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Introduction to Programming
Exercise Session Week 10
M. Piccioni
24/25 November 2008
Chair of Software Engineering
Announcement
In two weeks (December 9th)...
Mock exam 2
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Featuring today
Genericity
Recursion
 Recursion

Recursion

Recursion

Recursion

Recursion
and Trees!
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Genericity: Type parametrization
Type parameterization
LIST_OF_
PEOPLE
Type parameterization
LIST_OF_
ANIMALS
LIST_OF_
CARS
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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
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A Generic List
class LINKED_LIST[G]
feature
Generic parameter
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.
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A “natural” example
class ANIMAL
create
make
feature -- Initialization
make (a_genus: STRING)
do
genus := a_genus
end
feature -- Status
genus: STRING
...
end
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Type safe Containers
x: ANIMAL
animal_list: LINKED_LIST [ANIMAL]
a_rock: MINERAL
animal_list.put(a_rock) -- does this rock?
the animals:
animal_list.start
from ____________________
animal_list.after _______________
until__________________
loop
animal_list.item
x := _____________
print(x.genus)
animal_list.forth
________________
end
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A Constrained Generic List
note: “Storage for resources”
class STORAGE [G ->RESOURCE] inherit LIST[G]
consume_all
do
Constrained generic
from start until after loop
parameter
item.consume
forth
item is checked for
conformance with
end
RESOURCE
end
-- client code
...
sf: STORAGE [FISH]
end
sg: STORAGE [GRAIN]
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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.
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Yes, we can (constrain)
class PLANT
...
species: STRING
...
end
Usage:
herbs: HASH_TABLE [HERB, STRING]
bushes: HASH_TABLE [BUSH, STRING]
...
herbs.add(myherb, myherb.species)
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Today
 Recursion
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Thoughts
Better use iterative approach if reasonable
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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
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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
end
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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
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Recursion exercise 3
Print a given string
in reverse order
using a recursive function
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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.
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Magic Squares
 The sums in every row and column is constant
 Numbers are all different
4
3
8
9
5
1
2
7
6
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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
There exist 72 magic 9x9
squares (8 of which distinct)
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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
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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.
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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
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Tree
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Tree
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Tree – in a more abstract way
Node
Tree:
“ROOT”
“LEAF”
 One root
 Typically several leaves
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Binary Tree
Node
“ROOT”
“LEAF”
Binary tree:
 One root
 Typically several leaves
 Each node can have at most 2 children (possibly 0 or 1)
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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
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Binary Search Tree
10
8
4
“ROOT”
13
9
20
“LEAF”
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
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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
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Questions?
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Backup slides
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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
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