CS 411 Fall 2025  >  Outline for September 12, 2025

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CS 411 Fall 2025
Outline
for September 12, 2025

Outline

Brute Force for Geometric Problems [L 3.3]

• Geometric Problems
• Closest Pair
  • The Closest-Pair Problem
  • Brute-Force Algorithm
    • Check distance of every pair, keeping track of closest
    • How to iterate through all pairs, each exactly once, using nested loops.
  • Analysis
  • Optimization
• Convex Hull
  • Convex region, convex hull
  • The Convex-Hull Problem
    • Convex hull of a finite point set is interior of polygon with some of the points as vertices: extreme points.
    • Finding the convex hull of a finite point set means finding its vertices.
    • Why do we care?
  • Brute-Force Algorithm for 2-D Case
    • Two points \(A\), \(B\) both lie on the boundary of the convex hull if every point lies on the same side of the line between \(A\), \(B\) (where on the line counts as same side).
    • Algorithm based on the above fact
  • Coding it
  • Analysis