Tries are a special kind of tree data structure used to store and manage sets of words. Imagine a branching tree where each branch represents a letter in a word.
Basic Idea:
- Each word is represented by a path from the root of the tree to a leaf (end node).
- As you travel down the path, each branch represents a character in the word.
- Unlike a regular tree, all nodes (except the root) store a single character, building the word step-by-step.
Classifications:
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Standard Trie:
* This is the basic trie structure described above. * Every path from root to leaf represents a complete word. * No word in the set can be a prefix (beginning part) of another word. -
Compressed Trie:
- A more space-efficient version of the standard trie.
- It identifies and merges redundant branches that contain the same characters.
- This reduces wasted space but requires internal nodes to have at least two branches (
$degree >= 2$ ).
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Compact Trie (Similar to Compressed Trie):
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This is a compressed trie with an additional numeric representation for efficiency.
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It uses an array to store the actual words themselves.
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Each node in the trie holds three values
$(i, j, k)$ :-
$i$ : Index in the word array pointing to the first word containing the substring represented by the node. -
$j$ : Starting position of the substring within the word at index$i$ . -
$k$ : Ending position of the substring within the word at index$i$ .
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Benefits of Tries:
By using tries, we can perform various operations on sets of words very efficiently, such as searching for specific words, finding words with a common prefix (e.g., autocomplete suggestions), and implementing spell checkers.
A suffix trie is a specialized trie data structure designed to efficiently search within a single word (or string). It works by storing all possible suffixes (endings) of the word in a compressed trie.
Here's a breakdown of the concept:
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Suffix Breakdown:
- We start by taking the given word and creating a list containing all its suffixes.
- Remember, a suffix is any ending portion of the word.
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Standard Trie Construction:
- Next, we build a regular trie using this list of suffixes.
- In a standard trie, each complete path from root to leaf represents a complete suffix.
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Compression for Efficiency:
- To save space, we then transform the standard trie into a compressed trie.
- This process identifies and merges branches that share the same characters, reducing redundancy.
Since there's just a single word, we don't need an index to separate words. Therefore, each node in a suffix trie simply stores two integers:
- Starting index: This represents the starting position of the suffix within the original word.
- Ending index: This represents the ending position of the suffix within the original word.
With this structure, suffix tries enable efficient operations like finding all occurrences of a substring within the word or identifying repeated patterns.