Tries

Tries, also known as prefix trees, are an efficient data structure used for storing and retrieving strings.

A trie is a tree-like structure where each node represents a character from a word. The root node represents an empty string, and the children of each node represent successive characters of the word. The word is stored by following the path from the root to the leaf node.

Tries provide an efficient way to search for a given word in a large set of words. They have a time complexity of O(L), where L is the length of the word.

Here's an example of a Trie data structure for storing words like "apple", "banana", and "cherry":

1            ''
2          ↙   ↘
3        a       b
4       |       |
5       p       a
6       |       |
7       p       n
8       |   ↙   ↘
9       l e       a
10                 |
11                 n
12                 |
13                 a

In the above example, each path from the root to a leaf represents a complete word. The path from the root to the node 'l' represents the word "apple".

Tries are commonly used in tasks such as autocomplete, spell checkers, and word search puzzles.

Let's take a look at the implementation of a Trie data structure in C++:

1<<code>>

In the code snippet above, we define a TrieNode struct that represents a node in the trie. Each TrieNode contains a map of characters to their corresponding child TrieNode, representing the children of the current node. We also define a Trie class that consists of the root TrieNode and provides the insert and search operations.

Try running the code to see how the Trie data structure can be used to insert and search for words.

Use Cases

Tries are useful in scenarios where we need to efficiently search for strings or perform operations based on string prefixes. Some common use cases for tries include:

• Autocompletion: Tries are commonly used in autocomplete features to suggest words as the user types.
• Spell checkers: Tries can be used to efficiently check the spelling of words by searching for them in a dictionary.
• Word search puzzles: Tries can be used to solve word search puzzles by efficiently searching for words in a grid of characters.
• IP routing: Tries can be used to store IP addresses and perform fast lookups for routing packets in computer networks.

Tries are a powerful data structure for handling string-related operations efficiently.

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}

#include <iostream>

#include <unordered_map>

​

using namespace std;

​

// Trie node

struct TrieNode {

    unordered_map<char, TrieNode*> children;

    bool isEndOfWord;

};

​

// Trie class

class Trie {

private:

    TrieNode* root;

​

public:

    // Constructor

    Trie() {

        root = new TrieNode();

    }

​

    // Insert a word into the trie

    void insert(string word) {

        TrieNode* curr = root;

        for (char c : word) {

            if (curr->children.find(c) == curr->children.end()) {

                curr->children[c] = new TrieNode();

            }