6.170 recitation
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6.170 Recitation. Godfrey Tan. Announcements. Quiz 1 Review 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!. - PowerPoint PPT PresentationTRANSCRIPT
6.170 Recitation
Godfrey Tan
Announcements Quiz 1 Review
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
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
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
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 Listclass 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 InvariantIf 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 InvariantIf 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!