chapter 13: stacks and queues

Programming and Problem SolvingWith Java

Copyright 1999, James M. Slack

Chapter 13: Stacks and QueuesStacksApplications of StacksImplementation of a Stack ClassQueuesImplementation of the Queue ClassSimulation

Programming and Problem Solving With Java 2

StacksCommon in real world

PapersBooksCDsPlatesBowls

What can we do with a stack?Put new item on topTake topmost item off


Stacks: OperationsJava has a standard Stack class

java.util.StackMethods:

push(): put a new item on top of a stackpop(): get the topmost item from the stack, and remove it

from the stackpeek(): get the value of the topmost item from the stack,

but don't remove the item from the stackempty(): return true if the stack is empty search(): tell how far a value is from the top of the stack,

or -1 if the value is not in the stackA stack is a LIFO structure

Last-in, first-out


Stacks: Push and Pop

A

Push A

Pop C

A

B

C

Pop B

Push B

A

B

A

B

Pop A

Push C

A

B

C

A


Stacks: Demonstration// This program is a simple demonstration of how to// use Java's standard Stack class.

import java.util.Stack;

public class SimpleStackDemo{ public static void main(String[] args) throws java.io.IOException { Stack myStack = new Stack();

// Push some values on the stack (all must be objects) myStack.push("Hello"); myStack.push(new Integer(123)); myStack.push(new Double(5.678));

// Display the stack System.out.println("The contents of the stack: " + myStack); // Pop the objects off the stack and display them double dValue = ((Double) myStack.pop()).doubleValue(); System.out.println("Popped " + dValue);

int iValue = ((Integer) myStack.pop()).intValue(); System.out.println("Popped " + iValue);

String sValue = (String) myStack.pop(); System.out.println("Popped " + sValue); // Display the stack System.out.println("The contents of the stack: " + myStack); }} The contents of the stack: [Hello, 123, 5.678]

Popped 5.678Popped 123Popped HelloThe contents of the stack: []


Stacks: DemonstrationLonger demonstration of Java’s Stack class

// This program lets you push characters onto the// stack, and pop them off. It makes sure you don't try to pop// a character from an empty stack. This is a demonstration of// how to use the Stack class.

import java.util.Stack;import TextMenu;import Keyboard;

public class StackDemoApp extends TextMenu{ static final int PUSH_COMMAND = 1; static final int POP_COMMAND = 2; static final int TOP_COMMAND = 3;

// Constructor public StackDemoApp() { super("Stack Test Menu"); addSelection("Push a new element", '1', PUSH_COMMAND); addSelection("Pop an element", '2', POP_COMMAND); addSelection("Get topmost element", '3', TOP_COMMAND); addSelection("Quit program", 'q', TextMenu.QUIT); }


Stacks: DemonstrationStackDemoApp (continued)

// Handle each event as user selects a command public int handleEvent(int event) throws java.io.IOException { char character;

switch (event) { case PUSH_COMMAND: character = Keyboard.readChar("Character to push: "); charStack.push(new Character(character)); break; case POP_COMMAND: if (charStack.empty()) { System.out.println("Stack is empty"); } else { character = ((Character) charStack.pop()).charValue(); System.out.println("Character popped: " + character); } break; case TOP_COMMAND: if (charStack.empty()) { System.out.println("Stack is empty"); } else { character = ((Character) charStack.peek()).charValue(); System.out.println("Character on top: " + character); } break; } return event; }


Stacks: DemonstrationStackDemoApp (continued)

// Instance variables private Stack charStack = new Stack();

public static void main(String[] args) throws java.io.IOException { StackDemoApp stackDemo = new StackDemoApp(); stackDemo.run(); }}


Stacks: DemonstrationStackDemoApp (sample run)

+--- Stack Test Menu ---| 1) Push a new element 2) Pop an element 3) Get topmost element| q) Quit program| Enter selection: 1Character to push: X

+--- Stack Test Menu ---| 1) Push a new element 2) Pop an element 3) Get topmost element| q) Quit program| Enter selection: 1Character to push: Y

+--- Stack Test Menu ---| 1) Push a new element 2) Pop an element 3) Get topmost element| q) Quit program| Enter selection: 2Character popped: Y

+--- Stack Test Menu ---| 1) Push a new element 2) Pop an element 3) Get topmost element| q) Quit program| Enter selection: 2Character popped: X

+--- Stack Test Menu ---| 1) Push a new element 2) Pop an element 3) Get topmost element| q) Quit program| Enter selection: q


Stacks: Postfix ExpressionsPostfix notation

Also called reverse Polish notation (RPN)Enter operator after operandsExample: 6+8 is 6 8 + in Postfix

Infix notationConventional notation: 6 + 8

Advantages of postfixParentheses not needed

(8 + 7) x (2 - 8) 8 7 + 2 8 - xEasy to evaluate by computer


Stacks: Postfix ExpressionsEvaluation of postfix expression

Get symbol from expression If symbol is number, push on stack If symbol is operator, pop two numbers from stack, do

operation, push result back onto stackRepeat until all symbols read from expression. At end,

result is on top of stack


Stacks: Postfix ExpressionsExample

Evaluate 6 8 +

6

Input

+

Stack

8

Input

Stack

14

14

c. Read 8and push it

f. Result is14, push it

Input

8 +

Stack

6

6 + 8 Input

Stack

b. Read 6and push it

e. Pop 2numbers, add

them

Input

6 8 +

Stack

6

Input

Stack

8

+

a. Ready tostart

d. Read +


Stacks: Postfix ExpressionsExample: Program to evaluate postfix expressions

Single digit numbers onlyNo spacesNo error checking

// This program evaluates postfix expressions. The// operators +, -, *, and /. This program does NO error checking.

import java.util.Stack;import Keyboard;

public class EvaluatePostFix{


Stacks: Postfix Expressions // doOperation: Returns firstOperand oper secondOperand // Note: oper must be '+', '-', '*', or '/'. If oper is '/', // then secondOperand cannot be zero static int doOperation(int firstOperand, int secondOperand, char oper) { int returnValue = 0; switch (oper) { case '+': returnValue = firstOperand + secondOperand; break; case '-': returnValue = firstOperand - secondOperand; break; case '*': returnValue = firstOperand * secondOperand; break; case '/': returnValue = firstOperand / secondOperand; break; } return returnValue; }


Stacks: Postfix Expressions public static void main(String[] args) throws java.io.IOException { Stack stack = new Stack(); char inputChar;

System.out.println("--- Evaluate postfix expressions ---"); System.out.println("--- (Single digit integers ONLY) ---"); System.out.println();

String expression = Keyboard.readString("Enter a postfix expression: ");


Stacks: Postfix Expressions for (int pos = 0; pos < expression.length(); pos++) { inputChar = expression.charAt(pos); System.out.println(); System.out.println("Next character is " + inputChar + ", stack is " + stack); switch (inputChar) { case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9': System.out.println(" Push " + inputChar); stack.push(new Integer(Character.digit(inputChar, 10))); break; case '+': case '-': case '*': case '/': int firstOperand = ((Integer) stack.pop()).intValue(); System.out.println(" Pop " + firstOperand); int secondOperand = ((Integer) stack.pop()).intValue(); System.out.println(" Pop " + secondOperand); int result = doOperation(secondOperand, firstOperand, inputChar); System.out.println(" Compute " + secondOperand

+ " " + inputChar + " " + firstOperand + " and push result " + result);

stack.push(new Integer(result)); break; case ' ': break; // Do nothing } } System.out.println(" Pop result " + stack.pop()); }}

(Debugging

statements

in blue)


Stacks: Postfix ExpressionsSample run of EvaluatePostFix: 6 8 +

--- Evaluate postfix expressions ------ (Single digit integers ONLY) ---

Enter a postfix expression: 6 8 +

Next character is 6, stack is [] Push 6

Next character is , stack is [6]

Next character is 8, stack is [6] Push 8

Next character is , stack is [6, 8]

Next character is +, stack is [6, 8] Pop 8 Pop 6 Compute 6 + 8 and push result 14 Pop result 14


Stacks: Postfix ExpressionsAnother evaluation: 8 7 + 2 8 - x

--- Evaluate postfix expressions ------ (Single digit integers ONLY) ---

Enter a postfix expression: 8 7 + 2 8 - *

Next character is 8, stack is [] Push 8

Next character is , stack is [8]



Next character is +, stack is [8, 7] Pop 7 Pop 8 Compute 8 + 7 and push result 15Next character is , stack is [15]



Next character is 8, stack is [15, 2] Push 8

Next character is , stack is [15, 2, 8]

Next character is -, stack is [15, 2, 8] Pop 8 Pop 2 Compute 2 - 8 and push result -6

Next character is , stack is [15, -6]

Next character is *, stack is [15, -6] Pop -6 Pop 15 Compute 15 * -6 and push result -90


Stacks: Translate Infix to PostfixTranslation of infix to postfix

If we can translate expression to postfix, then can use EvalPostfix to evaluate

Can use a stack to convert infix to postfixWill require fully parenthesized infix expressions

Fully parenthesized: parentheses for each operatorExample: (1 + (8 x 2))Not fully parenthsized: ((9 + 3 - 2) / 5)Keeps translation algorithm simple


Stacks: Translate Infix to PostfixTranslation of infix to postfix by hand

( 1 + ( 8 x 2 ) )

Move eachoperators to its

right parenthesis

1 8 2 +x

Remove theparentheses


Stacks: Translate Infix to PostfixAlgorithm to translate infix to postfix

For each input character•If character is operand, output character•If character is operator, push character on stack•If character is right parenthesis, pop operator and output operator•If character is left parenthesis, ignore

Resulting output is postfix equivalent of infix expression


Stacks: Translate Infix to PostfixExample: translate (1 + (8 * 2))

InputNextCharacter Action Stack Output

(1 + ((8 * 2)) (start) []1 + ((8 * 2)) ( ignore []+ ((8 * 2)) 1 output [] 1((8 * 2)) + push [+] 1(8 * 2)) ( ignore [+] 18 * 2)) ( ignore [+] 1* 2)) 8 output [+] 1 82)) * push [+, *] 1 8)) 2 output [+, *] 1 8 2) ) pop and output [+] 1 8 2 *

) pop and output [] 1 8 2 * +


Stacks: Activation RecordsComputer uses run-time stack

Each running method has activation record on the stackKeeps track of method calls and returns

Each method’s activation record containsReturn pointLocal variable valuesParameter values

Stack works well here if A calls B, then B must finish before A can resumeLast-in, first-out stack


Stacks: Activation Records (DPL)Example: Simple programming language DPL

No parametersNo variablesNo return valuesBasically just method calls

DPL statementsCOMMENT: ignoredTYPE: display argumentEND: end program (ends automatically if no more

statements)METHOD: Begin method definitionRETURN: Return from methodCALL: Call method


Stacks: Activation Records (DPL)Control starts with first statement (ignores

COMMENT)First statement should be TYPE, END, or CALL

Example DPL programCALL SomeMethodTYPE Finished!END

METHOD SomeMethod TYPE Now in SomeMethodRETURN

OutputNow in SomeMethodFinished!

Next slide shows activation records on run-time stack for this program


return to

Stack

Push returnaddress

CALL SomeMethodTYPE Finished!END






Display

Start method

Stack

Display

In method

Stack

Display

return to

return to

Stack

Pop returnaddress







Now in SomeMethod

Display

Return frommethod

Stack

Now in SomeMethod

Display

Ready to end

Stack

Now in SomeMethodFinished!

Display

return to


Stacks: Activation Records (DPL)COMMENT This is an example of theCOMMENT demonstration programming language DPL.COMMENT It shows how methods work.

COMMENT ---- Main program ---- TYPE >> Starting main program TYPE -- Call FirstMethod from main ... CALL FirstMethod TYPE -- Back in main from FirstMethod TYPE -- Call SecondMethod from main ... CALL SecondMethod TYPE -- Back in main from SecondMethod TYPE << Ending main programEND

METHOD FirstMethod TYPE >> Entering FirstMethod TYPE << Leaving FirstMethodRETURN

METHOD SecondMethod TYPE >> Entering SecondMethod TYPE -- Call FirstMethod from SecondMethod ... CALL FirstMethod TYPE -- Back in SecondMethod from FirstMethod TYPE << Leaving SeconMMdMethodRETURN

>> Starting main program-- Call FirstMethod from main ...>> Entering FirstMethod<< Leaving FirstMethod-- Back in main from FirstMethod-- Call SecondMethod from main ...>> Entering SecondMethod-- Call FirstMethod from SecondMethod ...>> Entering FirstMethod<< Leaving FirstMethod-- Back in SecondMethod from FirstMethod<< Leaving SecondMethod-- Back in main from SecondMethod<< Ending main program


Stacks: Activation Records (DPL)DPL interpreter logic

Read program from file into memorySet program counter to first statementWhile haven't reached END statement or past end

•If TYPE: display the argument•If CALL: push address of CALL statement, set program counter to address of METHOD statement•If RETURN: pop program counter•If COMMENT or blank line: ignore line•If METHOD: error•Increment program counter


Stacks: Activation Records (DPL)Error if control reaches METHOD statement

TYPE The next statement should give a run-time errorMETHOD Wrong TYPE Control shouldn't reach here!RETURN

Output$ java TestDPL test1.dplThe next statement should give a run-time errorError: METHOD without CALL2: METHOD WrongProgram halted


Stacks: Activation Records (DPL)// This program implements an interpreter for a// small demonstration programming language (DPL). Each line // in DPL is a statement. Each statement begins with a keyword // and may be followed by an argument. The statements are:

// COMMENT: Line is ignored by the interpreter.// TYPE: Display the argument (rest of the line) on the// screen.// END: End the program. The program ends automatically// if there are no more statements.// METHOD: Begin a method definition. The name follows.// RETURN: Return from a method. Each method must have// a RETURN statement.// CALL: Call a method by name.

// DPL is case insensitive, and allows blank lines.

import java.io.*;import java.util.Stack;

// ----------------- DPLstatement class ------------------

class DPLstatement{ static final int TYPE_COMMAND = 1; static final int END_COMMAND = 2; static final int METHOD_COMMAND = 3; static final int RETURN_COMMAND = 4; static final int CALL_COMMAND = 5; static final int COMMENT_COMMAND = 6; static final int BLANK_LINE = 7; static final int UNKNOWN_COMMAND = 8;

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) // Constructor: Converts a program line into an internal form public DPLstatement(String line) { String commandString; // Remove blanks on both ends of line line = line.trim();

// Look for first blank (separates command from argument) int blankLoc = line.indexOf(" ");

// Separate command from argument if (blankLoc == -1) { commandString = line.toUpperCase(); } else { commandString = line.substring(0, blankLoc).toUpperCase(); argument = line.substring(blankLoc + 1).trim(); }

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) // Convert command to internal form if (commandString.equals("TYPE")) { command = TYPE_COMMAND; } else if (commandString.equals("END")) { command = END_COMMAND; } else if (commandString.equals("METHOD")) { command = METHOD_COMMAND; } else if (commandString.equals("RETURN")) { command = RETURN_COMMAND; } else if (commandString.equals("CALL")) { command = CALL_COMMAND; } else if (commandString.equals("COMMENT")) { command = COMMENT_COMMAND; } else if (commandString.trim().equals("")) { command = BLANK_LINE; } else { command = UNKNOWN_COMMAND; argument = line; } } DPL In

terpret

er

(TestD

PL.java

)


Stacks: Activation Records (DPL) // getCommand: Returns the command as an integer public int getCommand() { return command; }

// getArgument: Returns the argument as a string (null if no // argument) public String getArgument() { return argument; }

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) // toString: Returns the statement as a string (for error // messages) public String toString() { String result = ""; switch (command) { case TYPE_COMMAND: result = "TYPE "; break; case END_COMMAND: result = "END"; break; case METHOD_COMMAND: result = "METHOD "; break; case RETURN_COMMAND: result = "RETURN"; break; case CALL_COMMAND: result = "CALL "; break; case COMMENT_COMMAND: result = "COMMENT "; break; case BLANK_LINE: result = ""; break; case UNKNOWN_COMMAND: result = ""; break; }

if (argument != null) { result = result + argument; }

return result; } private int command; private String argument;}

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL)// ----------------- DPL class ------------------

class DPL{ static final int MAX_STATEMENTS = 100; // Maximum number of // statements in // a program

// Constructor: Reads the program from the given file, returns // true if successful public DPL(String fileName) throws java.io.IOException { String line; // Initialize the input file variable File inFile = new File(fileName); if (inFile.exists() && inFile.canRead()) { // Create an input stream and attach it to the file BufferedReader fileInStream = new BufferedReader(new FileReader(inFile));

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) // Read lines from the file into the array line = fileInStream.readLine(); while (numStatements < statement.length && line != null) { statement[numStatements] = new DPLstatement(line); numStatements++; line = fileInStream.readLine(); }

// Make sure all lines were read if (line != null) { error("Too many statements"); }

// Close the stream fileInStream.close(); } else { // Can't open input file error("Can't open input file " + fileName); } }

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) // interpretProgram: Interprets the statements of the program public void interpretProgram() { Stack runTimeStack = new Stack(); boolean stop = false; String argument;

// Step through the program, executing statements while (programCounter < numStatements && !stop) { switch (statement[programCounter].getCommand()) { case DPLstatement.TYPE_COMMAND: argument = statement[programCounter].getArgument(); if (argument == null) { argument = ""; } System.out.println(argument); break; case DPLstatement.END_COMMAND: stop = true; break; case DPLstatement.METHOD_COMMAND: error("METHOD without CALL"); break;

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) case DPLstatement.RETURN_COMMAND: if (runTimeStack.empty()) { error("RETURN command without CALL"); } else { programCounter = ((Integer) runTimeStack.pop()).intValue(); } break; case DPLstatement.CALL_COMMAND: runTimeStack.push(new Integer(programCounter)); programCounter = findMethod(statement [programCounter].getArgument()); break; case DPLstatement.COMMENT_COMMAND: case DPLstatement.BLANK_LINE: // Do nothing break; case DPLstatement.UNKNOWN_COMMAND: error("Unknown command"); break; }

programCounter++; } }

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) // findMethod: Returns the location of the METHOD command // with the given name private int findMethod(String methodName) { methodName.toUpperCase();

for (int position = 0; position < numStatements; position++) { if (statement[position].getCommand() == DPLstatement.METHOD_COMMAND && statement[position].getArgument(). equals(methodName)) { return position; } }

error("Undefined METHOD " + methodName); return 0; }

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL) // error: Displays the error message and halts the program private void error(String message) { System.out.println("Error: " + message); if (statement[programCounter] != null) { System.out.println((programCounter + 1) + ": " + statement[programCounter]); } System.out.println("Program halted"); System.exit(2); }

// Instance variables DPLstatement[] statement = new DPLstatement[MAX_STATEMENTS]; int programCounter = 0, numStatements = 0;}

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL)// ----------------- TestDPL class ------------------

public class TestDPL{ public static void main(String[] args) throws java.io.IOException { DPL program = new DPL(args[0]); program.interpretProgram(); }}

DPL Inter

preter

(TestD

PL.java

)


Stacks: Activation Records (DPL2)DPL2: Add a LOOP statement to DPL

SyntaxLOOP ... ASK x ...AGAIN

LOOP -- marks the top of the loopASK x -- user enters character, if it matches x, control

goes to statement after AGAIN, otherwise statement after ASK

AGAIN -- jump to LOOP


Stacks: Activation Records (DPL2)Loop statement example

LOOP TYPE What's 4 + 5? ASK 9 TYPE No, try again.AGAINTYPE That's right!

OutputWhat's 4 + 5?8No, try again.What's 4 + 5?9That's right!

Nested loop exampleLOOP TYPE Enter the number 1 ASK 1 LOOP TYPE Do you know your numbers? (y/n) ASK y TYPE A number is between 0 and 9 AGAINAGAINTYPE Correct!

OutputEnter the number 1XDo you know your numbers? (y/n)nA number is between 0 and 9Do you know your numbers? (y/n)yEnter the number 11Correct!


Stacks: Activation Records (DPL2)More realistic example of DPL2 (capitals.dpl)

COMMENT This is an example of the second versionCOMMENT of the demonstration programming language. ThisCOMMENT version has loops of the form LOOP ... ASK ... AGAIN.

CALL IntroductionLOOP CALL USAcapital CALL NewZealandCapital CALL GreatBritainCapital CALL AustraliaCapital TYPE Do you want to take this quiz again (y/n)? ASK nAGAINTYPE Bye!END

METHOD Introduction TYPE This is a quiz that tests your knowledge of country TYPE capitals. TYPE Here is the first question ... TYPERETURN


Stacks: Activation Records (DPL2)METHOD AustraliaCapital LOOP TYPE What is the capital city of Australia? TYPE 1. Canberra TYPE 2. London TYPE 3. Washington, DC TYPE 4. Wellington ASK 1 TYPE Hint: The design of the capital of Australia won an TYPE international competition in 1911. AGAINRETURN

METHOD GreatBritainCapital LOOP TYPE What is the capital city of Great Britain? TYPE 1. Canberra TYPE 2. London TYPE 3. Washington, DC TYPE 4. Wellington ASK 2 TYPE Hint: The capital of Great Britain is on both sides TYPE of the Thames River. AGAINRETURN


Stacks: Activation Records (DPL2)METHOD NewZealandCapital LOOP TYPE What is the capital city of New Zealand? TYPE 1. Canberra TYPE 2. London TYPE 3. Washington, DC TYPE 4. Wellington ASK 4 TYPE Hint: The capital of New Zealand is at the southern tip of TYPE Cook Strait. AGAINRETURN

METHOD USAcapital LOOP TYPE What is the capital city of the United States of America? TYPE 1. Canberra TYPE 2. London TYPE 3. Washington, DC TYPE 4. Wellington ASK 3 TYPE Hint: The capital of the United States of America was named TYPE after it's first president. AGAINRETURN


Stacks: Activation Records (DPL2)Sample run of capitals.dpl

This is a quiz that tests your knowledge of countrycapitals.Here is the first question ...

What is the capital city of the United States of America?1. Canberra2. London3. Washington, DC4. Wellington2Hint: The capital of the United States of America was namedafter it's first president.What is the capital city of the United States of America?1. Canberra2. London3. Washington, DC4. Wellington3


Stacks: Activation Records (DPL2)Sample run of capitals.dpl (continued)

What is the capital city of New Zealand?1. Canberra2. London3. Washington, DC4. Wellington4What is the capital city of Great Britain?1. Canberra2. London3. Washington, DC4. Wellington2What is the capital city of Australia?1. Canberra2. London3. Washington, DC4. Wellington1Do you want to take this quiz again (y/n)?nBye!


Stacks: Activation Records (DPL2)// This program implements DPL2. It extends the DPL

// small demonstration programming language (DPL). Each line // in DPL is a statement. Each statement begins with a keyword // and may be followed by an argument. The statements are:

// COMMENT: Line is ignored by the interpreter.// TYPE: Display the argument (rest of the line) on the// screen.// END: End the program. The program ends automatically// if there are no more statements.// METHOD: Begin a method definition. The name follows.// RETURN: Return from a method. Each method must have// a RETURN statement.// CALL: Call a method by name.

// LOOP ... ASK ... AGAIN:// The LOOP command begins a loop. The ASK command// asks the user for a response, and compares it to // the single character argument. If equal, control// continues with the statement following AGAIN. If// not equal, control continues with the statement// following ASK. When control reaches the AGAIN// command, it continues with the statement following// the associated LOOP command.

// DPL2 is case insensitive, and allows blank lines.

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2)import Keyboard;

import java.io.*;import java.util.Stack;

// ----------------- DPLstatement class ------------------

class DPLstatement{ static final int TYPE_COMMAND = 1; static final int END_COMMAND = 2; static final int METHOD_COMMAND = 3; static final int RETURN_COMMAND = 4; static final int CALL_COMMAND = 5; static final int COMMENT_COMMAND = 6; static final int BLANK_LINE = 7; static final int UNKNOWN_COMMAND = 8; static final int LOOP_COMMAND = 9;

static final int ASK_COMMAND = 10; static final int AGAIN_COMMAND = 11;

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // Constructor: Converts a program line into an internal form public DPLstatement(String line) { String commandString; // Remove blanks on both ends of line line = line.trim();

// Look for first blank (separates command from argument) int blankLoc = line.indexOf(" ");

// Separate command from argument if (blankLoc == -1) { commandString = line.toUpperCase(); } else { commandString = line.substring(0, blankLoc).toUpperCase(); argument = line.substring(blankLoc + 1).trim(); }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // Convert command to internal form if (commandString.equals("TYPE")) { command = TYPE_COMMAND; } else if (commandString.equals("END")) { command = END_COMMAND; } else if (commandString.equals("METHOD")) { command = METHOD_COMMAND; } else if (commandString.equals("RETURN")) { command = RETURN_COMMAND; } else if (commandString.equals("CALL")) { command = CALL_COMMAND; }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) else if (commandString.equals("LOOP"))

{ command = LOOP_COMMAND; } else if (commandString.equals("ASK")) { command = ASK_COMMAND; } else if (commandString.equals("AGAIN")) { command = AGAIN_COMMAND;

} else if (commandString.equals("COMMENT")) { command = COMMENT_COMMAND; } else if (commandString.trim().equals("")) { command = BLANK_LINE; } else { command = UNKNOWN_COMMAND; argument = line; } }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // getCommand: Returns the command as an integer public int getCommand() { return command; }

// getArgument: Returns the argument as a string (null if no // argument) public String getArgument() { return argument; }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // toString: Returns the statement as a string (for error // messages) public String toString() { String result = ""; switch (command) { case TYPE_COMMAND: result = "TYPE "; break; case END_COMMAND: result = "END"; break; case METHOD_COMMAND: result = "METHOD "; break; case RETURN_COMMAND: result = "RETURN"; break; case CALL_COMMAND: result = "CALL "; break; case COMMENT_COMMAND: result = "COMMENT "; break; case BLANK_LINE: result = ""; break; case UNKNOWN_COMMAND: result = ""; break; case LOOP_COMMAND: result = "LOOP"; break;

case ASK_COMMAND: result = "ASK "; break; case AGAIN_COMMAND: result = "AGAIN"; break;

}

if (argument != null) { result = result + argument; }

return result; } private int command; private String argument;}

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2)// ----------------- DPL2 class ------------------

class DPL2{ static final int MAX_STATEMENTS = 100; // Maximum number of // statements in // a program

// Constructor: Reads the program from the given file, returns // true if successful public DPL2(String fileName) throws java.io.IOException { String line; // Initialize the input file variable File inFile = new File(fileName); if (inFile.exists() && inFile.canRead()) { // Create an input stream and attach it to the file BufferedReader fileInStream = new BufferedReader(new FileReader(inFile));

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // Read lines from the file into the array line = fileInStream.readLine(); while (numStatements < statement.length && line != null) { statement[numStatements] = new DPLstatement(line); numStatements++; line = fileInStream.readLine(); }

// Make sure all lines were read if (line != null) { error("Too many statements"); }

// Close the stream fileInStream.close(); } else { // Can't open input file error("Can't open input file " + fileName); } }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // interpretProgram: Interprets the statements of the program public void interpretProgram() throws java.io.IOException { Stack runTimeStack = new Stack(); boolean stop = false; char inputChar, correctResponse; String argument;

// Step through the program, executing statements while (programCounter < numStatements && !stop) { switch (statement[programCounter].getCommand()) { case DPLstatement.TYPE_COMMAND: argument = statement[programCounter].getArgument(); if (argument == null) { argument = ""; } System.out.println(argument); break; case DPLstatement.END_COMMAND: stop = true; break;

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) case DPLstatement.METHOD_COMMAND: error("METHOD without CALL"); break; case DPLstatement.RETURN_COMMAND: if (runTimeStack.empty()) { error("RETURN command without CALL"); } else { programCounter = ((Integer) runTimeStack.pop()).intValue(); } break; case DPLstatement.CALL_COMMAND: runTimeStack.push(new Integer(programCounter)); programCounter = findMethod(statement [programCounter].getArgument()); break; case DPLstatement.COMMENT_COMMAND: case DPLstatement.BLANK_LINE: // Do nothing break;

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) case DPLstatement.UNKNOWN_COMMAND: error("Unknown command"); break;

case DPLstatement.LOOP_COMMAND: runTimeStack.push(new Integer(programCounter)); break;

case DPLstatement.ASK_COMMAND: argument = statement[programCounter].getArgument(); if (argument.length() != 1) { error("ASK argument not a single character"); } correctResponse = argument.charAt(0); inputChar = Keyboard.readChar(); if (Character.toUpperCase(inputChar) == Character.toUpperCase(correctResponse)) { if (runTimeStack.empty()) { error("ASK command not in LOOP"); } else { // Pop the location of the LOOP and toss it runTimeStack.pop(); } programCounter = findAgainCommand(); } break;

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) case DPLstatement.AGAIN_COMMAND:

// Note: this is a crude check - see exercises if (runTimeStack.empty()) { error("AGAIN command has no LOOP"); } else { // Go back to the top of the loop (leave the LOOP // command location on the stack) programCounter = ((Integer) runTimeStack.peek()).intValue(); }

}

programCounter++; } }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // findMethod: Returns the location of the METHOD command // with the given name private int findMethod(String methodName) { methodName.toUpperCase();

for (int position = 0; position < numStatements; position++) { if (statement[position].getCommand() == DPLstatement.METHOD_COMMAND && statement[position].getArgument(). equals(methodName)) { return position; } }

error("Undefined METHOD " + methodName); return 0; }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // findAgainCommand: Returns the location of the AGAIN

// command at the same level as when // the method started private int findAgainCommand() { int loopCount = 1, position = programCounter;

while (position < numStatements - 1 && loopCount != 0) { position++; switch (statement[position].getCommand()) { case DPLstatement.LOOP_COMMAND: loopCount++; break;

case DPLstatement.AGAIN_COMMAND: loopCount--; break; case DPLstatement.METHOD_COMMAND: case DPLstatement.RETURN_COMMAND: error("LOOP/AGAIN cannot cross method boundaries"); break; } }

if (loopCount != 0) { error("Missing AGAIN command"); }

return position; }

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: Activation Records (DPL2) // error: Displays the error message and halts the program private void error(String message) { System.out.println("Error: " + message); if (statement[programCounter] != null) { System.out.println((programCounter + 1) + ": " + statement[programCounter]); } System.out.println("Program halted"); System.exit(2); }

// Instance variables DPLstatement[] statement = new DPLstatement[MAX_STATEMENTS]; int programCounter = 0, numStatements = 0;}

// ----------------- TestDPL2 class ------------------

public class TestDPL2{ public static void main(String[] args) throws java.io.IOException { DPL2 program = new DPL2(args[0]); program.interpretProgram(); }}

DPL2 Inter

preter

(TestD

PL2.jav

a)


Stacks: ImplementationSimple data structureCommon implementations

Array-based (java.util.Stack uses this approach)Link-based

We’ll examine the linked-based approachOptions

Write from scratchUse List class (from previous chapter)


Stacks: Implementing from ScratchLet’s write from scratch

Stack is a list of nodes (almost like List)Can use ListNode to store nodes

One instance variable// Instance variablesprivate ListNode first;

Constructor// Constructorpublic Stack(){ first = null;}


Stacks: Implementing from ScratchSteps for push()

Allocate new ListNodeCopy value into nodeLink new node to beginning of lisMake new node first

Similar to List.insertFirst()Code

// push: Pushes the item onto the stack.public void push(Object item){ ListNode newNode = new ListNode(item, first); first = newNode;}


Stacks: Implementing from ScratchSteps for pop()

Get value out of first nodeDelete first nodeReturn value

Same as List.removeFirst()Code

// pop: Returns the last item pushed onto the stack, and// removes it from the stack.// Note: Stack must not be emptypublic Object pop(){ Object item;

Debug.assert(!empty(), "Stack.pop(): stack is empty"); item = first.getItem(); first = first.getNext(); return item;}


Stacks: Implementing from ScratchSteps for peek()

Return value of first nodeCode

// peek: Returns the last item pushed onto the stack, but// doesn't remove it from the stack.// Note: Stack is not emptypublic Object peek(){ Debug.assert(!empty(), "Stack.peek(): stack is empty"); return first.getItem();}

What about this version??// peek: Returns the last item pushed onto the stack, but// doesn't remove it from the stack.// Note: Stack is not emptypublic Object peek(){ Object element = pop(); push(element); return element;}


Stacks: Implementing from ScratchSteps for empty()

Return true if there’s at least one element on the stackReturn false if no elements

Code// empty: Returns true if the stack is empty, false// otherwisepublic boolean empty(){ return first == null;}


Stacks: Implementing with ListSimpler approach

Use List class to implement StackOptions

InheritanceAggregation


Stacks: Implementing with ListInheritance approach

class InheritStack extends List{ // push: Pushes the item onto the stack. public void push(Object element) { insertFirst(element); }

// pop: Returns the last item pushed onto the stack, and // removes it from the stack. Stack can’t be empty public Object pop() { return removeFirst(); }

// peek: Returns the last item pushed onto the stack, but // doesn't remove it from the stack. Stack can’t be empty public Object peek() { goFirst(); return get(); }

// empty: Returns true if the stack is empty, false otherwise public boolean empty() { return super.empty(); }}


Stacks: Implementing with ListProblems with inheritance approach

InheritStack has lots of unnecessary methods (from List)public void insertFirst(Object item)public void insertFirst(int item)public void insertFirst(long item)public void insertLast(Object item)public void insert(Object item)public void put(Object item)public Object get()public Object removeFirst()public Object removeLast()public Object remove()public void append(List source)public boolean find(Object data)public void goFirst()public void goLast()public void goNext()public void goPrevious()public String toString()public boolean isDefined()public int count()

A stack is not a list! (Inheritance is inappropriate)


Stacks: Implementing with ListAggregation approach (skeleton)

import List;

public class Stack{ // push: Pushes the item onto the stack. public void push(Object item) { }

// pop: Returns the last item pushed onto the stack, and // removes it from the stack. Stack can’t be empty public Object pop() { }

// peek: Returns the last item pushed onto the stack, but // doesn't remove it from the stack. Stack can’t be empty public Object peek() { }

// empty: Returns true if the stack is empty, false // otherwise public boolean empty() { }

// Instance variables private List data = new List();}


Stacks: Implementing with ListProblems with the aggregation approach

More executable code than necessary•import statement drags in all List methods•Most of List methods don't apply to stacks•Executable code size especially important for applets

Operations are slower •Overhead of additional method calls•List routines are more general than we need

SummaryVersion Executable code size Programmer effortFrom scratch Small Takes more timeInheritance WRONG WRONGAggregation Large Easy


QueuesQueue is a waiting lineCommon in real life

First person in line isfirst person served

Queue is FIFO structureFirst-in, first-out

Operationsenqueue -- put element indequeue -- take element out


Queues: UsesCommunication line

Between fast CPU and slow peripheralExample: print spooler

Example: Input buffer

PrinterComputer Spooler

InputBuffer


Queues: UsesCan use whenever two systems communicate

Especially when they run at different speeds


Queues: PalindromesPalindrome: spelled the same way forward or

backward A dog, a plan, a canal: pagoda. A Toyota. Race fast, safe car. A Toyota Did I draw Della too tall, Edward? I did? Drab as a fool, aloof as a bard. Egad, a base tone denotes a bad age. Go hang a salami, doc. Note: I dissent, a fast never

prevents a fatness. I diet on cod, I'm a lasagna hog. No, it can, as it is, it is a war. Raw as it is, it is an action. Cigar? Toss it in a can. It is so tragic.

See http://www.jps.net/msyu/palindromes/ for more


Queues: PalindromesUse a stack and queue to test for palindrome

Read input character by character•If character is alphabetic, push and enqueue

After reading•Compare output from stack and queue•If the same, then we have palindrome


Queues: PalindromesProgram to test palindromes

Setup// This program uses a stack and a queue to test// whether the user's input is a palindrome. The user's input// ends at the end of the line.

import java.io.*;import java.util.Stack;import Queue; // Our queue class

public class TestPalindrome{ public static void main(String[] args) throws java.io.IOException { Stack stack = new Stack(); Queue queue = new Queue(); BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

char nextChar;

System.out.println("--- Palindrome Tester ---");


Queues: PalindromesRead input, test for palindrome

// Read input from user, put each character into both the // stack and the queue System.out.print("Input: "); nextChar = Character.toLowerCase((char) in.read()); while (nextChar != '\n') { if (Character.isLetter(nextChar)) { stack.push(new Character(nextChar)); queue.enqueue(new Character(nextChar)); } nextChar = Character.toLowerCase((char) in.read()); }

// Compare output of the stack and queue, stop at first // difference while (!stack.empty() && !queue.empty() && stack.pop().equals(queue.dequeue())) ;


Queues: PalindromesDisplay output

// Display output if (!stack.empty() && !queue.empty()) { System.out.println("Not a palindrome"); } else if (stack.empty() && queue.empty()) { System.out.println("Is a palindrome"); } else { System.out.println("Error in program"); } }}

--- Palindrome Tester ---Input: Able was I ere I saw Elba.Is a palindrome

--- Palindrome Tester ---Input: The quick brown fox.Not a palindrome


Queues: Radix SortRadix sort: algorithm used to sort punch cards

Punch cards used by businesses from 1890 to 1970’sEach card stores 1 line of up to 80 charactersCharacters encoded by punches in columns

01

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8

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0

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12345


Queues: Radix SortTabulating machines could copy, print, and sort

punch cardsSorting machine sorted cards one column at a time

To sort on more than one character, sort on least significant column first

Then sort on next-least significant column, etc.

Input bin

Output bins


Queues: Radix SortUse queues

to simulatebins insortingmachine

Example:sort 3-digitnumbersFirst sort on

1’s placecolumn

392 485 502 181 452 985 948 385 291

0 1 2 3 4 5 6 7 8

181 291

392 502 452

485 985 385

948

queue[0]

queue[1]

queue[2]

queue[3]

queue[4]

queue[5]

queue[6]

queue[7]

queue[8]

queue[9]

Enqueue accordingto 1's place digit

181 291 392 502 452 485 985 385 948

0 1 2 3 4 5 6 7 8

Dequeue,copy back

to array

1's Place Pass


502

948

452

181 485 985 385

queue[0]

queue[1]

queue[2]

queue[3]

queue[4]

queue[5]

queue[6]

queue[7]

queue[8]

291 392queue[9]


502 948 452 181 485 985 385 291 392

0 1 2 3 4 5 6 7 8

Dequeue,copy back

to array

181 291 392 502 452 485 985 385 948

0 1 2 3 4 5 6 7 8

10's Place Pass

Queues: Radix SortExample:

sort 3-digitnumbersNext sort result

of 1’s place on10’s placecolumn


181

291

385 392

452 485

502

queue[0]

queue[1]

queue[2]

queue[3]

queue[4]

queue[5]

queue[6]

queue[7]

queue[8]

948 985queue[9]


181 291 385 392 452 485 502 948 985

0 1 2 3 4 5 6 7 8

Dequeue,copy back

to array

502 948 452 181 485 985 385 291 392

0 1 2 3 4 5 6 7 8

100's Place Pass

Queues: Radix SortExample:

sort 3-digitnumbersFinally, sort

result of 10’s place on100’s placecolumn


Queues: Radix Sort// radixSort: The items in array are arranged in ascending order// Note: maxPowerOf10 should give the largest power of 10 used by a value in the// array. For example, if the largest value in the array is 456, then// maxPowerOf10 is 100. Doesn't work with negative numbers.static void radixSort(int[] array, int maxPowerOf10){ Queue[] queue = new Queue[10]; // One queue for each digit 0 - 9 // Create each of the 10 queues for (int queueNum = 0; queueNum < 10; queueNum++) { queue[queueNum] = new Queue(); } for (int powerOf10 = 1;powerOf10 <= maxPowerOf10; powerOf10 = powerOf10 * 10) { // Put each item into the queue corresponding with the // digit in the given powerOf10 position for (int item = 0; item < array.length; item++) { int digit = getDigit(array[item], powerOf10); queue[digit].enqueue(new Integer(array[item])); } // Copy items from queues back to array int item = 0; for (int queueNum = 0; queueNum < 10; queueNum++) { while (!queue[queueNum].empty()) { array[item] = ((Integer) queue[queueNum].dequeue()).intValue(); item++; } } }}


Queues: Radix SortgetDigit() method

// getDigit: Returns the digit in the given power of 10// position of the numberstatic int getDigit(int number, int powerOf10){ return number % (powerOf10 * 10) / powerOf10;}

Running time of radixSort() is O(sn), where s is number of character per valuen is number of values

Very fast for small keys (s is small)To work for letters, need queue for each letter

Could be improvedUse two sets of queues instead of copying back to array

on each pass


Queues: ImplementationHow to write Queue class?

From scratch, using a linked list to store dataFrom scratch, using an array to store dataExtend the List class (No! A queue is not a list!)Use List object inside Queue class (aggregation)

Aggregation approach: should weUse insertFirst() for enqueueing items, and removeLast()

for dequeueing?Use insertLast() for enqueueing items, and removeFirst()

for dequeueing?Which is best?


Queues: Implementation// Queue class

import List;

public class Queue{ // enqueue: Puts a new item onto the queue public void enqueue(Object item) { data.insertLast(item); }

// dequeue: Returns the item that is on the queue longest, and removes it // Note: Queue must not be empty public Object dequeue() { return data.removeFirst(); }

// empty: Returns true if the queue is empty, false otherwise public boolean empty() { return data.empty(); } // count: Returns the number of elements in the queue public int count() { return data.count(); }

// Instance variables private List data = new List();}


Queues: ImplementationAdvantages of aggregation approach

SimpleShort

DisadvantagesDrags in the whole List class (larger executable program)May be slower, because of the overhead of List methodsMay take more storage (needs room for List references)

If Queue used a lot, may pay to write from scratch


Queues: ImplementationExample of how to use the Queue class

// Example use of the Queue class

import Queue;

public class DemonstrateQueue{ public static void main(String[] args) { Queue stringQueue = new Queue();

// Put elements into the queue stringQueue.enqueue("First"); stringQueue.enqueue("Second"); stringQueue.enqueue("Third");

// Get elements out of the queue System.out.println(stringQueue.dequeue()); System.out.println(stringQueue.dequeue()); System.out.println(stringQueue.dequeue()); }}


Computer SimulationSimulation: imitate something that exists in the real

worldGoal of simulation

Summarize performance of a systemPredict performance of a design

To simulate, build modelConcentrate on essential features

Abstract modelMathematical equations or computer program


Simulation: AdvantagesCan test many designs before building physical

prototypeWright brothers tested about 200 wing designs in a small

wind tunnelUsually safer

Radar operators, airplane pilots often learn on simulatorsOften cheaper

Fighter jet simulators are much cheaper than real jets ($65 million or more for some...)


SimulationMany simulations are similar to computer gamesFlight simulators are more realistic

Real instrumentsMuch larger view (several screens)Hydraulic systems rotate and pitch the simulatorMetal plates push on pilot’s back to simulate acceleration

Virtual reality (VR)Attempt to put user in new environmentStill expensive for individuals


Simulation: UsesEconomics

Model economy of nation, regionBusiness

Model inventories, new management strategiesScience

Visualization of data


Simulation: ApproachesTwo major approaches in simulation

AnalyticNumeric

Analytic approach In the form of mathematical equationsSolve equations to get exact answerUse algebra and calculusAdvantage: insight and mathematical relationshipDisadvantage: requires advanced math, may not be

feasible for some models


Simulation: ApproachesSecond approach: numeric

Build model as computer programPut input in, watch outputs

Deterministic modelDoesn’t depend on random eventsCan try all input values (if not too many), giving complete

set of outputsUsually too many input values for this

Random modelDepends on random events (customer arrivals)


Simulation: ApproachesAdvantage of numeric approach

Works in more cases than analyticDisadvantages

Can have noise (unlikely outputs) in resultsMust do many simulations to smooth over noiseMust vary inputs to see how small changes affect outputs

(sensitivity analysis)


Simulation: Random NumbersUse random number generator in random

simulation Java’s java.util.Random is a class for random number

generationRandom.nextInt() method produces integers between

-2,147,483,648 and 2,147,483,647Pseudorandom: uses algorithm to produce numbers, not

truly randomSequence of pseudorandom numbers eventually repeats

(but sequence is long enough to appear random for most purposes)


Simulation: Random NumbersTo get a random integer between 3 and 9 (say):

Get a random integer with Random.nextInt()Make sure the number is positive with Math.abs()Adjust the number to between 0 and 6 with n % 7Add 3 to the result to get a number between 3 and 9

To make it easier, let’s write a new class// An extension of the Random class (first version)

import java.util.Random;

public class ExtendedRandom extends Random{ // nextIntUniform: Returns an int random value between // lowValue and highValue, inclusive public int nextIntUniform(int lowValue, int highValue) { return Math.abs(nextInt()) % (highValue - lowValue + 1) + lowValue; }}


Simulation: Random NumbersUniform distribution

Each number is equally likely to appear nextAppropriate for simulating the same behavior in the real

worldExample: roll of a six-sided die

// Simulate rolling a six-sided die

import ExtendedRandom; // Get our extended random class

public class SimulateADie{ public static void main(String[] args) { ExtendedRandom gen = new ExtendedRandom(); System.out.println("The number is " + gen.nextIntUniform(1, 6)); }}


Simulation: Random NumbersUniform distribution

Plot of 50,000 calls to ExtendedRandom.nextIntUniform()

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Simulation: Random Numbers// Test the random number generator by // counting the number of times each value is generated.


class TestRandomUniform{ static final int LOW_VALUE = 0; static final int HIGH_VALUE = 100; static final int NUM_TESTS = 50000; public static void main(String[] args) { ExtendedRandom generator = new ExtendedRandom();

int[] count = new int[HIGH_VALUE - LOW_VALUE + 1];

// Use random number generator, count results for (int i = 0; i < NUM_TESTS; i++) { int uniformValue = generator.nextIntUniform(LOW_VALUE, HIGH_VALUE); count[uniformValue]++; }

// Display counts for (int i = 0; i < count.length; i++) { System.out.println(i + "\t" + count[i]); } }}


Simulation: Random NumbersMost naturally-occurring events don’t follow uniform

distributionTendency to

cluster around a central value

Normaldistributionfollows thispattern

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-4 -3 -2 -1 0 1 2 3 4


Simulation: Random NumbersNormal distribution described by

AverageStandard deviation from the average

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35 45 55 65 75 85 95 105 115

Average of 75Standard deviation of 10


Simulation: Random NumbersNormal distribution

Area under curve one standard deviation from average is about 68% of all cases

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35 45 55 65 75 85 95 105 115




Area under curve two standard deviations from average is about 95% of all cases

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Simulation: Random NumbersRandom.nextGaussian() simulates normal

distributionReturns double with average 0.0, standard deviation 1.0

To simulate other normal distributionsMultiply result by desired standard deviationAdd desired average

Example: want average 75, standard deviation 10Suppose Random.nextGaussian() returns 0.65Multipy by 10 65.0Add 75 140.0


Simulation: Random NumbersTo make generating other normal distributions easier,

let’s add to the ExtendedRandom class// An extension of the Random class (second version)

import java.util.Random;

public class ExtendedRandom extends Random{ // nextIntUniform: Returns an int random value between // lowValue and highValue, inclusive public int nextIntUniform(int lowValue, int highValue) { return Math.abs(nextInt()) % (highValue - lowValue + 1) + lowValue; }

// nextGaussian: Returns a double random value from the // the normal distribution with the given average // and standard deviation public double nextGaussian(double average, double standardDeviation) { return super.nextGaussian() * standardDeviation + average; }

}


Simulation: Random NumbersProgram example: normal distribution

// This program shows how to use the nextGaussian()// method to simulate a normal distribution.

import ExtendedRandom; // Get our extended random classimport Keyboard;

public class DemonstrateNormalDistribution{ public static void main(String[] args) throws java.io.IOException { ExtendedRandom gen = new ExtendedRandom();

System.out.println("--- Generate normally distributed " + "random numbers ---"); double average = Keyboard.readDouble("Average: "); double stDev = Keyboard.readDouble("Standard deviation: "); int numValues = Keyboard.readInt("Number of values: "); System.out.println();

for (int i = 0; i < numValues; i++) { System.out.println(gen.nextGaussian(average, stDev)); } }}


Simulation: Random NumbersProgram output

--- Generate normally distributed random numbers ---Average: 50Standard deviation: 20Number of values: 10

25.95024016433164244.1282531841908829.1833154021459934.6738296877713955.86103814039131557.5061602444274628.7912243009566263.64242510850094463.0163656658744358.50500464319739



Plot of 50,000 calls to ExtendedRandom.nextGaussian()

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Simulation: Random Numbers// Test the random number generator by counting // the number of times each (integer) value is generated.


class TestRandomNormal{ static final int AVERAGE = 75; // Must be positive and // at least 3 * STD_DEV static final int STD_DEV = 10; // Must be positive static final int NUM_TESTS = 50000; public static void main(String[] args) { ExtendedRandom generator = new ExtendedRandom();

int[] count = new int[AVERAGE * 2];

// Use random number generator, count results for (int i = 0; i < NUM_TESTS; i++) { double normalValue = generator.nextGaussian(AVERAGE, STD_DEV); int arrayLocation = (int) Math.round(normalValue); count[arrayLocation]++; }

// Display counts for (int i = 0; i < count.length; i++) { System.out.println(i + "\t" + count[i]); } }}


Simulation: Waiting LinesQueueing model

Customers: wait in line for serviceServers: provide service to customers

SimulateWaiting lines in storesStreet intersectionsLogistic problems in factoriesComputer job processing


Simulation: Waiting Lines

That’s a lot of vowels in a row!

(The most of any word in English)

By the way...


Simulation: Waiting LinesSimplest waiting line simulation

One waiting lineOne server

CustomersServer


Simulation: Waiting LinesAnother common type of waiting line

Customers

Servers


Simulation: Waiting LinesYet another...

CustomersServers


Simulation: Waiting LinesWays to service the lines

FIFO: First in first out (most common)LIFO: Last in first out (sometimes used in inventory

accounting)Priority first: Customer with highest priority served first

(print queue -- shortest printout printed first)Circular: The customers arranged in a circle; each

customer gets a little service, then the server moves on. (CPU allocation)

Random: A random customer served first


Simulation: Waiting LinesWe’ll write a program that simulates waiting lines

Single waiting lineSeveral serversUse FIFO for serving each line

Simplifying assumptionsArrival rate of customers uniformly distributedService time is normally distributedServers are equally efficientOne customer arrives during each time unitSeveral servers can start serving customers during each

time unitCustomers don’t leave the line


Simulation: Waiting LinesGeneral approach

Get user input (number of servers, average service time, time to simulate, etc.)

For each time from 0 to time to simulate,•If new customer arrives, put at end of line•While there's someone in line and a server available,

–Have an available server serve customer from front of line–Accumulate statistics on this customer

Display the statistics


Simulation: Waiting LinesIn simulation, time is an integer counter

Don’t have to make the program run in real timeLet it run as fast as computer can run it

Arrival probabilityUser enters number between 0 and 100This is probability that customer will arrive during any

time unitWill use Random.nextInt() to generate a number between

0 and 100 If the random number < arrival probability, then will

simulate customer arrival


Simulation: Waiting LinesKeep track of customer by arrival time

Store customers in queue: just store arrival time for eachWhen customer ready to be served

Server will choose random service time from normal distribution

Departure time = arrival time + service timeServer will store customer’s departure time

Use list to store servers


Simulation: Waiting LinesServers class: stores all servers

Instance variables// Instance variablesList serverList = new List();double average, standardDeviation;Random randGen = new Random();

ConstructorPuts -1 in each server’s departure time, so its departure

time < current time (means ready)// Constructorpublic Servers(int numServers, double average, double standardDeviation){ this.average = average; this.standardDeviation = standardDeviation; // Initialize servers for (int i = 0; i < numServers; i++) { serverList.insertFirst(-1); }}


Simulation: Waiting LinesServers.findAvailable()

Server is available if departure time < current time// findAvailable: Returns true if at least one server is// available, and if so, sets the current// server to an available onepublic boolean findAvailable(int currentTime){ for (serverList.goFirst(); serverList.isDefined(); serverList.goNext()) { int serverTimeUp = ((Integer) serverList.get()).intValue(); if (serverTimeUp < currentTime) { return true; } } return false;}


Simulation: Waiting LinesServer.serveCustomer()

Requires a server to be available first// serveCustomer: Adds a customer to an available server, sets the// departure time for the customer in the server// Note: A server must be available and that server is the current// serverpublic void serveCustomer(int currentTime){ // Check precondition int serverTimeUp = ((Integer) serverList.get()).intValue(); Debug.assert(serverTimeUp < currentTime, "Server.serveCustomer(): No server available");

// Record the departure time for this customer in the server int departureTime = currentTime + (int) (Math.round(randGen.nextGaussian()) * standardDeviation + average); serverList.put(new Integer(departureTime));}


Simulation: Waiting LinesServer.numServing()

// numServing: Returns the number of servers serving customers at// currentTime. Also resets current server.public int numServing(int currentTime){ int count = 0;

for (serverList.goFirst(); serverList.isDefined(); serverList.goNext()) { int serverTimeUp = ((Integer) serverList.get()).intValue(); if (serverTimeUp >= currentTime) { count++; } } return count;}


Simulation: Waiting LinesWaitingLine class

Does most of the workKeeps track of servers, line of customers, all statistics

Instance variables// Instance variablesServers servers;Random randGen = new Random();Queue customerLine = new Queue();int totalWaitTime = 0;int longestWaitTime = 0;int longestLine = 0;int customersServed = 0;int customersBeingServed;


Simulation: Waiting LinesWaitiingLine constructor steps:

For each time from 0 to the time to simulate,•If new customer arrives, put that customer at end of the line•While there's someone in the line and a server available,

–Have an available server serve the customer at front of line–Accumulate statistics on this customer

Constructor code// Constructor: Simulates a single waiting line with numServers// servers for timeToSimulate time units. Each// server takes the given average amount of time// to service one customer, with the given standard// deviationpublic WaitingLine(int numServers, int arrivalProb, double averageServeTime, double standardDev, int timeToSimulate){ int arriveTime, waitTime;


Simulation: Waiting LinesConstructor code (continued)

servers = new Servers(numServers, averageServeTime, standardDev);

for (int currentTime = 0; currentTime < timeToSimulate; currentTime++) { if (Math.abs(randGen.nextInt()) % 100 < arrivalProb) { // Have a new arrival - put into the queue customerLine.enqueue(new Integer(currentTime)); }

// Keep servers busy if anyone in line while (!customerLine.empty() && servers.findAvailable(currentTime)) { // Available server serve customer at front of line arriveTime = ((Integer) customerLine.dequeue()).intValue(); servers.serveCustomer(currentTime);

while statement

keeps several

servers busy


Simulation: Waiting LinesConstructor code (continued)

// Accumulate statistics on this customer waitTime = currentTime - arriveTime; totalWaitTime = totalWaitTime + waitTime; if (waitTime > longestWaitTime) { longestWaitTime = waitTime; } if (customerLine.count() > longestLine) { longestLine = customerLine.count(); } customersServed++; } } customersBeingServed = servers.numServing(timeToSimulate);}


Simulation: Waiting LinesWaitingLine:displayResults()

// displayResults: Displays the results of the simulation public void displayResults() { System.out.println("---- Results ----"); System.out.println(" Customers served: " + customersServed); if (customersServed > 0) System.out.println(" Average wait time: " + Format.pad((double) totalWaitTime / customersServed, 0, 2)); System.out.println(" Longest wait time: " + longestWaitTime); System.out.println(" Longest line: " + longestLine); System.out.println(" Customers still waiting: " + customerLine.count()); System.out.println(" Customers still being served: " + customersBeingServed); }


Simulation: Waiting LinesExample use of program

Restaurant has two cashiers30% chance that a new customer will arrive in any minuteAverage of 5 minutes to serve a customer, standard

deviation of 3 minutesShould the manager hire another cashier?


Simulation: Waiting LinesTwo sample runs of the program

Number of servers: 2Probability of arrival during each time unit: 30Average service time: 5Standard deviation of service time: 3Time to simulate: 600---- Results ---- Customers served: 184 Average wait time: 0.97 Longest wait time: 8 Longest line: 4 Customers still waiting: 1 Customers still being served: 2

---- Waiting Line Simulation ----Number of servers: 3Probability of arrival during each time unit: 30Average service time: 5Standard deviation of service time: 3Time to simulate: 600---- Results ---- Customers served: 170 Average wait time: 0.56 Longest wait time: 6 Longest line: 3 Customers still waiting: 0 Customers still being served: 3


Simulation: Waiting LinesOther runs give different results




Simulation: Waiting LinesDifferent runs give very different results

Should run the simulation longer (or more times) to get a better feel for results

Also should do sensitivity analysis: how do small input changes affect the output?


Simulation: Other DistributionsThe gamma distribution

Often used to simulate servers Is a skewed distributionTakes two parameters,, (must be determined

empiricallyAdd to ExtendedRandom...

// nextDoubleGamma: Returns a double random value from// the gamma distribution given by alpha// and betapublic double nextDoubleGamma(int alpha, int beta){ double product = 1.0;

for (int i = 0; i < alpha; i++) { product = product * nextDouble(); }

return (-beta) * Math.log(product);}


Simulation: Other DistributionsGamma distribution

determines amount of skew

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Simulation: Other DistributionsGamma distribution with = 2, = 1

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Simulation: Other DistributionsThe Poisson distribution

Used to simulate customer arrivals in waiting line simulations (also number of accidents, cars arriving at intersection, telephone calls at a switchboard, ...)

Models time from one customer to the next oneTakes one parameter, (average events per time unit)Add to ExtendedRandom...

// nextDoublePoisson: Returns a normally distributed random// value from the Poisson distribution given// by alphadouble nextDoublePoisson(int alpha){ double product = 1.0; int k = 0; while (product >= Math.exp(-alpha)) { product = product * nextDouble(); k++; }

return k;}


Simulation: Other DistributionsPoisson distribution with = 75

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chapter 13: stacks and queues

Documents

stack mystack

stacka stack

new stack publ

standard stack classjava

javas standard stack

character charstack

mystack pop

command addselectionpop