A trie, also known as a prefix tree, is a tree-like data structure that is used to efficiently store and retrieve strings. Unlike other data structures such as arrays or linked lists, a trie organizes its data based on the characters that make up each string. This makes it particularly useful for tasks such as searching for words in a dictionary or implementing autocomplete functionality.

## How does a Trie work?

To understand how a trie works, let’s consider an example where we want to store a set of words: “apple”, “app”, “banana”, “bat”, and “ball”.

At the root of the trie, we start with an empty node. Each node has multiple branches, each corresponding to a character. In this case, the first level branches would be ‘a’, ‘b’, and ‘b’.

We create nodes for each character in the word and link them together. For example, to store the word “apple”, we start at the root node and follow the ‘a’ branch.

At this point, we create a new node for ‘a’. We then follow the ‘p’ branch from this new node and create another node for ‘p’. We repeat this process until we have visited all characters in the word.

**This is how our trie looks like:**

In the trie, each node can have multiple branches, representing the different characters that can follow the current character. Leaf nodes represent the end of a word.

**Advantages of using a Trie:**

### Efficient search:

Searching for a word in a trie is very efficient. It typically takes O(k) time, where k is the length of the word being searched for. This is because we only need to traverse the characters in the word.

### Space-efficient:

Tries are space-efficient when storing words with common prefixes. Since common prefixes share nodes, tries can save space compared to other data structures like hash tables or binary trees.

### Prefix matching and autocomplete:

Tries are particularly useful for tasks that involve prefix matching or implementing autocomplete functionality. By traversing down the trie, we can quickly find all words with a given prefix.

## Conclusion

A trie is a powerful data structure for efficient string storage and retrieval. Its ability to store and search for words based on their prefixes makes it highly suitable for applications such as autocomplete systems and spell checkers. By organizing strings based on their characters, tries provide an efficient way to store and search large sets of strings with minimal time complexity.

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