Tries, segment trees, Fenwick trees, B-trees, AVL and red-black trees, skip lists, bloom filters and disjoint sets.
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- What is a trie?
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A tree-based data structure where each node represents a character, used for efficient prefix-based searches.- What is the time complexity of searching in a trie?
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O(m) where m is the length of the search string.- What is the main disadvantage of tries regarding space?
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They use significant memory because each node can have up to 26 pointers for lowercase letters.- What is a common use case for tries?
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Autocomplete and spell-checking systems.- What property do tries enable for string searches?
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Prefix matching: finding all words that start with a given prefix.- What is a segment tree?
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A tree data structure used to efficiently answer range queries and update point values.- What is the time complexity for a range query in a segment tree?
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O(log n) where n is the size of the array.- What is the time complexity for updating a value in a segment tree?
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O(log n).- What is a common use case for segment trees?
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Range minimum, maximum, or sum queries on an array.- What is a Fenwick tree?
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A data structure that efficiently supports prefix sum queries and point updates in O(log n) time.- What is the time complexity of operations in a Fenwick tree?
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O(log n) for both updates and prefix sum queries.- What is a primary use case for Fenwick trees?
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Computing prefix sums and handling range sum updates efficiently.- What space advantage does a Fenwick tree have over a segment tree?
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Fenwick trees use O(n) space while segment trees typically use O(2n) space.- What is a B-tree?
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A self-balancing tree where each node can have multiple children and keys, designed for external storage systems.- What is the time complexity for search, insert, and delete in a B-tree?
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O(log n) in all cases.
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