Data StructuresHash Table (aka Dictionary)
i206
Fall 2010
John Chuang
Some slides adapted from Marti Hearst, Brian Hayes, Andreas Veneris, Glenn Brookshear,Nicolas Christin, or Ion Stoica.
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Outline
What is a data structure
Basic building blocks: arrays and linked lists
Data structures (uses, methods, performance):
-List, stack, queue
-Dictionary
-Tree
-Graph
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Dictionary
Also known as hash table, lookup table,associative array, or map
A searchable collection of key-value pairs
-each key is associated with one value
Many possible applications, e.g.,
-Address book
-Student record database
-Routing tables
-…
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Dictionary Methods
get(k): if the dictionary has an entry with key k,return its associated value; else return null
put(k,v): insert entry (k,v) into the dictionary; ifkey is not already in dictionary, return null; elsereturn old value associated with k
remove(k): if dictionary has an entry with key k,remove it from dictionary and return itsassociated value; else return null
size()
isEmpty()
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Dictionary in Python
Example:
>>> agents = {‘006’:’Jack Giddings’, ‘007’:’James Bond’}
>>> agents[‘001’] = ’Edward Donne’
>>> agents[‘007’]
‘James Bond’
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Desirable Properties
Fast search, insert and delete (get, put, andremove)
Efficient space usage
Arrays: O(1) operations; not space efficient
Linked lists: O(n) operations; space efficient
Binary trees: O(log n) operations; spaceefficient
Can we do better?
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Hash Table
A generalization of an array that, if properlydesigned, can realize fast insert/delete/searchoperations with good space efficiency
-average run-time of O(1)
-worst case run-time of O(n)
A hash table is:
-Good for storing and retrieving key-value pairs
-Not good for iterating through a list of items
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Hash Table
A hash table consists of two major components:
-Bucket array (for storing entries)
-Hash function (for mapping keys to buckets)
Obj5
key=1
obj1key=15
Obj4
key=2
Obj2
key=36
7
6
5
4
3
2
1
0
table
Obj3
key=4
buckets
hash value/index
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Hash Table Design
Bucket array is an array A of size N, where eachcell of A is considered a “bucket”
Hash function h maps each key k to an integerin the range [0, N -1]
Store entry (k,v) in the bucket A[h(k)]
Search for entry (k,v) in the bucket A[h(k)]
Choose hash function such that
-Can take arbitrary objects (keys) as input
-Hash computation is fast
-Key mappings evenly distributed across [0, N -1]
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Example Hash Function
h(k) = k mod N
mod stands for modulo, the remainder of the division of twonumbers. For example:
-8 mod 5 = 3
-9 mod 5 = 4
-10 mod 5 = 0
-15 mod 5 = 0
Observe that collisions are possible:
-two different keys hash to the same value
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Example
h(k) = k mod 5
0
1
2
3
4
key value
Insert (2,x)
2 x
0
1
2
3
4
key value
Insert (21,y)
2 x
21 y
0
1
2
3
4
key value
Insert (34,z)
2 x
21 y
34 z
Insert (54,w)
There is a
collision at
array entry #4
???
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Dealing with Collisions
Hashing with Chaining: every hash table entrycontains a pointer to a linked list of keys thathash in the same entry
0
1
2
3
4
key value
Insert (54,w)
2 x
21 y
54 w
34 z
CHAIN
0
1
2
3
4
Insert (101,x)
21 y
2 x
101 x
54 w
34 z
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Dictionary Performance
What is the run time for insert/search/delete?
-Insert: It takes O(1) time to compute the hash function and insert athead of linked list
-Search: It is proportional to the length of the linked list
-Delete: Same as search
0
1
2
3
4
key value
Insert (54,w)
2 x
21 y
54 w
34 z
CHAIN
0
1
2
3
4
Insert (101,x)
21 y
2 x
101 x
54 w
34 z
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Load Factor
Average length of the linked lists is a function of theload factor
-Load factor = number of items in hash table / array size
In Python, the implementation details are transparent tothe programmer (load factor kept under 2/3)
In Java, the programmer can set the initial table size(default=16) and/or the load factor (default = 0.75)
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Distributed Hash Table (DHT)
Similar to traditional hash table data structure, exceptdata is stored in distributed peer nodes
-Each node is analogous to a bucket in a hash table.
Applications: distributed search, e.g., peer-to-peernetworks, content distribution networks (CDNs), etc.
DHTs are typically designed to scale to large numbers ofnodes and to handle continual node arrivals anddepartures/failures.
Put(), Get() interface like a regular hash table:
-put(id, item);
-item = get(id);
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DHT Example: Chord
Nodes: n1(id=1),n2(id=2), n3(id=0),n4(id=6)
Items inserted:f1(id=7), f2(id=1)
0
1
2
3
4
5
6
7
i id+2i succ
0 2 2
1 3 6
2 5 6
Finger Table
i id+2i succ
0 3 6
1 4 6
2 6 6
Finger Table
i id+2i succ
0 1 1
1 2 2
2 4 6
Finger Table
7
Items
1
Items
i id+2i succ
0 7 0
1 0 0
2 2 2
Finger Table
Slide adapted from Ion Stoica, Nicolas Christin
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DHT Example: Chord
Upon receiving a query foritem id, a node:
Check if the item is storedlocally
If not, forwards the queryto the largest node in itssuccessor table that doesnot exceed id
0
1
2
3
4
5
6
7
i id+2i succ
0 2 2
1 3 6
2 5 6
Finger Table
i id+2i succ
0 3 6
1 4 6
2 6 6
Finger Table
i id+2i succ
0 1 1
1 2 2
2 4 6
Finger Table
7
Items
1
Items
i id+2i succ
0 7 0
1 0 0
2 2 2
Finger Table
query(7)
Slide adapted from Ion Stoica, Nicolas Christin