CS 411 Fall 2025  >  Outline for October 8, 2025

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CS 411 Fall 2025
Outline
for October 8, 2025

Outline

Closest Pair & Convex Hull (cont’d) [L 5.5]

See the October 6, 2025 lecture notes.

Transform and Conquer [L Ch 6 intro]

• Next algorithmic strategy: Transform and Conquer: transform instance of a problem to make problem easier to solve
• Note: Instance of a problem: specific example of input for a problem. Examples:
  • An instance of the convex-hull problem is a collection of points in the plane.
  • An instance of the sorting problem is a list.
  • An instance of the selection problem is a list along with an index.
• An algorithm is given a REPRESENTATION of an INSTANCE of a PROBLEM. We can classify Transform and Conquer algorithms by which of these they change.
  • Instance simplification: replace the INSTANCE with an instance of the same problem, for which the problem is easier to solve.
  • Representation change: Compute a different REPRESENTATION of the same instance.
  • Problem reduction: Replace with an instance of a different PROBLEM, so that the solution to this new problem gives us the solution to the original problem.
• Transform and Conquer follows a two-stage process: transform problem, then solve transformed problem. When analyzing, consider efficiency of both stages.

Presorting [L 6.1]

• Idea: In a problem where we are given an arbitrary list, sort the list, and then solve the same problem.
  • Example of instance simplification.
• Sometimes best way to solve the problem.
  • Example: finding a mode.
• Sometimes increases efficiency if same list will be reused.
  • Example: search a list for a given key.
  • If doing only one search, then Sequential Search is faster than sort + Binary Search.
  • If doing many searches with different keys on same list, then sort + multiple calls to Binary Search is faster than multiple calls to Sequential Search.
• Example not found in text where presorting can help: given a list, are items all distinct?