Tries
In computer science, a trie (pronounced “try”) is a tree-like data structure used to store a dynamic set or associative array where the keys are usually strings. The term “trie” comes from the word “retrieval,” and the structure is sometimes called a “prefix tree” because it can efficiently store and retrieve keys based on their prefixes. Each node represents a single character or a part of a key.
The root node represents the empty string, and each level of the tree corresponds to a character in the keys. The nodes in a trie have links (edges) to other nodes, typically representing characters. Traversing the edges from the root to a particular node spells out a key.
Tries excel at handling keys with common prefixes. This makes them particularly efficient for tasks like string matching or autocomplete, where a common prefix needs to be shared among multiple keys. Retrieving a key from a trie is also highly efficient, typically taking time proportional to the length of the key. This is because each level of the trie corresponds to a character in the key.
Tries tend to have a high space complexity, especially for large datasets with many keys sharing common prefixes. However, various optimizations, such as compressing branches with a single child, can reduce space requirements.
Implementation Considerations
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Memory Usage: Tries can be memory-intensive, especially when dealing with a large number of keys. Various techniques, such as compression and optimization, can be applied to reduce memory usage.
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Alphabet Size: The size of the alphabet (number of possible characters) can affect the performance of a trie. Larger alphabets may result in larger and more complex tries.
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Node Representation: Nodes in a trie can be implemented using arrays, linked lists, or other data structures. The choice of representation impacts both time and space complexity.
# Implementation Example of a Depth First Search within the Trie.
def PrintTree(rootNode):
print("---- Root Children ----")
#root nodes text
for key in rootNode.children:
print(key)
print("-----------------------")
#children of children.
stack = []
stack.append(rootnode)
while(len(stack) > 0):
currentNode = stack.pop()
print(currentNode.value)
for key in currentNode.children:
stack.append(currentNode.children[key])
Credit: UKL
Use Cases
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Autocomplete and Predictive Text: Tries are often used in autocomplete systems where users are presented with suggested words or phrases based on partial inputs.
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Spell Checking: Tries can be used in spell-checking algorithms to efficiently identify misspelled words by traversing the trie and checking for valid words.
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IP Routing Tables: In networking, tries are used in IP routers to efficiently search for the longest prefix match in IP routing tables.
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Symbol Tables: Tries are used in symbol tables for compilers and interpreters to efficiently look up variable and function names.
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Distributed Databases: Tries can be employed in distributed databases for efficiently storing and querying key-value pairs.
Pattern Searching using a Trie of all Suffixes
Count of distinct substrings of a string using Suffix Trie
Trie, Suffix Tree, Suffix Array