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.
1public class TrieNode {
2 public TrieNode[] children = new TrieNode[26];
3 public bool isEndOfWord;
4
5 public TrieNode() {
6 isEndOfWord = false;
7 }
8}
9
10public class Trie {
11 private TrieNode root;
12
13 public Trie() {
14 root = new TrieNode();
15 }
16
17 public void Insert(string word) {
18 TrieNode node = root;
19 foreach (char c in word) {
20 int index = c - 'a';
21 if (node.children[index] == null) {
22 node.children[index] = new TrieNode();
23 }
24 node = node.children[index];
25 }
26 node.isEndOfWord = true;
27 }
28
29 public bool Search(string word) {
30 TrieNode node = root;
31 foreach (char c in word) {
32 int index = c - 'a';
33 if (node.children[index] == null) {
34 return false;
35 }
36 node = node.children[index];
37 }
38 return node.isEndOfWord;
39 }
40
41 public bool StartsWith(string prefix) {
42 TrieNode node = root;
43 foreach (char c in prefix) {
44 int index = c - 'a';
45 if (node.children[index] == null) {
46 return false;
47 }
48 node = node.children[index];
49 }
50 return true;
51 }
52}This C# implementation defines a TrieNode class for tree nodes, each of which contains an array to store child pointers for letters and a boolean to identify word completions. The parent Trie class defines a root node to serve as the tree's foundation. The insert method navigates through characters of a supplied word from the root node, adding child nodes as needed and marking the final character's node as the end of a word. The search process follows character nodes down the tree, checking for final node's end-of-word marking. The startsWith method traverses character nodes ensuring their existence without requiring the end-of-word marking.
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.
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 node = node.children.setdefault(char, TrieNode())
14 node.is_end_of_word = True
15
16 def search(self, word: str) -> bool:
17 node = self.root
18 for char in word:
19 if char not in node.children:
20 return False
21 node = node.children[char]
22 return node.is_end_of_word
23
24 def startsWith(self, prefix: str) -> bool:
25 node = self.root
26 for char in prefix:
27 if char not in node.children:
28 return False
29 node = node.children[char]
30 return TrueIn this Python solution, each TrieNode contains a dictionary (children) providing direct access to only required child characters. This approach optimizes storage, especially reducing overhead when branching is sparse. The root provides the base node in the Trie. The insert method applies setdefault for dictionary operation - simplifying conditional insertion logic. Both search and startsWith check the presence of each character in sequence traversing the root to target node, utilizing dictionary fast access and probing methods.