Greedy Algorithms: Introduction

1. Greedy Algorithms:Introduction http://iti.wtf Algorithms and Data Structures Artem A. Golubnichiy artem@golubnichij.ru Department of Software of Computer Facilities and Automated Systems KatanovKhakass State University

2. STRUCTURE OF THE CLASS • Maximize Your Salary • Queue of Patients • Implementation and Analysis • Main Ingredients

3. WHAT’S COMING • Solve salary maximization problem • Come up with a greedy algorithm yourself • Solve optimal queue arrangement problem • Generalize solutions using the concepts of greedy choice, subproblem and safe choice

4. MAXIMIZE SALARY

5. MAXIMIZE SALARY

6. MAXIMIZE SALARY

7. LARGEST NUMBER

8. LARGEST NUMBER

9. LARGEST NUMBER

10. GREEDY STRATEGY {9, 8, 9, 6, 1} → ?????

11. GREEDY STRATEGY Find max {9, 8, 9, 6, 1} Find max digit

12. GREEDY STRATEGY Find max {9, 8, 9, 6, 1} Find maxdigit

13. GREEDY STRATEGY Find max Append {9, 8, 9, 6, 1} → Find maxdigit Append it to the number

14. GREEDY STRATEGY Find max Append {9, 8, 9, 6, 1} → 9 Find maxdigit Append it to the number

15. GREEDY STRATEGY Find max Append {9, 8, 9, 6, 1} → 9 Remove Find maxdigit Append it to the number Remove it from the list of digits

16. GREEDY STRATEGY Find max Append {9, 8, 9, 6, 1} → 9 Remove Find maxdigit Append it to the number Remove it from the list of digits

17. GREEDY STRATEGY Find max Append {8, 9, 6, 1} → 9 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

18. GREEDY STRATEGY Find max Append {8, 9, 6, 1} → 9 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

19. GREEDY STRATEGY Find max Append {8, 9, 6, 1} → 99 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

20. GREEDY STRATEGY Find max Append {8, 9, 6, 1} → 99 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

21. GREEDY STRATEGY Find max Append {8, 6, 1} → 99 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

22. GREEDY STRATEGY Find max Append {8, 6, 1} → 99 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

23. GREEDY STRATEGY Find max Append {8, 6, 1} → 998 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

24. GREEDY STRATEGY Find max Append {8, 6, 1} → 998 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

25. GREEDY STRATEGY Find max Append {6, 1} → 998 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

26. GREEDY STRATEGY Find max Append {6, 1} → 998 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

27. GREEDY STRATEGY Find max Append {6, 1} → 9986 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

28. GREEDY STRATEGY Find max Append {6, 1} → 9986 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

29. GREEDY STRATEGY Find max Append {1} → 9986 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

30. GREEDY STRATEGY Find max Append {1} → 9986 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

31. GREEDY STRATEGY Find max Append {1} → 99861 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

32. GREEDY STRATEGY Find max Append {1} → 99861 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

33. GREEDY STRATEGY Find max Append {} → 99861 Remove Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

34. GREEDY STRATEGY Find max Append {9, 8, 9, 6, 1} → 99861 Remove Success! Find maxdigit Append it to the number Remove it from the list of digits Repeat while there are digits in the list

35. QUEUE OF PATIENTS

36. QUEUE OF PATIENTS

37. QUEUE OF PATIENTS

38. QUEUE OF PATIENTS

39. QUEUE OF PATIENTS

40. QUEUE OF PATIENTS

41. QUEUE OF PATIENTS

42. QUEUE OF PATIENTS

43. QUEUE OF PATIENTS

44. QUEUE OF PATIENTS

45. GREEDY STRATEGY • Make some greedy choice • Reduce to a smaller problem • Iterate

46. GREEDY CHOICE • First treat the patient with the maximum treatment time • First treat the patient with the minimum treatment time • First treat the patient with average treatment time

47. GREEDY ALGORITHM • First treat the patient with the minimum treatment time

48. GREEDY ALGORITHM • First treat the patient with the minimum treatment time • Remove this patient from the queue

49. GREEDY ALGORITHM • First treat the patient with the minimum treatment time • Remove this patient from the queue • Treat all the remaining patients in such order as to minimize their total waiting time

50. SUBPROBLEM