1. Lecture # 31 Category Trees

3. Binary Trees 16 How many steps to reach a leaf? 4

4. Binary Trees N How many steps to reach a leaf? log 2 (N)

5. 4 branch trees 16 How many steps to reach a leaf? 2

6. 4 branch trees N How many steps to reach a leaf? Log 4 (N)

7. What is the General Algorithm? N How many steps to reach a leaf?

8. What is the General Algorithm? N How many steps to reach a leaf? Log M (N), where M = “branching factor? M

9. 4 branch trees If I double the number of branches, what happens to the number of steps to reach a leaf?

10. 4 branch trees If I double the number of branches, what happens to the number of steps to reach a leaf? It is cut in half

11. 10 branch trees Log 10 (N) Count digits

12. Binary Trees How many steps to reach a leaf? 16 leaves

13. Binary Trees Balanced Unbalanced

14. Binary Trees Really Unbalanced 16 leaves how many steps? Average of 8 - N/2

15. N branches If I have N leaves, why not just have N branches in the tree? –I can reach each leaf in one step The time to choose a leaf –Binary tree constant time –N-ary tree (N branches) N checks (one for each branch)

16. What if I don ’ t know which branch to choose? Try all of them Average N/2

17. Trees - time to find things Number of branches (B) –log B (N) –Too many branches searching for branches is a problem –Too few branches too many steps to a leaf Balance Probability of correct choice

18. Examples of trees Dewey Library of congress Biology Yahoo Menus File system

19. Dewey 000 Computers, information, & general reference 100 Philosophy & psychology 200 Religion 300 Social sciences 400 Language 500 Science 600 Technology 700 Arts & recreation 800 Literature 900 History & geography

20. Dewey 500 Science –510 Mathematics –520 Astronomy –530 Physics –540 Chemistry –550 Earth sciences & geology –560 Fossils & prehistoric life –570 Biology & life sciences –580 Plants (Botany) –590 Animals (Zoology)

21. Dewey 500 Science –550 Earth sciences & geology 551 Geology, hydrology, meteorology 552 Petrology 553 Economic geology 554 Earth sciences of Europe 555 Earth sciences of Asia 556 Earth sciences of Africa 557 Earth sciences of North America 558 Earth sciences of South America 559 Earth sciences of other areas

22. What are the numbers in the Dewey tree? A path name How many possibilities? –1000 Where do we get more? –343.123 c

23. Using the Dewey tree What is the Dewey Decimal number for Ostriches? If we don ’ t know how to choose then how do we find things? Search to get Dewey decimal number

24. What good is the system? If we can ’ t correctly choose the path to a book, then isn ’ t the search just linear (N/2)? Unique location for each book –Why not just assign them a number as each book comes into the library? Browsing - keep related books together

25. Library of Congress How many books? ~ 20 Million How many maps, documents, videos, photos? ~ 100 Million

26. Library of Congress A -- GENERAL WORKS B -- PHILOSOPHY. PSYCHOLOGY. RELIGION C -- AUXILIARY SCIENCES OF HISTORY D -- HISTORY: GENERAL AND OLD WORLD E -- HISTORY: AMERICA F -- HISTORY: AMERICA G -- GEOGRAPHY. ANTHROPOLOGY. RECREATION H -- SOCIAL SCIENCES J -- POLITICAL SCIENCE K -- LAW L -- EDUCATION M -- MUSIC AND BOOKS ON MUSIC N -- FINE ARTS P -- LANGUAGE AND LITERATURE Q -- SCIENCE R -- MEDICINE S -- AGRICULTURE T -- TECHNOLOGY U -- MILITARY SCIENCE V -- NAVAL SCIENCE Z -- BIBLIOGRAPHY. LIBRARY SCIENCE. INFORMATION RESOURCES (GENERAL)

27. Library of Congress A -- GENERAL WORKS B -- PHILOSOPHY. PSYCHOLOGY. RELIGION C -- AUXILIARY SCIENCES OF HISTORY D -- HISTORY: GENERAL AND OLD WORLD E -- HISTORY: AMERICA F -- HISTORY: AMERICA G -- GEOGRAPHY. ANTHROPOLOGY. RECREATION H -- SOCIAL SCIENCES J -- POLITICAL SCIENCE K -- LAW L -- EDUCATION M -- MUSIC AND BOOKS ON MUSIC N -- FINE ARTS P -- LANGUAGE AND LITERATURE Q -- SCIENCE R -- MEDICINE S -- AGRICULTURE T -- TECHNOLOGY U -- MILITARY SCIENCE V -- NAVAL SCIENCE Z -- BIBLIOGRAPHY. LIBRARY SCIENCE. INFORMATION RESOURCES (GENERAL) Why do these subjects get so much space in the tree? What is the purpose of the Library of Congress?

28. Organizing trees of information Branches Balance Can the user make a correct choice –Information about each choice

29. Which of these things is not like the others? If you are in first grade? If you are a biologist?

30. Which of these things is not like the others? Studying the arctic Studying child/adult animal behavior

31. Tree problems Literature Novels Whales... Industry Sea Whaling... Biology Mammals Whales...

32. Yahoo.com - a huge tree of WWW information What are the major items for? Why are the minor items here? Click Here

33. What is this? A path name in a tree Why doesn ’ t “ Animals ” follow “ Science ” ?

34. What is this section for? To identify the user ’ s purpose

35. Tree problems Literature Novels Whales... Industry Sea Whaling... Biology Mammals Whales...

36. Aliases - connect tree branches Literature Novels Whales... Industry Sea Whaling... Biology Mammals Whales Stories Industry...

37. Aliases - Windows Shortcuts Named objects that contain the path name of other objects Lets us organize a tree in many ways Shortcut symbol

38. Challenge If you run a commercial art house and want to organize all of your pictures into a tree If you are creating a new program and want to organize your menu items into a tree Who has the answer to the organization? –The users

39. How to get user input Get samples –100 pictures –Names of menu items on 3x5 cards Give them to users –Tell them to organize them into 7-12 stacks –Tell them to write name on each stack –Video tape the process and ask them to talk about what they are doing

40. Trees - time to find Number of branches (B) –log B (N) –Too many branches searching for branches is a problem –Too few branches too many steps to a leaf Balance Probability of correct choice “ Similar ” things together –Aliases to apply multiple organizations