Class 45: Binary Search

Held: Tuesday, 22 April 2008

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

Related Pages:

• EBoard.
• Lab: Binary Search.
• Reading: Searching.

Notes:

• EC for tonight's talk on mental health.
• EC for some Pride Week activity, particularly the Saturday parade.
• EC for Thursday's convo.
• EC for Thursday's Thursday Extra (Dr. Davis).
• Are there questions on the project?
• There is no reading for Wednesday.

Overview:

• The problem of searching.
• Analyzing algorithmic efficiency.
• Making searching more efficient using divide-and-conquer.

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 search, look at each element in turn.
• Sometimes, the collection is sorted. 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.

Lab

• Do The lab.
• Be prepared to reflect.