Tries

A Trie (pronounced “try” or “tree”) is a tree-like data structure used for efficiently storing and searching a dynamic set of strings or sequences. It’s particularly useful when you need to perform prefix-based searches, like finding all words that start with a given prefix. Tries are commonly used in tasks involving dictionaries, autocomplete, spell checkers, and more.

A Trie is organized as a tree where each node represents a character. The path from the root node to a specific node forms a string. The edges represent characters, and each node may have multiple child nodes. Tries are often used with alphabets, but they can also be adapted for other types of sequences.

Basic Operations:

1. Insertion: Adding a new string to the Trie involves traversing the Trie and creating nodes for each character in the string. This creates a path representing the string in the Trie.
2. Search: Searching for a string involves traversing the Trie by following the edges corresponding to the characters. If you reach the end of the string and find a node, the string is present.
3. Prefix Search: To find all strings with a given prefix, navigate to the node corresponding to the last character of the prefix and explore its subtree.

Example:
Consider inserting the words “apple,” “app,” “banana,” and “bat” into a Trie:

        root
       / | | \
      a  b b  c
     /    |    |
    p     a    a
   / \     \    \
  p   l     n    t
 /             /
l             a

Applications:
Tries have various applications:

• Dictionary: Tries can be used to store a dictionary of words for fast word lookups.
• Autocomplete: They’re useful for providing suggestions as you type, by finding all words with a given prefix.
• Spell Checker: Tries can be used to quickly check if a given word is spelled correctly.
• IP Routing: Tries are used in networking for efficient IP address routing.
• Phonebook Search: Tries can help search for names/numbers in phonebooks.

Pros:

• Efficient for prefix-based searches and string lookups.
• Minimal memory usage for storing similar prefixes.
• Supports quick insertion and search.

Cons:

• Can consume memory, especially for a large alphabet size.
• May not be the best choice for cases with highly varied sequences.

In summary, a Trie is a tree-like data structure used for storing and searching strings or sequences efficiently. It excels at prefix-based searches and is valuable in various applications involving dictionaries, autocomplete, spell checkers, and more.

Tries Problems:

• Concatenated Words
  Given a list of words, you need to find all the concatenated words in the list. A concatenated word is defined as a word that can be formed by concatenating at least two other words from the given list.
• Design Add and Search Words Data Structure
  Design a data structure that supports adding new words and searching for words with a given pattern.
• Implement Trie (Prefix Tree)
  A Trie (Prefix Tree) is a tree-like data structure used to efficiently store a dynamic set of strings while allowing efficient prefix search. In this problem, you need to implement a Trie data structure that supports the following operations:
• Word Break
  Given a string s and a dictionary of words dict, you need to determine if s can be segmented into a space-separated sequence of one or more dictionary words.