2. Chair of Software Engineering 1 Introduction to Programming Exercise Session Week 10 M. Piccioni 24/25 November 2008

3. Chair of Software Engineering 2 Announcement In two weeks (December 9th)... Mock exam 2

4. Chair of Software Engineering 3 Featuring today  Genericity  Recursion  Recursion and Trees!

5. Chair of Software Engineering 4 Genericity: Type parametrization LIST_OF_ ANIMALS LIST_OF_ PEOPLE LIST_OF_ CARS Type parameterization

6. Chair of Software Engineering 5 Genericity - why?  To parametrize a class, abstracting away all the operations in common  A single class text may be reused for many different objects types.  To provide an implementation of type safe containers  Helps avoiding objects-test/assignment attempt

7. Chair of Software Engineering 6 A Generic List class LINKED_LIST[G] feature item: G -- the element cursor is pointing at do... end append(value: G) -- append a value to the list do... end end G will be replaced by the compiler with the needed type that has to be specified at some point. Generic parameter

8. Chair of Software Engineering 7 A “natural” example class ANIMAL create make feature -- Initialization make (a_genus: STRING) ‏ do genus := a_genus end feature -- Status genus: STRING... end

9. Chair of Software Engineering the animals: from ____________________ until__________________ _______________ loop x := _____________ print(x.genus)‏ ________________ end 8 Type safe Containers x: ANIMAL animal_list: LINKED_LIST [ANIMAL] a_rock: MINERAL animal_list.put(a_rock) -- does this rock? Hands-On animal_list.start animal_list.after animal_list.item animal_list.forth

10. Chair of Software Engineering Constrained generic parameter note: “Storage for resources” class STORAGE [G ->RESOURCE] inherit LIST[G] consume_all do from start until after loop item.consume forth end... end 9 A Constrained Generic List item is checked for conformance with RESOURCE -- client code sf: STORAGE [FISH] sg: STORAGE [GRAIN]

11. Chair of Software Engineering 10 The Waldgarten Project We need to associate each plant in the same category (categories are trees, bushes, herbs and mosses) to a unique id. Suggest one or more classes for the specified context. Hands-On

12. Chair of Software Engineering 11 Yes, we can (constrain) Solution class PLANT... species: STRING... end Usage: herbs: HASH_TABLE [HERB, STRING] bushes: HASH_TABLE [BUSH, STRING]... herbs.add(myherb, myherb.species)

13. Chair of Software Engineering Today  Recursion 12

14. Chair of Software Engineering Thoughts 13 „ To iterate is human, to recurse - divine!“ but … computers are built by humans Better use iterative approach if reasonable ?

15. Chair of Software Engineering Iteration vs. Recursion  Every recursion could be rewritten as an iteration and vice versa.  BUT, depending on how the problem is formulated, this can be difficult or might not give you a performance improvement 14

16. Chair of Software Engineering Recursion warm-up exercise 1 If we pass n=4, how many numbers will be printed and in which order? print_int (n: INTEGER) do print (n) if n>1 then print_int (n-1) end 15 Hands-On

17. Chair of Software Engineering Recursion warm-up exercise 2 If we pass n=4, how many numbers will be printed and in which order? print_int (n: INTEGER) do if n>1 then print_int (n-1) end print (n) end 16 Hands-On

18. Chair of Software Engineering Recursion exercise 3 Print a given string in reverse order using a recursive function 17 Hands-On

19. Chair of Software Engineering Sequences and Recursion Write a recursive and an iterative program to print the following: 111,112,113,121,122,123,131,132,133, 211,212,213,221,222,223,231,232,233, 311,312,313,321,322,323,331,332,333. 18 Hands-On

20. Chair of Software Engineering Magic Squares  The sums in every row and column is constant  Numbers are all different 19 438 951 276

21. Chair of Software Engineering Magic Squares and Permutations  Finding a magic square 3x3 is related to finding the permutations of 1 to 9 123456789 123456798 123456879 123456897 123456978 123456987... 987654321 20 There exist 72 magic 9x9 squares (8 of which distinct)

22. Chair of Software Engineering Find the Magic Squares Write a program that finds all the eight 9x9 magic squares. Hint 1: Refactor the previous recursive algorithm applying it to permutations (enforce no repetitions) Hint 2: Use two arrays of 9 elements, one for the current permutation and one to know if a number has already been used or not Hint 3: If you are desperate, have a look at the posted solution with the debugger 21 Hands-On

23. Chair of Software Engineering Going backwards pays off  When the program finds, at the 9th recursion, that a square is not magical, it goes back on the call stack to the previous instance of the function, and even more back if needed.  This technique is called BackTracking and is used in many recursive programs. 22

24. Chair of Software Engineering Data structures You have seen several data structures  ARRAY, LINKED_LIST, HASH_TABLE, … We will now look at another data structure  (Binary) tree and its recursive traversal 23

25. Chair of Software Engineering Tree 24

26. Chair of Software Engineering Tree 25

27. Chair of Software Engineering Tree – in a more abstract way Node Tree:  One root  Typically several leaves “ROOT” “LEAF” 26

28. Chair of Software Engineering Binary Tree Node Binary tree:  One root  Typically several leaves  Each node can have at most 2 children (possibly 0 or 1) “ROOT” “LEAF” 27

29. Chair of Software Engineering Recursive traversal of a binary tree  Implement class NODE with an INTEGER attribute  In NODE implement a recursive feature that traverses the tree and prints out the INTEGER value of each NODE object  Test your code by class APPLICATION which builds a binary tree and calls the traversal feature 28 Hands-On

30. Chair of Software Engineering Binary Search Tree 10 813 4920 Binary search tree:  Binary tree where each node has a COMPARABLE value  Left sub-tree of a node contains only values less than the node’s value  Right sub-tree of a node contains only values greater than or equal to the node’s value “ROOT” “LEAF” 29

31. Chair of Software Engineering Creating a binary search tree  Implement command put (n: INTEGER) in class NODE which creates and links a new NODE object at the right place in the binary search tree rooted by Current  Test your code by class APPLICATION which builds a binary search tree using put and prints out the values using the traversal feature  Hint: you might need to adapt the traversal feature such that the values are printed out in order 30 Hands-On

32. Chair of Software Engineering 31 Questions?

33. Chair of Software Engineering 32 Backup slides

34. Chair of Software Engineering Searching in a binary search tree  Implement feature has(n: INTEGER): BOOLEAN in class NODE which returns true if and only if n is in the tree rooted by Current  Test your code by class APPLICATION which builds a binary search tree and calls has 33 Hands-On