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Iteration. Chapter 6 Fall 2006 CS 101 Aaron Bloomfield. Java looping. Options while do-while for Allow programs to control how many times a statement list is executed. Averaging values. Averaging. Problem

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Iteration l.jpg

Iteration

Chapter 6

Fall 2006

CS 101

Aaron Bloomfield


Java looping l.jpg
Java looping

  • Options

    • while

    • do-while

    • for

  • Allow programs to control how many times a statement list is executed



Averaging l.jpg
Averaging

  • Problem

    • Extract a list of positive numbers from standard input and produce their average

      • Numbers are one per line

      • A negative number acts as a sentinel to indicate that there are no more numbers to process

  • Observations

    • Cannot supply sufficient code using just assignments and conditional constructs to solve the problem

      • Don’t how big of a list to process

    • Need ability to repeat code as needed


Averaging5 l.jpg
Averaging

  • Algorithm

    • Prepare for processing

    • Get first input

    • While there is an input to process do {

      • Process current input

      • Get the next input

    • }

    • Perform final processing


Averaging6 l.jpg
Averaging

  • Problem

    • Extract a list of positive numbers from standard input and produce their average

      • Numbers are one per line

      • A negative number acts as a sentinel to indicate that there are no more numbers to process

  • Sample run

    Enter positive numbers one per line.

    Indicate end of list with a negative number.

    4.5

    0.5

    1.3

    -1

    Average 2.1


Slide7 l.jpg

public class NumberAverage {

// main(): application entry point

public static void main(String[] args) {

// set up the input

// prompt user for values

// get first value

// process values one-by-one

while (value >= 0) {

// add value to running total

// processed another value

// prepare next iteration - get next value

}

// display result

if (valuesProcessed > 0)

// compute and display average

else

// indicate no average to display

}

}


Slide8 l.jpg

int valuesProcessed = 0;

double valueSum = 0;

// set up the input

Scanner stdin = new Scanner (System.in);

// prompt user for values

System.out.println("Enterpositivenumbers1perline.\n"

+ "Indicate end of the list with a negative number.");

// get first value

double value = stdin.nextDouble();

// process values one-by-one

while (value >= 0) {

valueSum += value;

++valuesProcessed;

value = stdin.nextDouble();

}

// display result

if (valuesProcessed > 0) {

double average = valueSum / valuesProcessed;

System.out.println("Average: " + average);

} else {

System.out.println("No list to average");

}


Program demo l.jpg
Program Demo

  • NumberAverage.java


While syntax and semantics l.jpg

Logical expression that

Action is either a single

determines whether Action

statement or a statement

is to be executed

list within braces

While syntax and semantics

Expression

Action

while

(

)


While semantics for averaging problem l.jpg

Test expression is evaluated at the

start of each iteration of the loop.

If test expression is true, these statements

are executed. Afterward, the test expression

is reevaluated and the process repeats

While semantics for averaging problem

// process values one-by-one

while ( value >= 0 ) {

// add value to running total

valueSum += value;

// we processed another value

++valueProcessed;

// prepare to iterate – get the next input

value = stdin.nextDouble();

}


While semantics l.jpg

Expression is

evaluated at the

start of each

iteration of the

loop

If Expression is

true, Action is

executed

If Expression is

false, program

execution

continues with

next statement

While Semantics

Expression

false

true

Action


Execution trace l.jpg
Execution Trace

Suppose input contains: 4.50.51.3-1

Suppose input contains: 4.50.51.3 -1

Suppose input contains: 4.5 0.5 1.3 -1

Suppose input contains: 4.5 0.5 1.3 -1

Suppose input contains: 4.50.5 1.3 -1

valuesProcessed

1

0

3

2

4.5

valueSum

0

6.3

5.0

int valuesProcessed = 0;

double valueSum = 0;

double value = stdin.nextDouble();

while (value >= 0) {

valueSum += value;

++valuesProcessed;

value = stdin.nextDouble();

}

if (valuesProcessed > 0) {

double average = valueSum / valuesProcessed;

System.out.println("Average: " + average);

}

else {

System.out.println("No list to average");

}

int valuesProcessed = 0;

double valueSum = 0;

double value = stdin.nextDouble();

while (value >= 0) {

valueSum += value;

++valuesProcessed;

value = stdin.nextDouble();

if (valuesProcessed > 0) {

double average = valueSum / valuesProcessed;

System.out.println("Average: " + average);

value

1.3

4.5

-1

0.5

average

2.1




Converting text to strictly lowercase l.jpg
Converting text to strictly lowercase

public static void main(String[] args) {

Scanner stdin = new Scanner (System.in);

System.out.println("Enter input to be converted:");

String converted = "";

while (stdin.hasNext()) {

String currentLine = stdin.nextLine();

String currentConversion =

currentLine.toLowerCase();

converted += (currentConversion + "\n");

}

System.out.println("\nConversion is:\n" +

converted);

}


Sample run l.jpg

An empty line

was entered

A Ctrl+z was

entered. I

t is the

Windows escape

sequence for

indicating

end-of-file

Sample run


Program demo18 l.jpg
Program Demo

  • LowerCaseDisplay.java


Program trace l.jpg
Program trace

public static void main(String[] args) {

Scanner stdin = new Scanner (System.in);

System.out.println("Enter input to be converted:");

String converted = "";

while (stdin.hasNext()) {

String currentLine = stdin.nextLine();

String currentConversion =

currentLine.toLowerCase();

converted += (currentConversion + "\n");

}

System.out.println("\nConversion is:\n" +

converted);

}

public static void main(String[] args) {

Scanner stdin = new Scanner (System.in);

System.out.println("Enter input to be converted:");

String converted = "";

while (stdin.hasNext()) {

String currentLine = stdin.nextLine();

String currentConversion =

currentLine.toLowerCase();

converted += (currentConversion + "\n");

}

System.out.println("\nConversion is:\n" +

converted);

}


Program trace20 l.jpg

The append assignment operator updates the representation

of converted to include the current input line

Representation of lower case

Newline character is needed

conversion of current input line

because method nextLine()

"strips" them from the input

Program trace

converted += (currentConversion + "\n");



Loop design l.jpg
Loop design

  • Questions to consider in loop design and analysis

    • What initialization is necessary for the loop’s test expression?

    • What initialization is necessary for the loop’s processing?

    • What causes the loop to terminate?

    • What actions should the loop perform?

    • What actions are necessary to prepare for the next iteration of the loop?

    • What conditions are true and what conditions are false when the loop is terminated?

    • When the loop completes what actions are need to prepare for subsequent program processing?


Reading a file l.jpg

Same Scanner class!

filename is a String

The File class allows access to files

It’s in the java.io package

Reading a file

  • Background

Scanner fileIn = new Scanner (new File (filename) );


Reading a file24 l.jpg
Reading a file

  • Class File

    • Allows access to files (etc.) on a hard drive

  • Constructor File (String s)

    • Opens the file with name s so that values can be extracted

    • Name can be either an absolute pathname or a pathname relative to the current working folder


Reading a file25 l.jpg
Reading a file

Scanner stdin = new Scanner (System.in);

System.out.print("Filename: ");

String filename = stdin.nextLine();

Scanner fileIn = new Scanner (new File (filename));

String currentLine = fileIn.nextLine();

while (currentLine != null) {

System.out.println(currentLine);

currentLine = fileIn.nextLine();

}

Scanner stdin = new Scanner (System.in);

System.out.print("Filename: ");

String filename = stdin.nextLine();

Scanner fileIn = new Scanner (new File (filename));

String currentLine = fileIn.nextLine();

while (currentLine != null) {

System.out.println(currentLine);

currentLine = fileIn.nextLine();

}

Set up standard input stream

Determine file name

Set up file stream

Process lines one by one

Get first line

Make sure got a line to process

Display current line

Get next line

Make sure got a line to process

If not, loop is done

Close the file stream




The for statement28 l.jpg

The body of the loop iterates

while the test expression is

Initialization step

true

is performed only

After each iteration of the

once -- just prior

body of the loop, the update

to the first

expression is reevaluated

evaluation of the

test expression

The body of the loop displays the

current term in the number series.

It then determines what is to be the

new current number in the series

The For Statement

int

currentTerm = 1;

for ( int i = 0; i < 5; ++i ) {

System.out.println(currentTerm);

currentTerm *= 2;

}


Slide29 l.jpg

Evaluated once

at the beginning

of the for

statements's

The ForExpr is

execution

evaluated at the

start of each

iteration of the

loop

If ForExpr is true,

Action is

executed

After the Action

If ForExpr is

has completed,

false, program

the

execution

PostExpression

continues with

is evaluated

next statement

After evaluating the

PostExpression, the next

iteration of the loop starts

ForInit

ForExpr

true

false

Action

PostExpr


For statement syntax l.jpg

Logical test expression that determines whether the action and update step are

executed

Initialization step prepares for the

first evaluation of the test

Update step is performed after

expression

the execution of the loop body

The body of the loop iterates whenever

the test expression evaluates to true

for statement syntax

ForInit

ForExpression

ForUpdate

Action

for

(

;

;

)


For vs while l.jpg
for vs. while and update step are

  • A for statement is almost like a while statement

    for ( ForInit; ForExpression; ForUpdate ) Action

    is ALMOST the same as:

    ForInit;

    while ( ForExpression ) {

    Action;

    ForUpdate;

    }

  • This is not an absolute equivalence!

    • We’ll see when they are different in a bit


Variable declaration l.jpg
Variable declaration and update step are

  • You can declare a variable in any block:

    while ( true ) {

    int n = 0;

    n++;

    System.out.println (n);

    }

    System.out.println (n);

Variable n gets created (and initialized) each time

Thus, println() always prints out 1

Variable n is not defined once while loop ends

As n is not defined here, this causes an error


Variable declaration33 l.jpg
Variable declaration and update step are

  • You can declare a variable in any block:

    if ( true ) {

    int n = 0;

    n++;

    System.out.println (n);

    }

    System.out.println (n);

Only difference from last slide


Execution trace34 l.jpg
Execution Trace and update step are

i

0

2

1

3

System.out.println("i is " + i);

}

System.out.println("all done");

System.out.println("i is " + i);

}

System.out.println("all done");

i is 0

i is 1

i is 2

all done

for (

int i = 0;

int i = 0;

i < 3;

i < 3;

++i

++i

) {

Variable i has gone out of scope – it

is local to the loop


For vs while35 l.jpg
for vs. while and update step are

  • An example when a for loop can be directly translated into a while loop:

    int count;

    for ( count = 0;count < 10; count++ ) {

    System.out.println (count);

    }

  • Translates to:

    int count;

    count = 0;

    while (count < 10) {

    System.out.println (count);

    count++;

    }


For vs while36 l.jpg
for vs. while and update step are

  • An example when a for loop CANNOT be directly translated into a while loop:

    for ( int count = 0;count < 10; count++ ) {

    System.out.println (count);

    }

  • Would (mostly) translate as:

    int count = 0;

    while (count < 10) {

    System.out.println (count);

    count++;

    }

only difference

count is NOT defined here

count IS defined here


For loop indexing l.jpg
for loop indexing and update step are

  • Java (and C and C++) indexes everything from zero

  • Thus, a for loop like this:

    for ( int i = 0; i < 10; i++ ) { ... }

  • Will perform the action with i being value 0 through 9, but not 10

  • To do a for loop from 1 to 10, it would look like this:

    for ( int i = 1; i <= 10; i++ ) { ... }


Nested loops l.jpg

i is 0 and update step are

j is 0

j is 1

i is 1

j is 0

j is 1

i is 2

j is 0

j is 1

Nested loops

int m = 2;

int n = 3;

for (int i = 0; i < n; ++i) {

System.out.println("i is " + i);

for (int j = 0; j < m; ++j) {

System.out.println(" j is " + j);

}

}


Nested loops39 l.jpg

i is 0 and update step are

i is 1

j is 0

i is 2

j is 0

j is 1

i is 3

j is 0

j is 1

j is 2

Nested loops

int m = 2;

int n = 4;

for (int i = 0; i < n; ++i) {

System.out.println("i is " + i);

for (int j = 0; j < i; ++j) {

System.out.println(" j is " + j);

}

}


Another optical illusion l.jpg
Another optical illusion and update step are


Loop controls l.jpg

Loop controls and update step are


The continue keyword l.jpg
The continue keyword and update step are

  • The continue keyword will immediately start the next iteration of the loop

    • The rest of the current loop is not executed

      for ( int a = 0; a <= 10; a++ ) {

      if ( a % 2 == 0 ) {

      continue;

      }

      System.out.println (a + " is odd");

      }

  • Output: 1 is odd

    3 is odd

    5 is odd

    7 is odd

    9 is odd


The break keyword l.jpg
The break keyword and update step are

  • The break keyword will immediately stop the execution of the loop

    • Execution resumes after the end of the loop

      for ( int a = 0; a <= 10; a++ ) {

      if ( a == 5 ) {

      break;

      }

      System.out.println (a + " is less than five");

      }

  • Output: 0 is less than five

    1 is less than five

    2 is less than five

    3 is less than five

    4 is less than five


Today s demotivators44 l.jpg
Today’s demotivators and update step are


Four hobos l.jpg

Four Hobos and update step are


Four hobos46 l.jpg
Four Hobos and update step are

  • An example of a program that uses nested for loops

  • Credited to Will Shortz, crossword puzzle editor of the New York Times

    • And NPR’s Sunday Morning Edition puzzle person

  • This problem is in section 6.10 of the text


Problem l.jpg
Problem and update step are

  • Four hobos want to split up 200 hours of work

  • The smart hobo suggests that they draw straws with numbers on it

  • If a straw has the number 3, then they work for 3 hours on 3 days (a total of 9 hours)

  • The smart hobo manages to draw the shortest straw

  • How many ways are there to split up such work?

  • Which one did the smart hobo choose?


Analysis l.jpg
Analysis and update step are

  • We are looking for integer solutions to the formula:

    a2+b2+c2+d2 = 200

    • Where a is the number of hours & days the first hobo worked, b for the second hobo, etc.

  • We know the following:

    • Each number must be at least 1

    • No number can be greater than 200 = 14

    • That order doesn’t matter

      • The combination (1,2,1,2) is the same as (2,1,2,1)

        • Both combinations have two short and two long straws

  • We will implement this with nested for loops


Implementation l.jpg
Implementation and update step are

public class FourHobos {

public static void main (String[] args) {

for ( int a = 1; a <= 14; a++ ) {

for ( int b = 1; b <= 14; b++ ) {

for ( int c = 1; c <= 14; c++ ) {

for ( int d = 1; d <= 14; d++ ) {

if ( (a <= b) && (b <= c) && (c <= d) ) {

if ( a*a+b*b+c*c+d*d == 200 ) {

System.out.println ("(" + a + ", " + b

+ ", " + c + ", " + d + ")");

}

}

}

}

}

}

}

}


Program demo50 l.jpg
Program Demo and update step are

  • FourHobos.java


Results l.jpg
Results and update step are

  • The output:

    (2, 4, 6, 12)

    (6, 6, 8, 8)

  • Not surprisingly, the smart hobo picks the short straw of the first combination


Alternate implementation l.jpg
Alternate implementation and update step are

  • We are going to rewrite the old code in the inner most for loop:

    if ( (a <= b) && (b <= c) && (c <= d) ) {

    if ( a*a+b*b+c*c+d*d == 200 ) {

    System.out.println ("(" + a + ", " + b

    + ", " + c + ", " + d + ")");

    }

    }

  • First, consider the negation of

    ( (a <= b) && (b <= c) && (c <= d) )

    • It’s ( !(a <= b) || !(b <= c) || !(c <= d) )

    • Or ( (a > b) || (b > c) || (c > d) )


Alternate implementation53 l.jpg
Alternate implementation and update step are

  • This is the new code for the inner-most for loop:

    if ( (a > b) || (b > c) || (c > d) ) {

    continue;

    }

    if ( a*a+b*b+c*c+d*d != 200 ) {

    continue;

    }

    System.out.println ("(" + a + ", " + b + ", "

    + c + ", " + d + ")");


3 card poker l.jpg

3 card poker and update step are


3 card poker55 l.jpg
3 Card Poker and update step are

  • This is the looping HW from a previous fall

  • The problem: count how many of each type of hand in a 3 card poker game

  • Standard deck of 52 cards (no jokers)

    • Four suits: spades, clubs, diamonds, hearts

    • 13 Faces: Ace, 2 through 10, Jack, Queen, King

  • Possible 3-card poker hands

    • Pair: two of the cards have the same face value

    • Flush: all the cards have the same suit

    • Straight: the face values of the cards are in succession

    • Three of a kind: all three cards have the same face value

    • Straight flush: both a flush and a straight


The card class l.jpg
The Card class and update step are

  • A Card class was provided

    • Represents a single card in the deck

  • Constructor: Card(int i)

    • If i is in the inclusive interval 1 ... 52 then a card is configured in the following manner

      • If 1 <= i <= 13 then the card is a club

      • If 14 <= i <= 26 then the card is a diamond

      • If 27 <= i <= 39 then the card is a heart

      • If 40 <= i <= 52 then the card is a spade

      • If i % 13 is 1 then the card is an Ace;

      • If i % 13 is 2, then the card is a 2, and so on.


Card class methods l.jpg
Card class methods and update step are

  • String getFace()

    • Returns the face of the card as a String

  • String getSuit()

    • Returns the suit of the card as a String

  • int getValue()

    • Returns the value of the card

  • boolean equals(Object c)

    • Returns whether c is a card that has the same face and suit as the invoking card

  • String toString()

    • Returns a text representation of the card. You may find this method useful during debugging.


The hand class l.jpg
The Hand class and update step are

  • A Hand class was (partially) provided

    • Represents the three cards the player is holding

  • Constuctor: Hand(Card c1, Card c2, Card c3)

    • Takes those cards and puts them in sorted order


Provided hand methods l.jpg
Provided Hand methods and update step are

  • public Card getLow()

    • Gets the low card in the hand

  • public Card getMiddle()

    • Gets the middle card in the hand

  • public Card getHigh()

    • Gets the high card in the hand

  • public String toString()

    • We’ll see the use of the toString() method later

  • public boolean isValid()

    • Returns if the hand is a valid hand (no two cards that are the same)

  • public boolean isNothing()

    • Returns if the hand is not one of the “winning” hands described before


Hand methods to implement l.jpg
Hand Methods to Implement and update step are

  • The assignment required the students to implement the other methods of the Hand class

    • We haven’t seen this yet

  • The methods returned true if the Hand contained a “winning” combination of cards

    • public boolean isPair()

    • public boolean isThree()

    • public boolean isStraight()

    • public boolean isFlush()

    • public boolean isStraightFlush()


Class handevaluation l.jpg
Class HandEvaluation and update step are

  • Required nested for loops to count the total number of each hand

  • Note that the code for this part may not appear on the website


Program demo62 l.jpg
Program Demo and update step are

  • HandEvaluation.java


Becoming an ieee author l.jpg
Becoming an IEEE author and update step are


Triangle counting l.jpg

Triangle counting and update step are


The programming assignment l.jpg
The programming assignment and update step are

  • This was the looping HW from two springs ago

  • List all the possible triangles from (1,1,1) to (n,n,n)

    • Where n is an inputted number

    • In particular, list their triangle type

  • Types are: equilateral, isosceles, right, and scalene


Sample execution l.jpg

Enter n: and update step are5

(1,1,1) isosceles equilateral

(1,2,2) isosceles

(1,3,3) isosceles

(1,4,4) isosceles

(1,5,5) isosceles

(2,2,2) isosceles equilateral

(2,2,3) isosceles

(2,3,3) isosceles

(2,3,4) scalene

(2,4,4) isosceles

(2,4,5) scalene

(2,5,5) isosceles

(3,3,3) isosceles equilateral

(3,3,4) isosceles

(3,3,5) isosceles

(3,4,4) isosceles

(3,4,5) right scalene

(3,5,5) isosceles

(4,4,4) isosceles equilateral

(4,4,5) isosceles

(4,5,5) isosceles

(5,5,5) isosceles equilateral

Sample execution


Program demo67 l.jpg
Program Demo and update step are

  • TriangleDemo.java


The triangle class l.jpg
The Triangle class and update step are

  • That semester we went over classes by this homework

    • So they had to finish the class

    • We will be seeing class creation after spring break

  • Methods in the class:

    • public Triangle()

    • public Triangle (int x, int y, int z)

    • public boolean isTriangle()

    • public boolean isRight()

    • public boolean isIsosceles()

    • public boolean isScalene()

    • public boolean isEquilateral()

    • public String toString()


The triangledemo class l.jpg
The TriangleDemo class and update step are

  • Contained a main() method that tested all the triangles

  • Steps required:

    • Check if the sides are in sorted order (i.e. x < y < z)

      • If not, then no output should be provided for that collection of side lengths

    • Create a new Triangle object using the current side lengths

    • Check if it is a valid triangle

      • If it is not, then no output should be provided for that collection of side lengths

    • Otherwise, indicate which properties the triangle possesses

      • Some side length values will correspond to more than 1 triangle

      • e.g., (3, 3, 3) is both isosceles and equilateral

      • Thus, we can’t assume that once a property is present, the others are not.


Look at that them there code l.jpg
Look at that them there code… and update step are

  • TriangleDemo.java


Today s demotivators71 l.jpg
Today’s demotivators and update step are


End of this slide set l.jpg
End of this slide set? and update step are


Fibonacci numbers l.jpg

Fibonacci numbers and update step are


Fibonacci sequence l.jpg
Fibonacci sequence and update step are

  • Sequences can be neither geometric or arithmetic

    • Fn = Fn-1 + Fn-2, where the first two terms are 1

      • Alternative, F(n) = F(n-1) + F(n-2)

    • Each term is the sum of the previous two terms

    • Sequence: { 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … }

    • This is the Fibonacci sequence

    • Full formula:


Fibonacci sequence in nature l.jpg
Fibonacci sequence in nature and update step are

13

8

5

3

2

1


Reproducing rabbits l.jpg
Reproducing rabbits and update step are

  • You have one pair of rabbits on an island

    • The rabbits repeat the following:

      • Get pregnant one month

      • Give birth (to another pair) the next month

    • This process repeats indefinitely (no deaths)

    • Rabbits get pregnant the month they are born

  • How many rabbits are there after 10 months?


Reproducing rabbits77 l.jpg
Reproducing rabbits and update step are

  • First month: 1 pair

    • The original pair

  • Second month: 1 pair

    • The original (and now pregnant) pair

  • Third month: 2 pairs

    • The child pair (which is pregnant) and the parent pair (recovering)

  • Fourth month: 3 pairs

    • “Grandchildren”: Children from the baby pair (now pregnant)

    • Child pair (recovering)

    • Parent pair (pregnant)

  • Fifth month: 5 pairs

    • Both the grandchildren and the parents reproduced

    • 3 pairs are pregnant (child and the two new born rabbits)


Reproducing rabbits78 l.jpg
Reproducing rabbits and update step are

  • Sixth month: 8 pairs

    • All 3 new rabbit pairs are pregnant, as well as those not pregnant in the last month (2)

  • Seventh month: 13 pairs

    • All 5 new rabbit pairs are pregnant, as well as those not pregnant in the last month (3)

  • Eighth month: 21 pairs

    • All 8 new rabbit pairs are pregnant, as well as those not pregnant in the last month (5)

  • Ninth month: 34 pairs

    • All 13 new rabbit pairs are pregnant, as well as those not pregnant in the last month (8)

  • Tenth month: 55 pairs

    • All 21 new rabbit pairs are pregnant, as well as those not pregnant in the last month (13)


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Reproducing rabbits and update step are

  • Note the sequence:

    { 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … }

  • The Fibonacci sequence again


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Fibonacci sequence and update step are

  • Another application:

  • Fibonacci references from http://en.wikipedia.org/wiki/Fibonacci_sequence


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Fibonacci sequence and update step are

  • As the terms increase, the ratio between successive terms approaches 1.618

  • This is called the “golden ratio”

    • Ratio of human leg length to arm length

    • Ratio of successive layers in a conch shell

  • Reference: http://en.wikipedia.org/wiki/Golden_ratio


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The Golden Ratio and update step are


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Number counting and update step are


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The programming assignment and update step are

  • This was the looping HW from last fall

  • Get an integer i from the user

  • The homework had four parts

    • Print all the Fibonacci numbers up to i

    • Print all the powers of 2 up to i

    • Print all the prime numbers up to i

    • Time the previous three parts of the code


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Sample execution and update step are

Input an integer i: 10

The 10th Fibonacci number is 55

Computation took 1 ms

2 3 5 7 11 13 17 19 23 29

The 10th prime is 29

Computation took 0 ms

The 10th power of 2 is 1024

Computation took 6 ms

2 4 8 16 32 64 128 256 512 1024

BigInteger: The 10th power of 2 is 1024

Computation took 2 ms


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Background: Prime numbers and update step are

  • Remember that a prime number is a number that is ONLY divisible by itself and 1

  • Note that 1 is not a prime number!

    • Thus, 2 is the first prime number

  • The first 10 prime numbers: 2 3 5 7 11 13 17 19 23 29

  • The easiest way to determine prime numbers is with nested loops


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How to time your code and update step are

  • Is actually pretty easy:

    long start = System.currentTimeMillis();

    // do the computation

    long stop = System.currentTimeMillis();

    long timeTakenMS = stop-start;

  • This is in milliseconds, so to do the number of actual seconds:

    double timeTakenSec = timeTakenMS / 1000.0;


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Program Demo and update step are

  • NumberGames.java

  • Note what happens when you enter 100

    • With the Fibonacci numbers

    • With the powers of 2


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BigIntegers and update step are

  • An int can only go up to 2^31 or about 2*109

  • A long can only go up to 2^63, or about 9*1018

  • What if we want to go higher?

  • 2100 = 1267650600228229401496703205376

  • To do this, we can use the BigInteger class

    • It can represent integers of any size

      • This is called “arbitrary precision”

    • Not surprisingly, it’s much slower than using ints and longs

  • The Fibonacci number part didn’t use BigIntegers

    • That’s why we got -980107325 for the 100th term

    • It “flowed over” the limit for ints – called “overflow”


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BigInteger usage and update step are

  • BigIntegers are in the java.math library

    • import java.math.*;

  • To get nn:

    BigInteger bigN = new BigInteger (String.valueOf(n));

    BigInteger biggie = new BigInteger (String.valueOf(1));

    for ( int i = 0; i < n; i++ )

    biggie = biggie.multiply (bigN);

    System.out.println (biggie);


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Look at that them there code… and update step are

  • NumberGames.java