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.
1typedef struct TrieNode {
2 struct TrieNode *children[26];
3 bool isEndOfWord;
4} TrieNode;
5
6TrieNode* createNode() {
7 TrieNode *node = (TrieNode *)malloc(sizeof(TrieNode));
8 node->isEndOfWord = false;
9 for(int i = 0; i < 26; i++)
10 node->children[i] = NULL;
11 return node;
12}
13
14typedef struct {
15 TrieNode *root;
16} Trie;
17
18Trie* trieCreate() {
19 Trie *trie = (Trie *)malloc(sizeof(Trie));
20 trie->root = createNode();
21 return trie;
22}
23
24void trieInsert(Trie* obj, char * word) {
25 TrieNode *node = obj->root;
26 while (*word) {
27 int index = *word - 'a';
28 if (!node->children[index])
29 node->children[index] = createNode();
30 node = node->children[index];
31 word++;
32 }
33 node->isEndOfWord = true;
34}
35
36bool trieSearch(Trie* obj, char * word) {
37 TrieNode *node = obj->root;
38 while (*word) {
39 int index = *word - 'a';
40 if (!node->children[index])
41 return false;
42 node = node->children[index];
43 word++;
44 }
45 return node->isEndOfWord;
46}
47
48bool trieStartsWith(Trie* obj, char * prefix) {
49 TrieNode *node = obj->root;
50 while (*prefix) {
51 int index = *prefix - 'a';
52 if (!node->children[index])
53 return false;
54 node = node->children[index];
55 prefix++;
56 }
57 return true;
58}
59
60void trieFree(Trie* obj) {
61 // A function to recursively free nodes would be here if needed.
62 free(obj);
63}We first define a TrieNode structure with a children array to hold 26 letters and a boolean isEndOfWord to check if a node marks the end of a word. The createNode function initializes each node. TrieCreate initializes the trie by setting the root node.
The methods work by converting each character of the word or prefix into an index (0-25 for 'a'-'z'), navigating the children array of nodes for insertion or search operations. The insert function loops through each character, generating nodes along the path if needed, setting the isEndOfWord flag at the end. The search verifies both existence and termination of the string in the Trie, while startsWith logic only requires the prefix traversal.
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.