Class 42: Basics of Searching and Sorting

Held Wednesday, April 18, 2001

Summary

Notes

• Reading for tomorrow: Searching Methods.
• Expect to see the next homework assignment released this afternoon.
• Advance warning: Mr. Walker will be observing class next week. He's visiting in preparation for my tenure review.
• Yes, I'm hoping to hand back exam 2 next Monday (if not before).
• I recently received a survey about minors at Grinnell. I'd like to hear a little bit about your opinions on the matter.
  • Do you want minors?
  • If so, why?
• Preregistration is coming soon, and some of you wanted to know about what to take next year.
  • Standard Math option for prospective CS majors: MAT215 (Linear Algebra) in the fall, MAT218 (Combinatorics) in the spring.
  • Standard CS option for prospective CS majors: CSC152 (aka "Data Structures and Algorithms in Java") in the fall, CSC223 (aka "Software Design") in the spring. This schedule is also applicable for people who just want some more CS.
  • Preferred CS option for prospective CS majors: CSC195 (aka "Under the Hood with C") in the fall, CSC152 in the spring. This schedule is also applicable for people who just want more CS.
  • Insane option: CSC152 and CSC195 in the fall; CSC223 in the spring.
  • Other options: E-Commerce in the spring (not in schedule of courses yet); CSC341 in the spring; electronics in the fall.
  • Even more options: Whoever is serving as visiting professor in the fall will be teaching a special topics course. We're currently debating who to hire and what the prereqs will be.

Overview

Fun with Punch Cards

• We're going to start today's work with a stack of things that are sort of like punch cards. You'll each receive two of them.
• Orient the card with the cut-out corner in the upper-right-hand side.

  +-------------------+
  |                    \
  |  O   O   O   O   O  \
  |                      +
  |                      |
  |                      |
  |  O   O   O   O   O   |
  |                      |
  +----------------------+
  

• Write your last name on the card in big letters.
• You'll notice two rows of holes, one along the top and one along the bottom. We'll be encoding the first two letters of your last name (the first letter along the top, the second letter along the bottom).
• Use the following table to figure out how to encode each letter.
  • A: 00001
  • B: 00010
  • C: 00011
  • D: 00100
  • E: 00101
  • F: 00110
  • G: 00111
  • H: 01000
  • I: 01001
  • J: 01010
  • K: 01100
  • L: 01101
  • M: 01110
  • N: 01111
  • O: 10000
  • P: 10001
  • Q: 10010
  • R: 10011
  • S: 10100
  • T: 10101
  • U: 10110
  • V: 10111
  • W: 11000
  • X: 11001
  • Y: 11010
  • Z: 11011
• A 1 means cut out the card between the edge and the corresponding hole; a 0 means leave the hole as is.
• Here's the card for "Rebelsky" (R is 10011, E is 00101)

  +-+ +---------+ +-+ +
  | | |         | | | |\
  | +-+  O   O  +-+ +-+ \
  |                      +
  |                      |
  |                      |
  |  O   O  +-+  O  +-+  |
  |         | |     | |  |
  +---------+ +-----+ +--+
  

• Soon, we'll see some interesting things to do with the cards.

Common Problems and Algorithms

• As we discussed early in the semester, a key aspect of computer science is the design of algorithms: formalized 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: An array 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 search, look at each element in turn.
• 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 ordered by name.
• Sequential search also works for ordered lists.
• 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 alrge, so discard and try again.
  • If the middle is just right, you're done.

Sorting

• Given an unordered list, how do we make it ordered? That's the problem of sorting, which we'll return to later this week and early next week.
• We may do one example, though.