Held: Wednesday, 27 April 2016

Back to Outline 46 - Analyzing Procedures. On to Outline 48 - Association Lists.

Summary

We consider the general problem of searching and binary search, one of the most efficient algorithms for searching.

Related Pages

• EBoard 47 (Source 47)

Overview

• Analyzing algorithmic efficiency.
• The problem of searching.
• Making searching more efficient using divide-and-conquer.
• A demo: Destructive binary search.
• Considering the parameters to binary search.

Administrivia

• Continue partners (through Friday)
• I will continue to bring you food (or food-like substances) until I am caught up on grading.
  
  • Today: ???

Reminders

• Office hours this week
  • See http://rebelsky.youcanbook.me.
  • Ask me about other available times.
• Tutor hours
  • Sunday, 3-5 p.m.
  • Sunday-Thursday, 7-10 p.m.
• Review Sessions
  • Wednesday at 8pm in CS commons with Sarah
  • Thursday at 10 am with SamR
  • Thursday at 8pm in CS commons with Kumar

Upcoming Work:

• Reading for Friday, which should sound familiar: Association Lists
• Lab Writeup:
  • Send email titled CSC 151 Lab Writeup 47 (Your Names)
  • Do not include the underscores.
  • Send to CSC151-02-grader@grinnell.edu
  • Due before class on Monday.
• Projects due NEXT TUESDAY.
• Quiz Friday.
  • Higher-order procedures.
  • Files in Scheme.
  • Analyzing procedures.

Extra Credit

• Send your reports to rebelsky@grinnell.edu with subject "CSC 151 Extra Credit". (Do not include the quotation marks.)
• Send opportunities to me before class with subject "CSC 151 EXTRA CREDIT OPPORTUNITY!"

Academic / Artistic

• Scholars' Convocation: Dutch Global Horizons, Thursday, April 28, 11 am, JRC 101
• Damon Williams: Bigger Than The Cops, April 28, 4pm or 5:15 pm
• Met Opera, Saturday, April 30, talk at 11:30, Opera at noon.

Peer

• Friday, Break Beat Poets performing behind Eco House at 4:30 p.m.
  • Eco house is across from Cleveland.
• Maybe GMon, Thursday, 7:30 p.m., Loose Lounge.
• Rushdie's East/West, May 6/7 at 7:30 p.m.

Regular Peer

• Social Dance Workshop Tuesdays 7:00-8:00 in Bucksbaum Dance Studio
• Post-break ExCo on British Politics Wednesdays at 8:00 in JRC 203.
  Just show up; you don't need to sign up.
• Pun club Saturdays at 4pm in Younker
• Electronic Potpourri on KDIC Fridays at Five
• Space Odyssey KDIC Fridays at Six
• Bollywood, Fridays, 7:30-8:30, Younker
• Effective Altruism club, 2:30-3:30 Sundays in JRC 226.

Misc

Not for Extra Credit

• Third year students, design a logo or something for a vinyl sticker.
  Earn a gift card to PC! (And a bag-o-stickers!) Deadline Friday.

Common Problems and Algorithms

• As we discussed early in the semester, a key aspect of computer science is the design of algorithms, formalized processes that provide solutions to problems.
• There are a number of common problems for which computer scientists have developed common solutions.
• We'll visit two problems over the next few days: searching and sorting.
• As we develop algorithms, we'll consider intuitive ways that one might come up with the algorithms.

Searching

• Goal: Find a value in a collection.
• Typically, the collection is linear: A vector or list.
• Sometimes, the collection is also unordered. That is, there is no known arrangement to the list. For example, the books on the MathLan book shelves are not in an arrangement that would make it easy to search for a book with a particular title or by a particular author.
• For unordered collections, the typical search is sequential::N search, look at each element in turn.
  • If we distribute things between multiple computers, we can spend the same total computing effort, but significantly less time.
• Sometimes, the collection is ordered. That is, the collection is organized by the primary key in which we search.
  
  • For example, a phone book is sorted by name.
• However, we can also use something known as binary search:
  • Look in the middle of the collection.
  • If the middle is too small, anything smaller is also too small, so discard and try again.
  • If the middle is too large, anything larger is also too large, so discard and try again.
  • If the middle is just right, you're done.

Demonstration: Destructive Binary Search

• We'll do a quick demonstration of binary search

Dsigning a Search API

Suppose we have data for various students on campus: Last Name (string), First Name (string), Graduation Year (integer), Box Number (integer), and Phone number (string). We might search by any of the four criteria (and by other criteria) and we might therefore order in various ways.

(define people
  (vector 
    ("Aanderson" "Aan"    2017 4114 "x4410")
    ("Brown"     "Bruin"  2016 8123 "x9000")
    ("Doe"       "J"      2018 9999 "none")
    ("Smith"     "Kieran" 2015 4112 "x9231")
    ("Taylor"    "Mic"    2017 1234 "x0001")))

• Right now, we have things sorted by last name (and, surprisingly, by first name), so we might search by last name (or by first name).
• If we wanted to search by year, we'd order by year (although that's not likely to give particularly useful results).
• If we wanted to search by box number, we'd order by box number.
• Our search algorithm needs to know how to find the key in an entry
  • Last name: car
  • First name: cadr
  • Year: caddr
  • Box number: cadddr
• Our search algorithm needs to know how the keys are ordered
  • Traditionally, strings are ordered alphabetically
  • Traditionally, numbers are ordered numerically, from smallest to largest
• So our binary search algorithm needs four parameters:
  • The vector to search
  • The key to search for
  • The instructions for getting a key from each element
  • The mechanism used to order the elements
• All of this is a bit more complicated if we have a compound key, such as "last name plus first name plus phone number"

Lab

• We will do the the lab next week.