Lecture 6

Today’s topics: Greedy Algorithms

• Introduction to Greedy Slides 1-15.
  • We will look a greedy algorithm for the coin-change problem. This only works with certain denomination coins. You should understand the proof of why it works, and when it works.
  • Interval scheduling. Again we met a dynamic programming solution before, here we will look at a simple greedy algorithm and understand why it is correct.
• Shortest Paths as a greedy algorithm. Slides 1-16
• All-Pairs Shortest path using Dynamic programming (The ‣ Bellman–Ford–Moore algorithm). Slides 33-41

Reading Guide

• Chapter 16 except 16.4 and 16.5 of CLRS3 or Chapter 15, 15.1,15.2 and 15.3 of CLRS4.

What should I know by the end of this lecture?

• How do I set up shortest paths as a dynamic program? How do I avoid cycles?
• How does Dijkstra’s algorithm work? Why is it correct?
• What is a greedy algorithm?
  • How do greedy algorithms compare with dynamic programming?
  • Are Greedy algorithms always optimal?