Advantages of Trie Data Structure
Trie is very effective when it comes to managing a dictionary and searching for strings.
Let us look at the advantages of Trie Data Structure -
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Trie allows us to input and locate strings in O(L) complexity. Here, 'L' refers to a word's length. The depth of the trie impacts the look-ups of the keys. If a tree is balanced, the look-up in the case of BST with 'N' keys will take O(log N) time.
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Trie allows for ordered iteration. If we iterate over a hash table, it will produce a pseudorandom order. It is determined by the hash function, which is typically useless. The order of hash collisions is also implementation specified.
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It helps in finding the match of the longest prefix. It assists in the discovery of the key with the longest possible prefix of characters. All the characters are unique.
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For short keys like integers and pointers, attempts are often quicker than hash tables since they skip the hash function.
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Compared to BST, the Trie data structure takes up less space. Since the keys are not explicitly saved, each key requires just an amortized fixed amount of space to be stored.
- Deletion is O(L) time complexity where ‘L’ is the word length to be deleted.
Complexity Analysis
We will now look into the analysis of Trie data structure complexities.
Time Complexity
The time complexity for Trie data structure: O(L)
Here, ‘L’ stands for word length.
Explanation: We iterate the whole word and continue inserting the node for each node if it is not there. All the operations, including insert, delete, and search methods, take O(L) time. The word is added, erased, or searched as soon as we iterate the complete word.
Space Complexity
The space complexity for the Trie data structure: O(L)
Here, ‘L’ stands for word length.
Explanation: We are entering each word in the Trie, and each letter of the word takes up some memory.
Implementing the Trie requires:
O(Alphabet Size * Number Of Words * Word Length)
= (26 * Number Of Words * Word Length)
Frequently Asked Questions
What are the terms used for Trie data structure?
Trie is also referred to as the ‘ReTrieval Tree’, ‘Prefix Tree’, and ‘Digital Tree’.
Mention some uses for Trie.
Trie is used to store the strings or key values, which can be represented in the form of a string. It contains nodes and edges. At max, 26 children connect each parent node to its children.
What is the advantage of Trie that you consider most important?
We can insert and search any string in the trie data structure in O(L) time where L is word length.
What is the disadvantage of Trie?
The main disadvantage of Trie is that it takes a lot of memory to store all the strings. For each node, we have too many node pointers(equal to the number of characters of the alphabet).
What are some applications of Trie?
Longest common prefix, pattern searching, autocomplete, and implementation of the dictionary are some of the common applications of a Trie Data Structure.
Conclusion
In this article, we covered an introduction to Trie. We then went along the advantages of Trie data structure. We have also discussed the time and space complexities. Here, a Trie is quicker, but it demands a lot of memory to store the strings.
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