Transcript Slide 1

COSC 1P03
The Stack
Research is what I'm doing when I don't know what
I'm doing.
Wernher Von Braun (1912-1977)
Data Structures and Abstraction
7.1
COSC 1P03
Container ADTs
 container
 collection of objects
 list-oriented collections
 positional
 access relative to position
 e.g. list
 keyed collections
 have a key
 accessed by key
 representations
 contiguous
 arrays
 linked
 linked-structures
Data Structures and Abstraction
7.2
COSC 1P03
Stack
 a list (initially empty) of items of some type to which items may
be added (pushed) at one end (called the top) and from which
items may be removed (popped) only from the same end (i.e. the
top)
 examples
 cafeteria plate stacker
 Pez™ candy dispenser
 behaviour
 example
 LIFO ordering
 operations
 push & pop
 viewing
 empty
 error conditions:
 underflow
 overflow
Pez Candy Dispenser
Data Structures and Abstraction
7.3
COSC 1P03
Character Stack ADT
 item type?
 say char
 CharStack interface
 methods
 push
 pop
 top
 empty
 exceptions
 NoItemException
 NoSpaceException
Data Structures and Abstraction
7.4
COSC 1P03
Character Stack ADT
Contiguous Implementation
 representation
 based on “variable-sized” array
 bottom is base (0th element)
 top is end of collection (nth element)
 implementation
 CharStacks package
 instance variables
 array (elts) and count (top)
 constructors
 empty stack
 methods
 exceptions
 defensive programming
 insertion/deletion don’t affect others O(1)
Data Structures and Abstraction
7.5
COSC 1P03
Character Stack ADT
Linked Implementation
 representation
 top is front
 list pointer points to top (front) node
 implementation
 instance variables
 top is list pointer
 constructor
 empty stack
 methods
 exceptions
 overflow?
 Node wrapper class
 Serializable
 insert/delete at front O(1)
Data Structures and Abstraction
7.6
COSC 1P03
Postfix (RPN) Notation
 algebraic expressions
 infix notation
 priority
 parentheses
 postfix notation aka Reverse Polish Notation (RPN)
 Jan Lukasiewicz
 no need for parentheses or operator priorities
 operator follows operands
 examples
 evaluate left to right
 hardware computation in ALU
Data Structures and Abstraction
7.7
COSC 1P03
Infix to Postfix Translation
 manual process
 insert all parentheses
 convert each sub-expression from inside out
 remove parentheses
 automated process?
 desire single left to right pass over input
 properties
 operands in same order
 operator after operands
 save operator
 cannot output operator until see next one
 if saved is higher priority output else save next operator
 at end must output saved operators in LIFO order
 use a stack
Data Structures and Abstraction
7.8
COSC 1P03
Rail Yard Algorithm
 operands output as seen
 operator
 lower/equal priority than one on stack  output stacked
 higher priority than one on stack  push
 open parenthesis then push, and assume lowest priority
 closed parenthesis then output operators on stack and discard
open parenthesis (from stack) , discard closed parenthesis
 when done
 emit stacked operators
 special cases
 no operator on stack  push
 have low priority operator ($) at bottom of stack
 end of expression  pop
 have low priority operator (#) at end of expression
Data Structures and Abstraction
7.9
COSC 1P03
Example: InfToPost
 client of CharStack
 translate method
 initialization
 create stack (ConCharStack or LnkCharStack)
 String as char array
 append #
 push $
 main loop
 process 1 character from input at a time
 operand  output
 operator  output some stacked operators then push
 operator priorities
 relative
 prio method
 #&$
Data Structures and Abstraction
7.10
COSC 1P03
Generic ADTs
 behaviour of stack independent of type of item
 generalize interface to allow any item type
 generic Stack interface
 based on hypothetical content type E
 generalization (abstraction) over the content type
 changes from CharStack
 change in name of exceptions
 change from char to E throughout
 addition of generic parameter <E> after interface name
 E is a type variable
 Collections package
 set of collection ADT (stack, queue, list, …)
 common names for exceptions
Data Structures and Abstraction
7.11
COSC 1P03
Client Classes
 cost of genericity
 little added complexity in the client class
 stacked items implement the interface of Stack <E>
 item type as E
 push OK
 automatic wrapping of primitive types
 autoboxing
 pop returns an object
 primitive types are unwrapped automatically
 autounboxing
 Linked implementation
 define Node with a generic formal type
 Node<E> is the type for Node.
 E is the type for the element stored within Node<E>
 Serializable, in case we want to write the stack to disk
Data Structures and Abstraction
7.12
COSC 1P03
Type Compatibility
 implements clause declares that the ActualTypeParameter for
Stack is whatever is supplied as ActualTypeParameter for
ConStack
 thus
ConStack<Character> implements Stack<Character>
and
ConStack<Student> implements Stack<Student>
 and so in
Stack<Character> opStack;
opStack = new ConStack<Character>(); is valid
opStack = new ConStack<Student>();
is invalid
Data Structures and Abstraction
7.13
COSC 1P03
Type Checking
 how does the compiler type check within generic class, e.g.
elts[top] = item;
 with ConStack<Character>, Character is substituted for E
so this is OK
 how does compiler know?
 ActualTypeParameter must be a ReferenceType
 all ReferenceTypes are subtypes of Object
 compiler type checks assuming TypeVariable is Object
 thus only operations available on the TypeVariable are those
available on Object
 note: compiler can still handle the elts array since it knows it is
an array of some reference type and thus each element is a
reference (4 bytes)
Data Structures and Abstraction
7.14
COSC 1P03
 note that in the constructor:
elts = (E[]) new Object[size];
is used instead of the expected
elts = new E[size];
 Java does not allow a type parameter to be used in an array
creation expression
 creating an array of Object and downcast it to E[] achieves
the desired effect
 enabling garbage collection
 setting array elements to null allows the nodes to be
garbage collected
 the generic Node class
 in the linked version, the Node class must be parametric since
the type of the contents is unknown.
 only nodes which wrap the same generic type can be put onto
a list which supports a nodes of that type.
 Node<Character> and Node<Student> are different types
 creation of a new Node is done via
top = new Node<E>(item,top);
Data Structures and Abstraction
7.15
COSC 1P03
Example: InfToPostG
 version of InfToPost using generic Stack
 Chararacter
 wrapper for char primitive type
 algorithm the same
 wrapping and unwrapping
 automatic in Java 1.5 and up.
 generics and templates
Data Structures and Abstraction
7.16
COSC 1P03
Java Collections Framework
 Java library for data structure ADTs
 java.util
 stacks, queues, lists, sets, maps
 Collection interface
 generic in element type
 operations common to all collections (except maps)
 methods return boolean if the operation changed the
collection (i.e. added or removed)
 Stack class
 generic in element type (E)
 array implementation (Vector) grows to fit (no overflow)
 some duplication of methods (legacy implementation)
 push returns item pushed
Data Structures and Abstraction
7.17
COSC 1P03
The End
Data Structures and Abstraction
7.45