1. Data Structures and Analysis (COMP 410)
David Stotts
Computer Science Department
UNC Chapel Hill

2. Sets and Maps

3. SET ADT Set is an abstract type add: SET x elt  SET
remove: SET x elt  SET
contains : SET x elt  boolean
size, empty, etc.
The add will enforce uniqueness… only one instance of an element may be in a SET
A variant of SET called MULTISET will allow multiple instances of an element, then you need a count function for an element (contains is count>0 )

4. MAP Map is an abstract type We insert/retrieve items using the key
a collection
stores “pairs” (key,value)
We insert/retrieve items using the key
Goal is to use the associated value
We are using this in the PrQUE
spot in min bin heap found from priority
want to retrieve and use the data
(process, name, diagnosis, etc.)

5. MAP ADT Map is an abstract type get: MAP x key  value
put: MAP x key x value  MAP
remove: MAP x key  MAP
hasKey : MAP x key  Boolean
keys: MAP  SET of key
values: MAP  “blob” of value
size, empty, etc.
“put” will enforce uniqueness of keys… only one of each key
several keys may MAP to the same value
“keys” returns a SET since keys are unique
“values” returns a list/collection of the values (and the
elements in the collection might not be unique)

6. MAP is like a Function
MAP is like a mathematical function… A math function f(x)  y give a domain element x, get back a range element y MAP(k)  v or, get(k)  v give a key k, get back a value v

7. MAP is like a Function Math functions are often continuous
f(x)  3x where x is a real
can’t enumerate all elements of the domain
In a MAP the function is discrete,
a set of ordered pairs (domain, range)
{ (123,”dave”), (234,”jane”), (345,”kim”),
(456,“pete”), (567,“amy”), (678,”bob”) }
keys (domain elements) are a finite enumerable set

8. MAP is like a Function 1 to 1 Keys must be unique
Each key maps to only one value Here is a MAP that might represent SSN mapped to names
1 to 1
Keys must be unique
Values are chosen to be unique
123
jane
234
dave No
kim
567
pete
345
bob
456
678
amy
keys
values

9. MAP is like a Function No Not necessarily 1 to 1 Keys must be unique
Each key maps to only one value Here is a MAP that might represent product mapped to price No
Not necessarily
1 to 1
Keys must be unique
Values can be duplicated
fuji
2.50
gala
2.25
redD
1.75
honey
goldD
1.25
mac
keys
values

10. MAP Implementation MAP can be implemented like SET
We store a (key,value) pair rather than only a key
Organized as a BST (balanced) we get this
put: O(log N) time, worst case and average
get: O(log N) time, worst case and average
hasKey: O(log N) time, worst case and average
remove: O(log N) time, worst case and average

11. MAP Implementation Java Collections has Tree Map Hash Map TreeMap
MAP elements stored in balanced BST
Hash Map
MAP elements stored using Hash Table
Next chapter, after break (chapter 5)

12. Hash MAP Why use hashing for MAP ? Average case times:
put: O(1)
get: O(1)
hasKey: O(1)
remove: O(1)
Worst case times: (the downside)
put: O(N)
get: O(N)
hasKey: O(N)
remove: O(N)
We will see that with care, these are rare

13. Beyond this is just templates
END
Beyond this is just templates

14. Example 9 21 18 11 19 3 12 24 16 41