This approach involves creating a basic Trie data structure using a tree of nodes. Each node represents a character in a word. Starting from a root node, each character of the word is inserted sequentially, with branches representing the progression to subsequent characters. This forms a chain of nodes (linked in a tree-like manner) from the root to the nodes representing complete words. For searching, we traverse these nodes based on the characters of the input word or prefix to check for existence.
Time Complexity: Insert, search, and startsWith operations are O(m), where m is the length of the word/prefix.
Space Complexity: O(26 * n * m) in the worst case, where n is the number of inserted words and m is the average length of the words. Each insertion can potentially add m nodes with 26 possible children each.
1class TrieNode:
2 def __init__(self):
3 self.children = {}
4 self.is_end_of_word = False
5
6class Trie:
7 def __init__(self):
8 self.root = TrieNode()
9
10 def insert(self, word: str) -> None:
11 node = self.root
12 for char in word:
13 if char not in node.children:
14 node.children[char] = TrieNode()
15 node = node.children[char]
16 node.is_end_of_word = True
17
18 def search(self, word: str) -> bool:
19 node = self.root
20 for char in word:
21 if char not in node.children:
22 return False
23 node = node.children[char]
24 return node.is_end_of_word
25
26 def startsWith(self, prefix: str) -> bool:
27 node = self.root
28 for char in prefix:
29 if char not in node.children:
30 return False
31 node = node.children[char]
32 return TrueIn the Python implementation, we make use of a TrieNode class with a dictionary to store pointers to child nodes and a boolean attribute to denote if the node is the end of a word. The Trie class creates the root node as part of the constructor. The insert method processes the word character by character, adding nodes for characters that are missing in the current sequence. The search and startsWith methods traverse down the trie nodes based on the characters of word or prefix, verifying each node's presence accordingly and checking the is_end_of_word flag when necessary for search.
This approach relies on maps (or hashmaps) for storing children nodes dynamically. The advantage of using maps over arrays in this context arises from reduced space consumption when handling sparse trees since only existing characters are stored. Nodes manage their children using hash references, leading to more flexible branching.
Time Complexity: O(m) per operation where m is the word/prefix length.
Space Complexity: O(n * m), where n estimates the word count and m accounts for varying lengths since nodes only maintain necessary mappings.
1#include <unordered_map>
2using namespace std;
3
4class TrieNode {
5public:
6 unordered_map<char, TrieNode*> children;
7 bool isEndOfWord;
8
9 TrieNode() : isEndOfWord(false) {}
10};
11
12class Trie {
13public:
14 TrieNode* root;
15
16 Trie() {
17 root = new TrieNode();
18 }
19
20 void insert(string word) {
21 TrieNode* node = root;
22 for (char c : word) {
23 if (node->children.find(c) == node->children.end()) {
24 node->children[c] = new TrieNode();
25 }
26 node = node->children[c];
27 }
28 node->isEndOfWord = true;
29 }
30
31 bool search(string word) {
32 TrieNode* node = root;
33 for (char c : word) {
34 if (node->children.find(c) == node->children.end()) {
35 return false;
36 }
37 node = node->children[c];
38 }
39 return node->isEndOfWord;
40 }
41
42 bool startsWith(string prefix) {
43 TrieNode* node = root;
44 for (char c : prefix) {
45 if (node->children.find(c) == node->children.end()) {
46 return false;
47 }
48 node = node->children[c];
49 }
50 return true;
51 }
52};This C++ implementation employs unordered_map in place of fixed-arrays to maintain child nodes in a Trie. Each TrieNode can dynamically allocate space only for characters that appear, leading to memory efficiency especially when nodes have very few immediate child nodes compared to the alphabet size. Insert, search, and startsWith operate similarly as before, now using map functionalities (find) to identify existing children and allocate if necessary.