1. 6.170 Recitation
Godfrey Tan

2. Announcements Quiz 1 Review Problem Set 3 Quiz 1 (L1-L10):
Sunday, March 3, 7:30pm,
Problem Set 3
Tuesday, March 5
Quiz 1 (L1-L10):
Wednesday, March 6 during class
Locations
for usernames a*-j*
for usernames k*-z*
Open book, but it is a short quiz!

3. Graph Basics Node Edge Nodes are connected via Edges
Station: id, name
Edge
Line: type, (in station, out station)
Nodes are connected via Edges
Graph is a collection of nodes and edges

4. Graph Requirements Directed Multi-graph Dynamic: add and remove nodes
Flexible: works for other applications

5. Graph Operations addNode, containsNode addEdge, containsEdge Traversal
Predecessors, successors

6. Graph Implementation Centralized Distributed Graph stores everything
May or may not require Node class
Distributed
Graph stores Nodes
Node stores Edges

7. Storing Nodes and Edges
Adjacency lists
Nodes
IN Edges, Out Edges for each Node
Adjacency matrices
Two dimensional arrays
HashMap
Stores (key, value)

8. Traversal Depth first search Breadth first search Operations
Mark: found, visited
Visit

9. Inputs and outputs Input: Harvard Alewife Output:
[Harvard(14), Porter(10), Davis(7), Alewife(8)]

10. Abstract Data Type: What?
Abstraction by specification
Operations (T = abstract type, t = some other type)
Constructors: t  T
Producers: T, t  T
Mutators: T, t  void
Observers: T, t  t
Designing an Abstract Type
Few, simple operations that can be combined in powerful ways
Operations should have well-defined purpose, coherent behavior
Set of operations should be adequate

11. Abstract Data Type: Why?
Allows us to:
abstract from the details of
how data objects are implemented
how they behave
defer decisions about the data structures
Interface to users is via operations; changes made to representation does not affect the operations
You can change the structures late in the game

12. Implementing an ADT Select the rep (representation of instances)
Implement operations in terms of that rep

13. Rep Data structure plus Set of conventions defined by rep invariant
abstraction function

14. A Rep example
We want a representation of a list of 3 integers sorted in ascending order
[ x1, x2, x3 ] where x1 <= x2 <= x3

15. Sorted List class SortedList { Vector v; Integer foo;
// requires: a <= b <= c
public SortedListA(Integer a, Integer b,
Integer c) {
v = new Vector();
foo = new Integer(666);
v.add(a); v.add(foo);
v.add(b); v.add(foo);
v.add(c); v.add(foo); }… }

16. Rep Data structure plus Set of conventions defined by rep invariant
abstraction function
What is the data structure for SortedList?

17. Rep Data structure plus Set of conventions defined by rep invariant
abstraction function
What is the data structure for SortedList?
Vector

18. Abstraction Function
What is the abstraction function?

19. Abstraction Function What is the abstraction function?
Mapping from vector elements to abstract values
[ v[0], v[2], v[4] ] maps to [ x1, x2, x3 ]

20. Is this implementation necessarily wrong?
class SortedList {
Vector v; Integer foo;
// requires: a <= b <= c
public SortedListA(Integer a, Integer b,
Integer c) {
v = new Vector();
foo = new Integer(666);
v.add(b); v.add(foo);
v.add(a); v.add(foo);
v.add(c); v.add(foo); }… }

21. Abstraction Function Just redefine the abstraction function!
[ v[2], v[0], v[4] ] maps to [ x1, x2, x3 ]
Abstraction function defines the convention or the way we interpret the underlying data structure for the abstraction it represents.

22. Representation Invariant
If I decide that my representation invariant is the following:
v != null &&
v.size() == 6 &&
all elements in v are Integers &&
foo == Integer(666)
Then all operations: constructors, producers, mutators, observers MUST maintain this property!!!

23. Representation Invariant
If I decide that my representation invariant is the following:
v != null &&
v.size() == 6 &&
all elements in v are Integers &&
foo == Integer(666)
Suppose I take out the last clause, then what does this imply?
Then the operators: the constructors, producers, mutators, observers cannot always expect foo == Integer(666) in their implementation!

24. Representation Invariant
The idea behind Representation Invariant is to allow the implementation of each operation to agree on a set of assumptions about the data structure!

25. Quiz 1 Questions?
Good luck on the quiz!