Hash Tables

Hash tablesDefinition: A data structure that uses a hash

function to map keys into index of an array element.

k1

k2 k3k4

k5

Some properties of hash tableSize of hash table (Example will be shown.)Hash function: map keys into index of an

array element. (To be continued…)Multiplication HashDivision Hash

Input to build a hash table: array of keys to store in the hash tableint [] input = {1,2,3,4,5,6,7,8}

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ExampleHash table size is 10

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Division Hashh1(k) = k mod m

Returns the index of arrayk is the keym is the size of the hash table. Good values of m: prime numbers smaller than

and closest to the size of the input. See Table 1.Java syntax of mod is %.

(input size, m value)

(500, 499)

(1000, 997)

(2000, 1999)

(4000, 3989)

Table 1.

Multiplication hashh2(k) = floor(m (kA mod 1) )

m is size of hash tableGood values of m: prime numbers smaller than

and closest to the size of the input. See table 1.k is keyA = 0.61803 (Came from (sqrt(5) - 1)/2 )

Hints: Use the decimal in your program is better, it may reduce your bugs.

CollisionsWhen hashing a key, if collision happens the

new key is stored in the linked list in that location

Number of collisions of a location = Number of elements in that location - 1

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# of collisions = 2-1=1

# of collisions = 3-1=2

"the 3 metrics"maxCollisions: Maximum number of collisions

of all locations in a hash tableminCollisions: Minimum number of collisions

of all locations in a hash tabletotalCollisions: Total collisions of all locations

in a hash tableExamples on the next slide

maxCollisions = 2 minCollisions = 1

(** Note that the minCollisions will be at least 1 if there exists collisions in some locations, even if there are locations with 0 collisions. If there is no collisions at all, return 0. )

totalCollisions = 4

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# of collisions = 1

# of collisions = 2

# of collisions = 1

DiscussionWhy metrics?

It can tell us which hash is better according to the collision metrics

Why 3 metrics, why not just measure totalCollisions?Let’s see an example.

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Hash table 1: totalCollisions = 4

Hash table 2: totalCollisions = 4

Which hash table is better?

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We not only want less collisions, but also want to distribute the collisions evenly into the hash table. That is why hash table 1 is better than hash table 2.

This lab is to implement two hash functions, division and multiplication and use metrics of collisions to demonstrate which hash is better.