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| title | TARGET DECK | FILE TAGS | tags | |
|---|---|---|---|---|
| Hashing | Obsidian::STEM | hashing |
|
Overview
A hash table T[0:m-1] uses a hash function to map a universe of keys into slots of the hash table. It can be seen as a generalization of direct addressing (which has "hash function" h(k) = k).
%%ANKI Basic With respect to hashing, what does the "universe" of keys refer to? Back: Every potential key that may be provided to the hash function. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What name is given to each position in a hash table? Back: A slot. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Basic
Given a hash table with hash function h, the element at slot k has what key?
Back: A key k' such that h(k') = k.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Given a hash table with hash function h, an element with key k is placed in what slot?
Back: h(k)
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Basic
Given a hash table T[0:m-1], what is the domain of a hash function?
Back: The universe of keys.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Basic
Given a hash table T[0:m-1], what is the codomain of a hash function?
Back: \{0, \ldots, m - 1\}
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What does a hash value refer to? Back: The result produced by a hash function. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What distinguishes a slot from a hash value? Back: The former is a memory address. The latter is the result of a hash function. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What relationship exists between slots and hash values? Back: A slot is often referred to by a hash value. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Cloze
Given hash function h, key k {hashes} to slot h(k).
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What combinatorial concept is used to prove the presence of hash table collisions? Back: The pigeonhole principle. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic When must there exist hash table collisions? Back: When the number of hashed keys is greater than the number of slots. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What does a hash table collision refer to? Back: Two keys hashing to the same slot. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic With respect to hash tables, what imagery is invoked by the term "hash"? Back: Random mixing and chopping. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic Are hash tables or direct-address tables more general? Back: Hash tables. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
How is a direct-address table reinterpreted as a hash table?
Back: It's a hash table with hash function h(k) = k.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Load Factor
Consider hash table T with m slots that stores n entries. Then the load factor \alpha for T is defined to be n / m, i.e. the average number of entries that map to the same slot.
%%ANKI Basic The load factor of a hash table is a ratio of what two numbers? Back: The number of entries in the table to the number of slots stored in the table. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Cloze The load factor of a hash table {increases} as the number of slots {decrease}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Cloze The load factor of a hash table {decreases} as the number of total entries {decrease}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
END%%
%%ANKI Cloze The load factor of a hash table {increases} as the number of total entries {increase}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Cloze The load factor of a hash table {decreases} as the number of slots {increase}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Let n / m denote the load factor of a hash table. What does n represent?
Back: The total number of entries in the table.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Let n / m denote the load factor of a hash table. What does m represent?
Back: The number of slots in the table.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Why is the load factor \alpha of a hash table defined the way it is?
Back: It represents the average number of entries stored at a slot.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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An independent uniform hash function is the ideal theoretical abstraction. For each possible input k in universe U, an output h(k) is produced randomly and independently chosen from range \{0, 1, \ldots, m - 1\}. Once a value h(k) is chosen, each subsequent call to h with the same input k yields the same output h(k).
Independent uniform hashing is universal, meaning the chance of any two distinct keys colliding is at most 1 / m.
%%ANKI Basic What is considered the ideal (though only theoretical) hash function? Back: The independent uniform hash function. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Given independent uniform hash function h, what about h is "independent"?
Back: Each key k has output h(k) determined independently from other keys.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Given independent uniform hash function h, what about h is "uniform"?
Back: Every output of h is equally likely to be any of the values in its range.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic With respect to hashing, a random oracle refers to what kind of hash function? Back: An independent uniform hash function. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Where does "memory" come into play with independent uniform hash functions?
Back: Once h(k) is determined, subsequent calls to h with k always yield the same value.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What is uniform hashing? Back: Any given element is equally likely to hash into any slot. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What is independent hashing? Back: The slot an element hashes to is independent of where other elements hash to. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Bibliography
- Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).