6.170 Recitation Godfrey Tan

Announcements Quiz 1 Review Problem Set 3 Quiz 1 (L1-L10): Sunday, March 3, 7:30pm, 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!

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

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

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

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

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

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

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

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

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

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

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

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

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); }… }

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

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

Abstraction Function What is the abstraction function?

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 ]

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); }… }

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.

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!!!

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!

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!

Quiz 1 Questions? Good luck on the quiz!