184 lines
6.6 KiB
Markdown
184 lines
6.6 KiB
Markdown
---
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title: Hashing
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TARGET DECK: Obsidian::STEM
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FILE TAGS: hashing
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tags:
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- hashing
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---
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## Overview
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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" $h(k) = k$).
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%%ANKI
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Basic
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With respect to hashing, what does the "universe" of keys refer to?
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Back: Every potential key that may be provided to the hash function.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716046153757-->
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END%%
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%%ANKI
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Basic
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What name is given to each position in a hash table?
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Back: A slot.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180959-->
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END%%
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%%ANKI
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Basic
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Given a hash table with hash function $h$, the element at slot $k$ has what key?
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Back: A key $k'$ such that $h(k') = k$.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180961-->
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END%%
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%%ANKI
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Basic
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Given a hash table with hash function $h$, an element with key $k$ is placed in what slot?
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Back: $h(k)$
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180962-->
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END%%
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%%ANKI
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Basic
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Given a hash table `T[0:m-1]`, what is the domain of a hash function?
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Back: The universe of keys.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180964-->
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END%%
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%%ANKI
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Basic
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Given a hash table `T[0:m-1]`, what is the codomain of a hash function?
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Back: $\{0, \ldots, m - 1\}$
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180965-->
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END%%
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%%ANKI
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Basic
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What does a hash value refer to?
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Back: The result produced by a hash function.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180967-->
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END%%
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%%ANKI
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Basic
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What distinguishes a slot from a hash value?
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Back: The former is a memory address. The latter is the result of a hash function.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180968-->
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END%%
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%%ANKI
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Basic
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What relationship exists between slots and hash values?
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Back: A slot is often referred to by a hash value.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180970-->
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END%%
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%%ANKI
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Cloze
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Given hash function $h$, key $k$ {hashes} to slot $h(k)$.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180971-->
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END%%
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%%ANKI
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Basic
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What combinatorial concept is used to prove the presence of hash table collisions?
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Back: The pigeonhole principle.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180973-->
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END%%
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%%ANKI
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Basic
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When *must* there exist hash table collisions?
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Back: When the number of hashed keys is greater than the number of slots.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180974-->
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END%%
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%%ANKI
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Basic
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What does a hash table collision refer to?
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Back: Two keys hashing to the same slot.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180976-->
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END%%
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%%ANKI
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Basic
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With respect to hash tables, what imagery is invoked by the term "hash"?
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Back: Random mixing and chopping.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180977-->
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END%%
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%%ANKI
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Basic
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Are hash tables or direct-address tables more general?
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Back: Hash tables.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180979-->
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END%%
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%%ANKI
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Basic
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How is a direct-address table reinterpreted as a hash table?
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Back: It's a hash table with hash function $h(k) = k$.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1716307180980-->
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END%%
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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 $h(k)$.
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%%ANKI
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Basic
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What is considered the ideal (though only theoretical) hash function?
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Back: The independent uniform hash function.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1718197741507-->
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END%%
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%%ANKI
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Basic
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Given independent uniform hash function $h$, what about $h$ is "independent"?
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Back: Each key $k$ has output $h(k)$ determined independently from other keys.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1718197741527-->
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END%%
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%%ANKI
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Basic
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Given independent uniform hash function $h$, what about $h$ is "uniform"?
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Back: Every output of $h$ is equally likely to be any of the values in its range.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1718197741537-->
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END%%
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%%ANKI
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Basic
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With respect to hashing, a random oracle refers to what kind of hash function?
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Back: An independent uniform hash function.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1718197741545-->
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END%%
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%%ANKI
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Basic
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Where does "memory" come into play with independent uniform hash functions?
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Back: Once $h(k)$ is determined, subsequent calls to $h$ with $k$ always yield the same value.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1718197741555-->
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END%%
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## Bibliography
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* Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). |