This document discusses greedy algorithms and their application to optimization problems such as coin change problems. It provides examples of using a greedy approach to count money by selecting the largest coins first, but notes that this can fail in some cases. Dynamic programming solutions are then introduced as alternatives to the greedy algorithm for making change that are guaranteed to find the optimal solution. The complexity of coin change problems is also examined.

1. Algorithms

2. Greedy Algorithm

3. Optimization Problems

4. Optimization Problems

5. Optimization Problems

6. Example: Counting Money

7. Example: Counting Money

8. Coin Change

9. Example: Counting Money

10. A failure of the Greedy Algorithm

11. A failure of the Greedy Algorithm

12. Greedy Algorithm for Coin Change

13. Making Change DP Solution

14. Making Change DP Solution

15. Making Change DP Solution

16. DP Algorithm for Making Change

17. DP Algorithm for Making Change

18. DP Algorithm for Making Change

19. Complexity of Coin Change

20. Coin Change

21. Design and Analysis
of
Algorithms