153 lines
6.1 KiB
Markdown
153 lines
6.1 KiB
Markdown
---
|
|
title: Closed Addressing
|
|
TARGET DECK: Obsidian::STEM
|
|
FILE TAGS: hashing::closed
|
|
tags:
|
|
- hashing
|
|
---
|
|
|
|
## Overview
|
|
|
|
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](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
|
|
<!--ID: 1718198717474-->
|
|
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](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
|
|
<!--ID: 1718198717484-->
|
|
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](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
|
|
<!--ID: 1718198717495-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Cloze
|
|
The following is an example of {closed} addressing.
|
|
![[closed-addressing.png]]
|
|
Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, [https://programming.guide/hash-tables-open-vs-closed-addressing.html](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
|
|
<!--ID: 1718198717506-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Cloze
|
|
The following is an example of {open} hashing.
|
|
![[closed-addressing.png]]
|
|
Reference: “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, [https://programming.guide/hash-tables-open-vs-closed-addressing.html](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
|
|
<!--ID: 1718198755496-->
|
|
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](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
|
|
<!--ID: 1718759188231-->
|
|
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](https://programming.guide/hash-tables-open-vs-closed-addressing.html).
|
|
<!--ID: 1718759188234-->
|
|
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).
|
|
<!--ID: 1718759188238-->
|
|
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).
|
|
<!--ID: 1718759188241-->
|
|
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).
|
|
<!--ID: 1718759188245-->
|
|
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).
|
|
<!--ID: 1718759188249-->
|
|
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).
|
|
<!--ID: 1718759188252-->
|
|
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).
|
|
<!--ID: 1718759188256-->
|
|
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).
|
|
<!--ID: 1718759188261-->
|
|
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).
|
|
<!--ID: 1718759188269-->
|
|
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).
|
|
<!--ID: 1718759188275-->
|
|
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).
|
|
<!--ID: 1718759188281-->
|
|
END%%
|
|
|
|
## Bibliography
|
|
|
|
* “Hash Tables: Open vs Closed Addressing | Programming.Guide,” accessed June 12, 2024, [https://programming.guide/hash-tables-open-vs-closed-addressing.html](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). |