a review session2013-T2

Lecture 16School of Engineering and Computer Science, Victoria University of

Wellington

CO

MP 1

03

Marcus Frean

2

But first: the cost of QuickSort

If Quicksort divides the array exactly in half, then: C(n) = n + 2 C(n/2) n log(n) comparisons

= O(n log(n)) (best case)

If Quicksort divides the array into 1 and n-1: C(n) = n + (n-1) + (n-2) + (n-3) + … + 2 + 1 = n(n-1)/2 comparisons

= O(n2) (worst case)

Average case? very hard to analyse. still O(n log(n)), and very good.

Quicksort is “in place”, MergeSort is not

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Stable or Unstable? Faster if almost-sorted?

MergeSort: Stable: doesn’t jump any item over an unsorted region

⇒ two equal items preserve their order

Same cost on all input “natural merge” variant doesn’t sort already-sorted

regions⇒ will be very fast: O(n) on almost sorted lists

QuickSort: Unstable: Partition “jumps” items to the other end

⇒ two equal items likely to reverse their order

Cost depends on choice of pivot. sensible choice of pivot ⇒ O(n log(n)) on almost sorted

lists

4

Some Big-O costs revisitedImplementing Collections:

ArrayList: O(n) to add/remove, except at end

Stack: O(1)

ArraySet: O(n) (cost of searching)

SortedArraySet O( log(n) ) to search (with binary

search)

O(n) to add/remove (cost of moving

up/down)

O( n2 ) to add n itemsO( n log(n) ) to initialise with n items. (with fast sorting)

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test: the warm-up question

Suppose you use a List called mypets to store information about your pets, represented as objects of type Pet. (Write code to declare and initialise an empty instance of such a list).

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a bit tougher

Many people today have more than one phone number at which they might be reached. Suppose you wish to use a Map called phoneNums to store the set of phone numbers associated with each of your friends, who are represented by a class Person. The Map needs to be from keys that are objects of class Person, to sets of integers. (Write code to declare and initialise an empty instance of such a map).

7

Iterable vs Iterator

In words, describe the difference between these two interfaces.

Iterable ensures that the class IS iterable, meaning it has a method iterator() which will return an appropriate Iterator. This allows an object to be the target of the ``foreach'' statement.

Iterator ensures that the class IS an iterator, ie. it has methods next(), hasNext() [oh, and remove()]

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Comparable vs Comparator

Java uses the method Collections.sort() to sort Lists into what is called a ``natural ordering''. What is the critical method that the class of objects in the list must have for this to work, and how is this ensured in Java?

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3 ways to loop – the first

List <String> mylist = new ArrayList <String>();

Suppose this list has been populated by scanning a file. Write code that prints the strings, by going through the list using a standard ‘for’ loop: for (int i=0;

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3 ways to loop – the second

List <String> mylist = new ArrayList <String>();

Write code that prints out the strings with a ``for each'' loop:

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3 ways to loop – the third

List <String> mylist = new ArrayList <String>();

Instead, explicitly get and use an Iterator :

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Carspublic class Car {

private int reg;

private Set <String> colours;

public Car(int registration, Set <String> cols) {

this.reg = registration;

this.colours = cols;

}

public Set<String> getColours() {

return colours;

}

}

Each car is identified by its unique registration number, and stores its colours in a Set.

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a file about cars

Imagine you’re working on code to keep track of the Cars in a yard. Information on an individual car is stored on a single line, in a simple text file. Here is a short example:

Mini 75673 blue red yellow

Golf 93888 black blue

Uno 02009 red

Mini 44637 red black

The 1st question involved reading this and building a Map

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a collection of collections

The class you’re working on involves a Map with a model (String) as its key, and a Set of Car objects as its value. Map <String, Set<Car> > modelsMap =

new HashMap <String, Set<Car>> ();

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printAllColours()

Write code which uses the Map to generate and print out the set of all the colours that appear on at least one car. public void printAllColours(

Map <String,Set<Car>> modelsMap) {

}

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printModelsGivenColour()

Write a new method, printModelsGivenColour(), which takes a colour (String) and the Map provided by mapModelToCars as arguments, and prints out the models in ascending order, without duplications.public void printModelsGivenColour(

String col, Map <String,Set<Car>> modelsMap) {

}