notebook/notes/hashing/addressing.md

title	TARGET DECK	FILE TAGS	tags
Addressing	Obsidian::STEM	hashing::addressing	addressing hashing

Overview

Direct

Given a universe of keys U = \{0, 1, \ldots, m - 1\}, a direct-address table has m slots. Each slot corresponds to a key in universe U.

%%ANKI Basic Given universe U, how many slots must a direct-address table have? Back: |U| Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What name is given to each position in a direct-address table? Back: A slot. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Given a direct-address table, the element at slot k has what key? Back: k. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Given a direct-address table, an element with key k is placed in what slot? Back: The $k$th slot. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Write pseudocode to test membership of x in direct-address table T[0:m-1]. Back:

bool membership(T, x) {
  return T[x.key] != NIL;
}

Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What is the worst-cast runtime complexity of direct-address table searches? Back: O(1) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Write pseudocode to insert x into direct-address table T[0:m-1]. Back:

void insert(T, x) {
  T[x.key] = x;
}

Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What is the worst-case runtime complexity of direct-address table insertions? Back: O(1) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Write pseudocode to delete x from direct-address table T[0:m-1]. Back:

void delete(T, x) {
  T[x.key] = NIL;
}

Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What is the worst-cast runtime complexity of direct-address table deletions? Back: O(1) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In what situation does direct addressing waste space? Back: When the number of keys used is less than the size of the universe. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In what situation is direct addressing impossible? Back: When the size of the universe is too large to hold in memory. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What distinguishes direct addressing from closed and open addressing? Back: Direct addressing isn't concerned with conflicting keys. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic Direct addressing sits between what other addressing types? Back: Open and closed addressing. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic What is the theoretical maximum load factor in direct addressing? Back: 1 Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

Closed

In closed addressing, a key is always stored in the bucket it's hashed to. Collisions are dealt with using separate data structures on a per-bucket basis.

%%ANKI Basic What does "closed" refer to in term "closed addressing"? Back: A key is always stored in the slot it hashes to. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic What does "open" refer to in term "open hashing"? Back: A key may resides in a data structure separate from the hash table. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Cloze {Closed} addressing is also known as {open} hashing. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Cloze The following is an example of {closed} addressing. ! Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Cloze The following is an example of {open} hashing. ! Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic What is the theoretical maximum load factor in closed addressing? Back: N/A Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic Why is the theoretical maximum load factor of closed addressing unbounded? Back: A closed addressing hash table can always have more entries inserted into it. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic When is the load factor of a closed addressing hash table 0? Back: When no entries are stored in the table. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic When is the load factor of a closed addressing hash table 1? Back: When there exist the same number of total entries as slots. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic When is the load factor of a closed addressing hash table > 1? Back: When there exist more total entries than number of slots. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

Chaining

The most common form of closed addressing is chaining. In this scheme, each slot j is a (nullable) pointer to the head of a linked list containing all the elements with hash value j.

%%ANKI Basic What is the most common implementation of closed addressing? Back: Chaining. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What data structure is typically used in a hash table with chaining? Back: Linked lists. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Consider a hash table with chaining. What is in an empty slot? Back: A NIL pointer. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Consider a hash table with chaining. What is in a nonempty slot? Back: A pointer to the head of a linked list. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Consider a hash table with chaining. How many linked list instances exist? Back: One for each slot in the hash table. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Cloze A hash table with chaining is an example of {closed} addressing. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Cloze A hash table with chaining is an example of {open} hashing. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What is the worst-case behavior of hashing with chaining? Back: All keys hash to the same slot. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic What is the load factor of a hash table in which all n keys hash to one of m slots? Back: n / m (the load factor is a property of the table, not the distribution of keys). Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In a hash table with chaining and independent uniform hashing, what is the average unsuccessful search runtime? Back: Given load factor \alpha, \Theta(1 + \alpha). Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In a hash table with chaining and independent uniform hash function h, which elements are examined in an unsuccessful search for element x? Back: All the elements in slot h(x.key). Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In a hash table with chaining and independent uniform hashing, what is the average successful search runtime? Back: Given load factor \alpha, \Theta(1 + \alpha). Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In a hash table with chaining and independent uniform hash function h, which elements are examined in a successful search for element x? Back: x and the elements preceding x in slot h(x.key). Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In a hash table with chaining and independent uniform hashing, what is the average seach runtime? Back: Given load factor \alpha, \Theta(1 + \alpha). Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic In a hash table with chaining and independent uniform hashing, when is the average runtime of search O(1)? Back: When the number of entries is at most proportional to the number of slots in the table. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic Suppose n is at most proportional to m. How is this denoted in complexity notation? Back: n = O(m) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

Open

In open addressing, keys always reside in the hash table. Collisions are dealt with by searching for other empty buckets within the hash table.

%%ANKI Basic What does "closed" refer to in term "closed hashing"? Back: A key must reside in the hash table. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic What does "open" refer to in term "open addressing"? Back: A key is not necessarily stored in the slot it hashes to. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Cloze {Open} addressing is also known as {closed} hashing. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Cloze The following is an example of {closed} hashing. ! Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Cloze The following is an example of {open} addressing. ! Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic What is the theoretical maximum load factor in open addressing? Back: 1 Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic Why is the theoretical maximum load factor of open addressing bounded? Back: An open addressing hash table can only store as many entries as slots. Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.

END%%

%%ANKI Basic When is the load factor of an open addressing hash table 0? Back: When no entries are stored in the table. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic When is the load factor of a open addressing hash table 1? Back: When there exist the same number of total entries as slots. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

%%ANKI Basic When is the load factor of an open addressing hash table > 1? Back: N/A Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

END%%

Bibliography

• “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, https://programming.guide/hash-tables-open-vs-closed-addressing.html.
• Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).