Arrays CSC 171 FALL 2001 LECTURE 10. History: Alan Turing Founder of Computer Science 1937 - Alan Turing developed the idea of a "Universal Machine" capable.

ArraysArrays

CSC 171 FALL 2001

LECTURE 10

History: Alan Turing History: Alan Turing Founder of Computer ScienceFounder of Computer Science

1937 - Alan Turing developed the idea of a "Universal Machine" capable of executing any describable algorithm, and forming the basis for the concept of "computability".

Turing's ideas differed from those of others who were solving arithmetic problems by introducing the concept of "symbol processing".

The Turing MachineThe Turing MachineTape memory (movable)

a c ab cbbaa

Read head

h

q3 q2

q1

q0

State machine

The Turing MachineThe Turing Machine

A Turing machine is a quintuple (K,,,s,H)– K is a finite set of states is an alphabet of symbols– s is the initial state– H is the halting state is the transition function

From (K-H) x To K x ( U {move_tape_left, move_tape_right})

The Turing TestThe Turing Test Turing put forward the idea of an 'imitation game',

in which a human being and a computer would be interrogated under conditions where the interrogator would not know which was which, the communication being entirely by textual messages.

Turing argued that if the interrogator could not distinguish them by questioning, then it would be unreasonable not to call the computer intelligent.

Turing's 'imitation game' is now usually called 'the Turing test' for intelligence.

ArraysArrays

Suppose we want to write a program that reads a set of test grades and prints them, marking the highest grade?65.2

81.7

31.3

95.4 < - highest grade

76.1

58.6

Individual data itemsIndividual data items

If we knew that there were always 150 students in the class, we could store the data as individual variables– score1,score2,score3, . . , score150

What would the data entry code look like?What would the printing code look like?How about finding the max?

ArraysArrays

An array is a collection of data items of the same type

Every element of the collection can be accessed separately.

Constructing ArraysConstructing Arrays

double [] data = new double[10];

Setting Array valuesSetting Array values

To get values into an array you need to specify which slot you want to use.

Specification is done with the [ ] operatorThe [ ] operator follows the name of the

arrayThe [ ] operator encloses and integer-valued

expression called the index or subscript

Setting array valuesSetting array values

data[4] = 29.95;

Using array valuesUsing array values

Similar to setting

int i = 4 ;

System.out.println(“data[“+i+”] ==“+ data[i]);

> data[4] ==29.95

Array data itemsArray data itemsSuppose we want to write a program that

reads a set of test grades and prints them, marking the highest grade?

What would the data entry code look like?What would the printing code look like?How about finding the max?

Array issuesArray issues

Does it work?


data[10] = 5.4;


Does it work?

double [] data = new double[10];data[10] = 5.4;

When the program runs, an out-of-bounds subscript generates an exception and terminates the program – why?


Can we search for the top grade as follows

double maxScore = data[0];

for (int i = 1;I<=data.length;i++)

If (data[i] > maxScore)

maxScore = data[i];


An array of length n has index values from 0 to (n-1)

double maxScore = data[0];

for (int i = 1;I<data.length;i++)

If (data[i] > maxScore)

maxScore = data[i];


Does it work?

public static void main(String[] args){ double[] data;

If (data[0] > 4.0)

System.out.println(“GT 4!”);

}


Arrays must be allocated!

public static void main(String[] args){ double[] data = new double[10];

If (data[0] > 4.0)


}


Arrays can be initialized!

public static void main(String[] args){ double[] data = {2,3,4,5,6};

If (data[0] > 4.0)


}

// note: new int[] {2,3,4,5,6} ; is also legal

Copying ArraysCopying Arrays

Is this ok?


double[] testScores;

testScores = data;


Is this ok?


double[] testScores;

testScores = data;

How many arrays are there?

Copying Array REFERENCESCopying Array REFERENCESdouble [] data = new double[10];double[] testScores;testScores = data;


So, what if we want to make two “real” copies – what does the code look like?

Write a method so that

int[] x = {3,4,5,6,7,8,9,10};

int[] y = myCopy(x);

CopyingCopying

public static int[] myCopy(int[] x){

int[] r_arry = new int[x.length];

for (int i = 0 ; i< x.length;i++)

r_arry[i] = x[i];

return r_arry;

}

System.arrayCopySystem.arrayCopy

//System.arraycopy(from,fromstart,to,toStart,count);System.arraycopy(data,0,prices,0,data.length);

CSC 171 GRADES FALL 2001

0

5

10

15

20

25

30

35

40

I N E D- D D+ C- C C+ B- B B+ A- A

GRADE

CO

UN

T

History: Colossus History: Colossus Bletchley ParkBletchley Park

1940 A major need for supporting the war effort was to decrypt the intercepted messages of the German forces. Encrypted in the early years using the US designed ENIGMA, a team at Bletchley Park, built a series of machines culminating in 1943 with Colossus.

More ArraysMore Arrays

Suppose we want to write a program that reads a set of test product names, prices, and quality scores prints them, marking the best value? (score/prices)Digital 500X, $3499.00, score 73

ZEOS Pentium-III/500, $2545.00, score 70

Micro Express MF, $2195.00, score 72 < - best value

Polywell Poly 450IP, $2099.00, score 30

Parallel ArraysParallel Arrays

One solution, can you think of a better one?

Arrays of ObjectsArrays of ObjectsEasier to deal with - arrays hold references

Multidimensional ArraysMultidimensional Arrays

Arrays of arrays– Arrays are objects– Arrays hold references to objects– Ergo, arrays can hold arrays

Tables are 2D arraysTables are 2D arraysint size = 5;int[][] mtable = new int[size][size];for(i=0;i<size;i++)

for(int j=0;j<size;j++)mtable[i][j] = (i+1)*(j+1);

1 2 3 4 5

2 4 6 8 10

3 6 9 12 15

4 8 12 16 20

5 10 15 20 25

// how easy to modify code ????

int[][] mtable = new int[5][5];

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

for(int j=0;j<5;j++)

mtable[i][j] = (i+1)*(j+1);

Arrays of ArraysArrays of Arrays

int [][] powers = new int[10][10];

Allocating arrays of arraysAllocating arrays of arrays

int size = 10;int[][] mtable = new int[size][];for(i=0;i<mtable.length;i++) {

mtable[i]= new int[size];for(int j=0;j<mtable[i].length;j++)

mtable[i][j] = (i+1)*(j+1);

}

AlternatelyAlternately

The following is legal.What is the structure?

int[][] b = new int[5][];

for (int i=0;i<b.length;i++)

b[i] = new int[i+1];

AlternatelyAlternately

int[][] b = new int[5][];

for (int i=0;i<b.length;i++)

b[i] = new int[i+1];

This is known as a triangular array

Is b[3][1] a legal reference or b[1][3]?

Passing ArraysPassing ArraysIn JAVA

– Primitives are passed by value A copy of the variable is made & used Modifications made do not affect calling value public void myAdd(int x) { x++;}

– Objects are passed by reference Since the reference is passed it is possible to change

the value in the calling method Public void myAdd (int[] x) {x[0]++;}

Pass by valuePass by value

public class passArry {

public static void main(String args[]){

int x1 = 3;

System.out.println("x1 == "+x1);

myAdd(x1);

System.out.println("x1 == "+x1);

}

public static void myAdd(int x) {x++;}

}

Pass by referencePass by reference

public class passArry {

public static void main(String args[]){

int[] x2 = {4,5,6};

System.out.println("x2[0] == "+x2[0]);

myAdd(x2);

System.out.println("x2[0] == "+x2[0]);

}

public static void myAdd(int[] x) {x[0]++;}

}

ExerciseExercise

Write a method that takes an integer array and prints the values

ExerciseExercise

Write a method that takes an integer array and prints the values

public static int myPrint(int[] x){

for (int i = 0 ; i<x.length;i++)

System.out.println(x + “[“+i+”] == “+ x[i]);

}

ExerciseExercise

Write a method that takes an integer array, and two integer indices and swaps the value

ExerciseExerciseWrite a method that takes an integer array,

and two integer indices and swaps the value

public static void mySwap(int[] x, int i, int j){ int temp = x[i];

x[i] = x[j];

x[j] = temp;

}

ExerciseExercise

Write a method that takes an integer array and returns the index of the maximum value

ExerciseExercise

Write a method that takes an integer array and returns the index of the maximum value

public static int myMax(int[] x){ int rvalue = 0;for (int i = 0 ; i<x.length;i++) if (x[i] > x[rvalue]) rvalue = i;return rvalue;

}

ExerciseExercise

Overload the max finder to take an array and an index – the method now returns the index of the maximum value >= the index passed in

ExerciseExercise

Overload the max finder to take an array and an index – the method now returns the index of the maximum value >= the index passed in

public static int myMax(int[] x, int j){

int rvalue = j;

for (int i = j ; i<x.length;i++)

if (x[i] > x[rvalue]) rvalue = i;

return rvalue;

}

SortingSorting

Write a method that takes an integer arrayLoop through all the positions in the array,

one after the otherAt each (current) position, find the max

from that position to the rest of the array.Swap the value with the current positionThis is termed selection sort

Selection SortSelection SortDoes it work?

public void selSort(int x){for (int i = 0 ; i<x.length;i++){

int temp = myMax(x,i);mySwap(x,i,temp);

}

Can you prove it works?What is the loop invariant?

SortingSorting

Write a method that takes an integer array Loop through all the positions in the array, one

after the other At each (current) position, compare the value to

the next in line. If the next is > the current swap the value with the

current position How many times do I have to do this? This is termed bubble sort

Bubble SortBubble SortDoes it work?

public void bubSort(int x){for (int i = 0 ; i<x.length;i++){

for (int j = 0 ; j<(x.length-1);j++){If (x[ j ] < x[ j+1 ])

mySwap(x,j,j+1); }}

}

Question to ponderQuestion to ponder

Which is “better” – bubble sort– selection sort

What do you mean by “better”?– Running time on same sized array– Number of swaps– Memory usage– Simplicity & reliability

Arrays CSC 171 FALL 2001 LECTURE 10. History: Alan Turing Founder of Computer Science 1937 - Alan Turing developed the idea of a "Universal Machine" capable.

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