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Course Review
A Few
Unanswered
Questions
Lecture 25
CS2110 – Fall 2008
2
Announcements
! Final Exam
" Thursday, Dec 18 " 2 - 4:30pm " Uris Auditorium
! Review Sessions
" Wednesday, Dec 17 " 7:30 - 9pm and 9 - 10:30pm " Upson B " Both sessions the same " Maybe an extra one Tuesday of next week - watch web site for an announcement
! For exam conflicts:
" Notify Kelly Patwell today " You must provide
Your entire exam schedule
Include the course numbers
! Definition of exam conflict:
" Two exams at the same time or " Three or more exams within 24 hours
! A5 due Monday, Dec 8, 11:59pm
" Sorry, no more extensions 3
Announcements
! Jealous of the glamorous life
of a CS consultant?
" We're recruiting next-semester consultants for CS1110 and CS " Interested students should fill out an application, available in 303 Upson
! Check the course website for
additional announcements as
the final exam approaches
" Consulting ends this week " Office hours continue until Final Exam
There may be changes (TAs
have exams, too)
Any changes will be announced
on the course website 4
Course Evaluations
! Worth one assignment point
" Will count as 1% of your course grade " This is a regular point, not a bonus point " Anonymity
We get a list of who completed the course evaluations and a list of
responses, but no link between names & responses
! Open now
! Closes Wednesday, December 10, midnight
! http://www.engineering.cornell.edu/CourseEval
" This link also appears on the CS2110 announcements page
Course Overview
! Programming concepts
We use Java, but the goal is to
understand the ideas rather than to become a Java expert " Recursion " Object-Oriented Programming " Interfaces " Graphical User Interfaces (GUIs)
! Data structure concepts
The goal here is to develop skill
with a set of tools that are widely useful " Induction " Asymptotic analysis (big-O) " Arrays, Trees, and Lists " Searching & Sorting " Stacks & Queues " Priority Queues " Sets & Dictionaries " Graphs
Programming Concepts
! Recursion
" Stack frames " Exceptions
! Object-oriented programming
" Classes and objects " Primitive vs. reference types " Dynamic vs. static types " Subtypes and Inheritance
Overriding
Shadowing
Overloading
Upcasting & downcasting
" Inner & anonymous classes
! Interfaces
" Type hierarchy vs. class hierarchy " The Comparable interface " Iterators & Iterable
! GUIs
" Components, Containers, & Layout Managers " Events & listeners
7
Data Structure Concepts
! Induction ! Grammars & parsing ! Asymptotic analysis (big-O) " Solving recurrences " Lower bounds on sorting ! Basic building blocks " Arrays " Lists
Singly- and doubly-linked
" Trees
Binary Search Trees (BSTs)
! Searching " Linear- vs. binary-search ! Sorting " Insertion-, Selection-, Merge-, Quick-, and Heapsort ! Useful ADTs (& implementations) " Stacks & Queues
Arrays & lists
" Priority Queues
Heaps
Array of queues
" Sets & Dictionaries
Bit vectors (for Sets)
Arrays & lists
Hashing & Hashtables
BSTs (& balanced BSTs)
" Graphs... 8
Overview of Graphs
! Mathematical definition of a graph (directed, undirected)
! Representations
" Adjacency matrix " Adjacency list
! Topological sort
! Coloring & planarity
! Searching (BFS & DFS)
! Dijkstra’s shortest path algorithm
! Minimum Spanning Trees (MSTs)
" Prim’s algorithm (growing a single tree) " Kruskal’s algorithm (build a forest by adding edges in order)
Some Unsolved
Problems
10 Complexity of Bounded-Degree Euclidean MST
! The Euclidean MST (Minimum
Spanning Tree) problem:
" Given n points in the plane, determine the MST " Can be solved in O(n log n) time by first building the Delaunay Triangulation
! Bounded-degree version:
" Given n points in the plane, determine a MST where each vertex has degree! d
Known to be NP-hard for d=
[Papadimitriou & Vazirani 84]
O(n log n) algorithm for d=5 or
greater ! Can show Euclidean MST has degree! 5
Unknown for d=
Complexity of Euclidean MST in Rd
! Given n points in dimension d,
determine the MST
" Is there an algorithm with runtime close to the "(n log n) lower bound?
! Can solve in time
O(n log n) for d=
! For large d, it appears that
runtime approaches O(n^2 )
! Best algorithms for general
graphs run in time linear in m
= number of edges
" But for Euclidean distances on points, the number of edges is n(n-1)/
O(n^2 ) Time for X+Y Sorting?
How long does it take to a sort an n-by-n table of numbers? ! O(n^2 log n) because there are n^2 numbers in the table ! What if it’s an addition table? " Shouldn’t it be easier to sort than an arbitrary set of n^2 numbers? ! There is a technique that uses just O(n^2 ) comparisons [Fredman 76] " (^) But it uses O(n^2 log n) time to decide which comparisons to use [Lambert 92] ! This problem is closely related to the problem of sorting the vertices of a line arrangement n-by-n
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Good luck on the final! Thanks for an enjoyable semester! Have a great winter break!
