Tries are a popular data structure used for efficient retrieval of keys in various applications. In this article, we will explore how tries are implemented in data structures and understand their underlying concepts.

## What is a Trie?

A trie, also known as a prefix tree, is an ordered tree-based data structure that stores a collection of strings or words. It provides fast and efficient retrieval of strings based on partial matches or prefixes.

Tries are widely used in applications like word autocomplete, spell-checking, IP routing tables, and much more. Their efficient search and retrieval capabilities make them an ideal choice for these scenarios.

## Trie Structure

A trie consists of nodes that represent characters or keys. Each node has multiple branches, typically equal to the number of unique characters in the dataset.

These branches connect to child nodes representing subsequent characters in the string. The root node represents an empty string or the starting point of all keys.

Let’s take an example to understand the trie structure better:

root / | \ c d p / \ / \ a h i o / \ | | t r n n

In this example, we have three keys: “cat”, “chat”, and “pin”. The trie represents these keys with character nodes connected through branches.

## Implementing a Trie

Now that we understand the basic structure of tries let’s dive into their implementation.

### Trie Node Structure

To implement a trie, we start by defining the structure for each node:

struct TrieNode { struct TrieNode* children[ALPHABET_SIZE]; bool isEndOfWord; };

Each trie node contains an array of pointers to child nodes, where `ALPHABET_SIZE`

represents the size of the character set. In English, this would typically be 26 (for A-Z).

The `isEndOfWord`

flag indicates whether the current node marks the end of a word or not.

### Trie Operations

Let’s discuss the key operations involved in trie implementation:

#### Insertion

To insert a new key into the trie, we start from the root and follow these steps:

- If the current character exists as a child node, move to that child.
- If the current character doesn’t exist as a child node, create a new node and link it to the current node.
- Repeat steps 1 and 2 until all characters of the key are processed.
- Mark the last node as an end-of-word node.

#### Search

To search for a key in a trie, we start from the root and follow these steps:

- If at any point there is no branch for the current character, return false (key not found).
- If all characters of the key are processed and we reach an end-of-word node, return true (key found).

#### Deletion

To delete a key from a trie, we start from the root and follow these steps:

- If at any point there is no branch for the current character, return false (key not found).
- If all characters of the key are processed and we reach an end-of-word node, mark it as a non-end-of-word node.
- If any intermediate node becomes useless (no child nodes and not an end-of-word node), remove it.

These are the basic operations involved in trie implementation. By combining these operations, we can build a fully functional trie data structure.

## Conclusion

Tries provide an efficient way to store and retrieve strings based on prefixes. They are widely used in various applications and offer fast search capabilities. Understanding the underlying concepts of tries and their implementation can help you leverage their power in your own projects.

Now that you have a solid understanding of how tries are implemented in data structures, you can explore further and experiment with them in your own code.