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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Basic
With respect to hashing, what does the "universe" of keys refer to?
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.
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Basic
The load factor 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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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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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).
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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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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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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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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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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).
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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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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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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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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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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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).
