Download Chapter 12

Going further
• Recursion
• Collections
• Beyond Java
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12-1
Recursion
• Recursion is a fundamental programming
technique that can provide an elegant solution
certain kinds of problems
• A recursive definition is one which uses the word
or concept being defined in the definition itself
– a recursive definition of an English word is often not
helpful
– In math and computer science, a recursive definition
can be an appropriate way to express a concept
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11-2
Recursive Definitions
• Consider the following list of numbers:
24, 88, 40, 37
• Such a list can be defined as follows:
A LIST is a:
or a:
number
number
comma
LIST
• That is, a LIST is defined to be a single number, or a
number followed by a comma followed by a LIST
• The concept of a LIST is used to define itself
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11-3
Recursive Definitions
• The recursive part of the LIST definition is used
several times, terminating with the non-recursive
part:
number comma LIST
24
,
88, 40, 37
number comma LIST
88
,
40, 37
number comma LIST
40
,
37
number
37
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11-4
Infinite Recursion
• All recursive definitions have to have a nonrecursive part
• If they didn't, there would be no way to terminate
the recursive path
• Such a definition would cause infinite recursion
• This problem is similar to an infinite loop, but the
non-terminating "loop" is part of the definition
itself
• The non-recursive part is often called the base
case
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11-5
Recursive Definitions
• N!, for any positive integer N, is defined to be the
product of all integers between 1 and N inclusive
• This definition can be expressed recursively as:
1!
N!
=
=
1
N * (N-1)!
• A factorial is defined in terms of another factorial
• Eventually, the base case of 1! is reached
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Recursive Definitions
5!
120
5 * 4!
24
4 * 3!
6
3 * 2!
2
2 * 1!
1
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11-7
Recursive Programming
• A method in Java can invoke itself; if set up that way, it is
called a recursive method
• The code of a recursive method must be structured to
handle both the base case and the recursive case
• Each call to the method sets up a new execution
environment, with new parameters and local variables
• As with any method call, when the method completes,
control returns to the method that invoked it (which may
be an earlier invocation of itself)
• See Factorial.java
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11-8
Recursive Programming
• Note that just because we can use recursion to
solve a problem, doesn't mean we should
• For instance, we usually would not use recursion
to solve the sum of 1 to N problem, because the
iterative version is easier to understand
• However, for some problems, recursion provides
an elegant solution, often cleaner than an
iterative version
• You must carefully decide whether recursion is
the correct technique for any problem
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11-9
Recursive Directory Listing
• Suppose you want to list all the files in a
directory including files in any
subdirectories that might be present.
• Algorithm
for each entry in the current directory
if it is a file, print its name
else // must be a directory
do recursive call on the entry
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11-10
Towers of Hanoi
• The Towers of Hanoi is a puzzle made up of
three vertical pegs and several disks that slide
on the pegs
• The disks are of varying size, initially placed on
one peg with the largest disk on the bottom with
increasingly smaller ones on top
• The goal is to move all of the disks from one peg
to another under the following rules:
– We can move only one disk at a time
– We cannot move a larger disk on top of a smaller one
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11-11
Towers of Hanoi
Original Configuration
Move 1
Move 2
Move 3
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11-12
Towers of Hanoi
Move 4
Move 5
Move 6
Move 7 (done)
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11-13
Towers of Hanoi
• An iterative solution to the Towers of Hanoi
is quite complex
• A recursive solution is much shorter and
more elegant
• See SolveTowers.java
• See TowersOfHanoi.java
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11-14
Fractals
• A fractal is a geometric shape made up of the
same pattern repeated in different sizes and
orientations
• The Koch Snowflake is a particular fractal that
begins with an equilateral triangle
• To get a higher order of the fractal, the sides of
the triangle are replaced with angled line
segments
• See KochSnowflake.java
• See KochPanel.java
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11-15
Koch Snowflakes
< x5 , y5 >
< x 5 , y5 >
< x 4 , y4 >
Becomes
< x3 , y 3 >
< x 2 , y2 >
< x1 , y1 >
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< x 1 , y1 >
11-16
Other Examples of Recursion
• Recursive sort algorithms
• Recursive data structures
– Chapter 12
– COMPSCI 225
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11-17
Collections
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12-18
Collections
• A collection is an object that serves as a
repository for other objects
• A collection usually provides services such as
adding, removing, and otherwise managing the
elements it contains
• Sometimes the elements in a collection are
ordered, sometimes they are not
• Sometimes collections are homogeneous,
containing all the same type of objects, and
sometimes they are heterogeneous
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12-19
Dynamic Structures
• A static data structure has a fixed size
• This meaning is different from the meaning of the
static modifier
• Arrays are static; once you define the number of
elements it can hold, the size doesn’t change
• A dynamic data structure grows and shrinks at
execution time as required by its contents
• A dynamic data structure is implemented using
links
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12-20
Object References
• Recall that an object reference is a variable that
stores the address of an object
• A reference also can be called a pointer
• References often are depicted graphically:
student
John Smith
40725
3.58
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12-21
References as Links
• Object references can be used to create
links between objects
• Suppose a Student class contains a
reference to another Student object
John Smith
40725
3.57
Jane Jones
58821
3.72
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12-22
References as Links
• References can be used to create a variety
of linked structures, such as a linked list:
studentList
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12-23
Queues
• A queue is similar to a list but adds items
only to the rear of the list and removes
them only from the front
• It is called a FIFO data structure: First-In,
First-Out
• Analogy: a line of people at a bank teller’s
window
enqueue
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dequeue
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Stacks
• A stack ADT is also a
linear data structure
Stacks often are drawn
vertically:
• Items are added and
removed from only one
end of a stack
push
pop
• It is therefore LIFO: LastIn, First-Out
• Example: a stack of
plates in a cupboard, a
stack of hay bales in a
barn
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12-25
Trees
• A tree is a non-linear data structure that consists
of a root node and potentially many levels of
additional nodes that form a hierarchy
• In a general tree, each node can have many
child nodes
• We often work with binary trees which have no
more than two children per node
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12-26
Binary Trees
• In a binary tree, each node can have no more
than two child nodes
• A binary tree can be defined recursively. Either it
is empty (the base case) or it consists of a root
and two subtrees, each of which is a binary tree
• Trees are typically are represented using
references as dynamic links, though it is possible
to use fixed representations like arrays
• For binary trees, this requires storing only two
links per node to the left and right child
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12-27
Graphs
• A graph is a non-linear structure
• Unlike a tree or binary tree, a graph does not
have a root
• Any node in a graph can be connected to any
other node by an edge
• Analogy: the highway system connecting cities
on a map
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12-28
The Java Collections API
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12-29
Collection Classes
• The Java standard library contains several
classes that represent collections, often referred
to as the Java Collections API
• Their underlying implementation is implied in the
class names such as ArrayList and
LinkedList
• Several interfaces are used to define operations
on the collections, such as List, Set,
SortedSet, Map, and SortedMap
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12-30
Generics
• As mentioned in Chapter 7, Java supports generic types,
which are useful when defining collections
• A class can be defined to operate on a generic data type
which is specified when the class is instantiated:
LinkedList<Book> myList =
new LinkedList<Book>();
• By specifying the type stored in a collection, only objects
of that type can be added to it
• Furthermore, when an object is removed, its type is
already established
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12-31
Beyond java
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12-32
Other Languages
• There are a number of other languages with a
syntax very similar to that of Java
– Java's syntax is based on that of C which is not objectoriented
– C++ was designed to be backwards-compatible with C
– C# was based on C/C++ without the backwardscompatibility
– Many of the scripting languages started from C's syntax
• JavaScript is a scripting language that is used
inside web pages
– It is not related to Java
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Other Languages: C#
• Like Java, C# is
– A modern, general-purpose object-oriented
language
– Based on C and C++
• C# is part of the .NET family of languages
supported by MicroSoft
– Multiple languages which can interoperate
– Languages compile to a common intermediate
language
– Common Language Runtime runs programs
from all the .NET languages
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C# Program Structure
• A program consists of one or more
files
• A file can contain one or more classes
and/or namespaces
– name of file is not tied to name of class
• At least one class must contain Main
– There are several allowed signatures
• return type is either int or void
• either no parameter or String array
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First Program
namespace FirstProgram {
class First {
static void Main() {
System.Console.WriteLine(
"Welcome to C#!");
}
}
}
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Console I/O
• System.Console.WriteLine( arg)
– argument can be any type
– for objects, ToString is invoked
• System.Console.ReadLine()
– returns a String
• System is a namespace
– using System; allows you to omit the
namespace when calling the method
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C# Types
• Value types
– simple types: primitive types from Java
plus unsigned types and decimal
• Reference types - objects
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Operators
• Has same operators as Java with
similar precedence and associativity
• == compares values for strings and
simple types, addresses for all other
objects
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C# on onyx
• mono is an open-source project that
provides facilities for running C# programs
under Linux
– http://www.mono-project.com
• Compile a program by typing
– mcs First.cs
• Run a program by typing
– mono First.exe
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C# using VMWare
• There is a Windows virtual machine on the
onyx workstations
– vmware &
• C# Express is installed on the virtual
machine
• You can download the .NET development
environment to your own Windows
machine for free using your MSDN account
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