CS114-009 Class 25

1
CS114-009 Class 25

• Today
• Another Class example
• Merge Sort
• Final exam review
• Announcements
• Final Exam, Thurs. Dec. 11 at 8-1030 am
• Location Our classroom
• Up to 2½ hours, but it will be only 50 longer
  than other exams
• Same format as other exams short answer,
  tracing, coding
• Open note, open book

2
Yet another class example

• void main ( )
• Account a1, a2(5000)
• cout ltlt a1.get_balance( ) ltlt endl
• cout ltlt a2.get_balance( ) ltlt endl
• a1.deposit (1000)
• a2.deposit (2000)
• cout ltlt a1.get_balance( ) ltlt endl
• cout ltlt a2.get_balance( ) ltlt endl
• a1.withdraw (700)
• a2.withdraw (4000)
• cout ltlt a1.get_balance( ) ltlt endl
• cout ltlt a2.get_balance( ) ltlt endl
• a2.deposit (2000)
• cout ltlt a2.get_balance( ) ltlt endl
• a2.withdraw (4000)
• cout ltlt a2.get_balance( ) ltlt endl
• a2.withdraw (4000)
• cout ltlt a2.get_balance( ) ltlt endl

• class Account
• float balance
• public
• Account ( )
• balance0
• Account (float b)
• balanceb
• float get_balance ( )
• return balance
• void deposit (float amount)
• balanceamount
• void withdraw (float amount)
• balanceamount

3
Class Exercises

• What is output of the Account program?
• Modify the second Account constructor so that the
  balance cannot be initialized to a negative value
• Modify the deposit( ) method so that the amount
  deposited must be positive
• Modify the withdraw( ) method so that the amount
  withdrawn must be positive
• Also modify the withdraw( ) method so that the
  balance can never become negative
• These methods should print error messages when
  the user attempts to violate any of these
  conditions
• Compile and run your modified program
• What is output now?

4
A better algorithm Merge Sort

• Basic idea
• A list of size one is sorted!
• It is easy to merge sorted lists into a larger
  sorted list
• Algorithm
• Break list up into lots of small (1 item) lists
• Merge these lists

• Example
• 90 5 35 25 20 50 10
• 5 10 20 25 35 50 90

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Efficiency of Merge Sort

• Two parts to algorithm
• Partition the array until you get to lists of
  size one
• Merge these pieces back together

• Efficiency of the algorithm
• Merging items is O(N)
• Why? To merge a list, must process each item once
• How many times do we merge these lists? O(log2
  N)
• Why? Start with partitions of size 1 (merge into
  list of size 2), then merge lists of size 2 into
  lists of size 4, etc. until we hit N items in the
  list (similar idea to binary search)
• Total is O(N log2 N)
• merge lists log2 N times, must do N work each time

6
Review merge sort algorithm

• Start
• Unsorted list
• Break it down into smaller lists (size 1)
• Those lists are sorted
• Merge the sorted lists back together

7
Class Exercises

• Sort the following arrays using merge sort,
  showing the steps in partitioning and merging
• 24 12 63 89 7 50 95 14
• 92 91 52 42 89 23 18 12
• 28 14 11 19 15 52 80 17 60 59 72 24
  11 34 37 72

8
Making smaller lists

• Basic idea
• Dont create new arrays
• Just keep track of where each sub-list starts
  and stops
• Once you get down to size 1, the small list is
  sorted

Subscripts on first list are 0 (first item in
list) and 3 (last item in list)
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The first smaller list has subscripts 0 and 1
The second smaller list has subscripts 2 and 3
list (0..0)
list (1..1)
list (2..2)
list (3..3)
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Merging lists together

• Basic idea
• Start with smallest in each array
• Loop while you have items left in both lists
• Compare, put smallest of two in new array
• Get another item from that list and repeat the
  loop
• When one list is empty, copy over all remaining
  items from other list

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Merge Sort algorithm part 1

• Parameters
• Array
• Start of this sublist
• End of this sublist
• If array is of size one, this part is sorted
• Otherwise, break into smaller pieces and sort
  them
• Merge the small sorted pieces together
• Use a different function

• void MergeSort ( int array , int a, int z )
  
• // 1 element array is sorted
• if (az) return
• // Find the middle of the array
• int mid (az)/2
• // Make smaller sorted lists
• MergeSort( array, a, mid )
• MergeSort( array, mid1, z )
• // Merge the two sorted halves
• Merge( array, a, mid, z )

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Merge Sort algorithm part 2

• Merge two adjacent lists
• That is why you only need 3 subscripts
• Lists adjacent in array

• int tempList10 // needed temp array
• // better way in CS 124
• void Merge ( int array , int f, int m, int l )
  
• int i f, j m1, k f
• // Merge arrays until one is exhausted
• while (i ltm j lt l)
• if (arrayi lt arrayj)
• tempListk arrayi
• else
• tempListk arrayj
• int low, high
• // Determine which array is left
• if (i gt m) low j high l
• else low i high m
• // Merge rest of unexhausted array
• for (int t low t lt high t)
• tempListk arrayt
• // Copy temp array back to arrayf..l
• for (k f k ltl k)

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Example executing merge sort

• Array 70 29 87 67
• Main callsMergeSort with
• Array 70, 29, 87, 67
• First 0
• Last 3

• Trace of the function calls
• Calling MergeSort with first0 last3
• Calling MergeSort with first0 last1
• Calling MergeSort with first0 last0
• Calling MergeSort with first1 last1
• Calling Merge with first0 middle0 last1
• Calling MergeSort with first2 last3
• Calling MergeSort with first2 last2
• Calling MergeSort with first3 last3
• Calling Merge with first2 middle2 last3
• Calling Merge with first0 middle1 last3

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29
87
67
70
29
87
67
87
29
70
67
29
70
67
87
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67
70
87
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Class Exercise

• The file sort.cpp contains a C program that
  implements merge sort and selection sort.
• Copy this program into Visual Studio .NET and
  compile it
• Run it a few times with small data (8 or 16 or 32
  or 128 items)
• Print the data before (youll have to add cout
  statements)
• Print the data afterwards
• Print the intermediate calls in merge sort
• Watch how long selection and merge sort take
• Try it with bigger data sets
• Dont do all the printing (before, after, calls)
• 1000 and 10,000 and 100,000 and 500,000 and
  1,000,000
• How do the speeds compare once you get to bigger
  data sets?

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Topics in CS 114 course (outline)

• Data types
• int, char, double, float, string
• Basic operators
• Arithmetic , , , /,
• Relational lt, lt, , !, gt, gt
• Boolean , , !
• Levels of precedence
• Sequence
• Assignment statements
• , , -, , etc
• Input and output
• cin, cout, file input output
• Selection
• If statement
• Switch statement (and break)
• Iteration
• While loop
• For loop

• Functions
• Declaration vs. definition
• Parameters
• Pass-by-value pass-by-reference
• Local variables
• Return type
• int, double, char, void, etc.
• Recursion
• Arrays
• One- multi-dimensional
• Passing arrays to functions
• Efficient algorithms
• Sequential search vs. Binary search
• Selection sort vs. Merge sort
• Character and string variables
• Classes
• What is a data type?
• Using new user-defined types

15
Review Questions

• Questions
• What is the difference in
• a a 1
• a
• a
• a 1
• What is the difference in
• include ltiostreamgt
• include ltfstreamgt
• What function allows you to test for end-of-file?
• Why is the file close() function used?

• Practice, evaluate
• int a5, b10, c15, d20
• cout ltlt c/b ltlt endl
• coutltlt(double) c/b ltltendl
• cout ltlt cd ltlt endl
• cout ltlt cb ltlt endl
• cout ltlt ab/cd ltlt endl
• cout ltlt b ltlt endl
• cout ltlt d ltlt endl

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Review Questions (page 2)

• Write using for
• int a10
• while (alt25)
• cout ltlt a ltlt endl
• Write using while
• for (int a100 agt0 a-5)
• cout ltlt a ltlt endl
• What does this do?
• for (int a0 alt10 a)
• cout ltlt a ltlt endl

• Evaluate
• for (int a0 alt5 a)
• switch (a)
• case 0
• if (a) coutltltYltltendl
• else cout ltlt Nltltendl
• case 1
• case 2
• cout ltlt 9(a1) ltlt endl
• break
• default
• cout ltlt a ltlt endl

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Review Questions (page 3)

• Questions
• How can you pass back three values from a
  function?
• Can you have a function with no parameters that
  returns void?
• Can you mix pass-by-value and pass-by-reference
  parameters in the same function?
• Can a function have a local variable and a
  parameter with the same name?

• Questions
• Which subscript refers to the first element in an
  array?
• Which subscript refers to the last element in an
  array of 500 items?
• When passing an array as a parameter to a
  function, do you have to declare its size?

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Review Questions (page 4)

• The size of the data (input) plays a role in how
  long it takes to execute a process
• The bigger the data set, the longer the time
• Some algorithms are not efficient
• Makes a difference with large data sets
• Classes
• What is a data type?
• Representation of the info
• Operations that can be performed on this info

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Course Evaluations

• This is a serious instrument.
• Department heads Deans take note of these
  numbers.
• Written comments are encouraged, if you have
  something to say beyond the numbers.
• The instructor is not supposed to be in the room
  while you fill it out. (so Im leaving!)
• I need a volunteer to take the completed surveys
  to the CS office (101 Houser).

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End of Class 25