that we have . At this node, we have three different nodes to traverse so that we have , , and . We can also further to have and and so on.
Diagram Source: https://www.geeksforgeeks.org/
Trie Node
Each Trie Node should have a children array with the size of for character to . Also it has a boolean variable to indicate if a word is ended at this node.
class TrieNode {
public:
// is a word ended at this node
bool isEndOfWord;
// children for 26 characters
TrieNode* children[26];
// constructor - setting initial values
TrieNode() {
// no word is ended here
isEndOfWord = false;
// not linking to other Trie node
for (int i = 0; i < 26; i++) {
children[i] = NULL;
}
}
};Initializing
Trie() {
// init Trie - define the very first node
root = new TrieNode();
}Searching
Given a word, search returns if the word is in the trie.
bool search(string word) {
// start from the root node
TrieNode* node = root;
// iterate the word
for (int i = 0; i < (int) word.size(); i++) {
// get the index of the character
// a -> 0
// b -> 1
// ...
// z -> 25
int idx = word[i] - 'a';
// if there is no such node, that means the word doesn't exist
if (!node->children[idx]) return false;
// otherwise, traverse the next node
node = node->children[idx];
}
// check if this node is marked with isEndOfWord = true
return node->isEndOfWord;
}Insertion
Given a word, insert inserts it into the trie.
void insert(string word) {
// start from the root node
TrieNode* node = root;
for (int i = 0; i < (int) word.size(); i++) {
// get the index of the character
// a -> 0
// b -> 1
// ...
// z -> 25
int idx = word[i] - 'a';
// traverse each node,
if (!node->children[idx]) {
// if the node doesn't exist,
// create a new node
node->children[idx] = new TrieNode();
}
// traverse the next one
node = node->children[idx];
}
// mark this node with isEndOfWord = true
node->isEndOfWord = true;
}startsWith
Given a prefix, startsWith checks if there is any word in the trie that starts with the given prefix.
bool startsWith(string prefix) {
// start from the root node
TrieNode* node = root;
// iterate each character in prefix
for (int i = 0; i < (int) prefix.size(); i++) {
// get the index of the character
// a -> 0
// b -> 1
// ...
// z -> 25
int idx = prefix[i] - 'a';
// if there is no such node, that means the word doesn't exist
if (!node->children[idx]) return false;
// otherwise, traverse the next node
node = node->children[idx];
}
// all target nodes have been traversed, return true here
return true;
}