6'170 Recitation

1
6.170 Recitation

• Godfrey Tan

2
Announcements

• Quiz 1 Review
• Sunday, March 3, 730pm, 34-101
• Problem Set 3
• Tuesday, March 5
• Quiz 1 (L1-L10)
• Wednesday, March 6 during class
• Locations
• 54-100 for usernames a-j
• 34-101 for usernames k-z
• Open book, but it is a short quiz!

3
Graph Basics

• Node
• 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
• 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

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 lt x2 lt x3

15
Sorted List

• class SortedList
• Vector v Integer foo
• // requires a lt b lt 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
• v0, v2, v4 maps to x1, x2, x3

20
Is this implementation necessarily wrong?

• class SortedList
• Vector v Integer foo
• // requires a lt b lt 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!
• v2, v0, v4 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!