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## PowerPoint Slideshow about ' Hash Tables' - prem

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Presentation Transcript

What is a Hash Table?

- Container of elements where each element has an associated key
- Each key is mapped to a value that determines the table cell where element should be placed
- Mapping is called the hash function

Hash Table Operations

- size()
- isEmpty()
- find(k) – find element with key k
- insertItem(k, e) – insert element e with key k
- removeElement(k) – remove element with key k
- elements() – return Iterator of elements
- keys() – return Iterator of keys

key is id number

map id number to array index

Array Implementation[0]

bob 1234

[1]

[2]

jane 1344

[3]

sally 1354

[4]

[5]

[6]

[7]

[8]

[9]

Why a Hash Table?

- Random access to items
- Don’t have to perform search to find item

- Complexity of find/remove?

Hash Function

- The hash function has to map the key to a value
- Bad option: add up ASCII values of characters in key and % by number of table elements
- Better option:
for(i=0; i < key.length(); i++)

hashVal= 37*hashVal + key[i]

hashVal %= tableSize

Collisions

- It is still possible that two keys will map to the same value
- Separate chaining
- each array slot is a pointer to a linked list of elements
- how would find/insert/remove work?

- Linear probing
- walk down the list until you find an empty slot

Collisions

- Quadratic probing
- A[i+f(j) mod N] for j=0, 1, 2, … where f(j) = j2

- Double Hashing
- probe at hash2(x), 2hash2(x), etc

Rehashing

- As table gets full, insertions may slow because of more collisions
- Rehash by creating table twice as large and reinserting all elements into new table
- requires rehashing all keys (because of new table size)

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