Arrays

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Arrays

• CSC 171 FALL 2001
• LECTURE 10

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History Alan Turing Founder 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".

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The Turing Machine
Tape memory (movable)
a
c
a
b
c
b
b
a
a
Read head
q0
h
q1
q3
q2
State machine
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The Turing Machine

• A Turing machine is a quintuple (K,S,d,s,H)
• K is a finite set of states
• S is an alphabet of symbols
• s is the initial state
• H is the halting state
• d is the transition function
• From (K-H) x S
• To K x (S U move_tape_left, move_tape_right)

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The 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.

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Arrays

• 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 lt - highest grade
• 76.1
• 58.6

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Individual 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?

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Arrays

• An array is a collection of data items of the
  same type
• Every element of the collection can be accessed
  separately.

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Constructing Arrays

• double data new double10

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Setting Array values

• To get values into an array you need to specify
  which slot you want to use.
• Specification is done with the operator
• The operator follows the name of the array
• The operator encloses and integer-valued
  expression called the index or subscript

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Setting array values

• data4 29.95

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Using array values

• Similar to setting
• int i 4
• System.out.println(datai datai)
• gt data4 29.95

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Array data items

• Suppose 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?

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Array issues

• Does it work?
• double data new double10
• data10 5.4

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Array issues

• Does it work?
• double data new double10
• data10 5.4
• When the program runs, an out-of-bounds subscript
  generates an exception and terminates the program
  why?

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Array issues

• Can we search for the top grade as follows
• double maxScore data0
• for (int i 1Iltdata.lengthi)
• If (datai gt maxScore)
• maxScore datai

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Array issues

• An array of length n has index values from 0 to
  (n-1)
• double maxScore data0
• for (int i 1Iltdata.lengthi)
• If (datai gt maxScore)
• maxScore datai

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Array issues

• Does it work?
• public static void main(String args) double
  data
• If (data0 gt 4.0)
• System.out.println(GT 4!)

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Array issues

• Arrays must be allocated!
• public static void main(String args) double
  data new double10
• If (data0 gt 4.0)
• System.out.println(GT 4!)

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Array issues

• Arrays can be initialized!
• public static void main(String args) double
  data 2,3,4,5,6
• If (data0 gt 4.0)
• System.out.println(GT 4!)
• // note new int 2,3,4,5,6 is also legal

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Copying Arrays

• Is this ok?
• double data new double10
• double testScores
• testScores data

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Copying Arrays

• Is this ok?
• double data new double10
• double testScores
• testScores data
• How many arrays are there?

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Copying Array REFERENCES

• double data new double10
• double testScores
• testScores data

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Copying Arrays

• 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)

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Copying

• public static int myCopy(int x)
• int r_arry new intx.length
• for (int i 0 ilt x.lengthi)
• r_arryi xi
• return r_arry

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System.arrayCopy

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

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History Colossus Bletchley 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.

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More 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 lt - best
  value
• Polywell Poly 450IP, 2099.00, score 30

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Parallel Arrays

• One solution, can you think of a better one?

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Arrays of Objects

• Easier to deal with - arrays hold references

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Multidimensional Arrays

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

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Tables are 2D arrays

• int size 5
• int mtable new intsizesize
• for(i0iltsizei)
• for(int j0jltsizej)
• mtableij (i1)(j1)

• // how easy to modify code ????
• int mtable new int55
• for(i0ilt5i)
• for(int j0jlt5j)
• mtableij (i1)(j1)

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Arrays of Arrays

• int powers new int1010

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Allocating arrays of arrays

• int size 10
• int mtable new intsize
• for(i0iltmtable.lengthi)
• mtablei new intsize
• for(int j0jltmtablei.lengthj)
• mtableij (i1)(j1)

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Alternately

• The following is legal.
• What is the structure?
• int b new int5
• for (int i0iltb.lengthi)
• bi new inti1

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Alternately

• int b new int5
• for (int i0iltb.lengthi)
• bi new inti1
• This is known as a triangular array
• Is b31 a legal reference or b13?

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Passing Arrays

• In 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) x0

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Pass 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

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Pass by reference

• public class passArry
• public static void main(String args)
• int x2 4,5,6
• System.out.println("x20 "x20)
• myAdd(x2)
• System.out.println("x20 "x20)
• public static void myAdd(int x) x0

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Exercise

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

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Exercise

• Write a method that takes an integer array and
  prints the values
• public static int myPrint(int x)
• for (int i 0 iltx.lengthi)
• System.out.println(x i xi)

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Exercise

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

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Exercise

• Write 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 xi
• xi xj
• xj temp

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Exercise

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

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Exercise

• 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 iltx.lengthi)
• if (xi gt xrvalue) rvalue i
• return rvalue

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Exercise

• Overload the max finder to take an array and an
  index the method now returns the index of the
  maximum value gt the index passed in

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Exercise

• Overload the max finder to take an array and an
  index the method now returns the index of the
  maximum value gt the index passed in
• public static int myMax(int x, int j)
• int rvalue j
• for (int i j iltx.lengthi)
• if (xi gt xrvalue) rvalue i
• return rvalue

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Sorting

• Write a method that takes an integer array
• Loop through all the positions in the array, one
  after the other
• At each (current) position, find the max from
  that position to the rest of the array.
• Swap the value with the current position
• This is termed selection sort

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Selection Sort

• Does it work?
• public void selSort(int x)
• for (int i 0 iltx.lengthi)
• int temp myMax(x,i)
• mySwap(x,i,temp)
• Can you prove it works?
• What is the loop invariant?

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Sorting

• 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 gt the current swap the value with
  the current position
• How many times do I have to do this?
• This is termed bubble sort

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Bubble Sort

• Does it work?
• public void bubSort(int x)
• for (int i 0 iltx.lengthi)
• for (int j 0 jlt(x.length-1)j)
• If (x j lt x j1 )
• mySwap(x,j,j1)

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Question 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