1. Introduction to Computer Science and Object-Oriented Programming
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2. Tonight More Array Operations Sorting and Searching Potpourri
Test 2 Review
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3. A Small Challenge Write the code for the swap method
In some class you have
an instance variable int[] val
and a method private void swap(int i, int j)
that swaps the values in positions i and j
Write the code for the swap method
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4. How many assignments does it take to swap?
A Small Challenge
private void swap(int i, int j) {
int temp = a[i];
a[i] = a[j];
a[j] = temp; }
How many assignments does it take to swap?
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5. Another Challenge Same set up What’s this method do?
private void mystery(int left, int right) {
int temp = a[right];
for (int j = right-1; j >= left; j--)
a[j] = a[j-1]; }
a[left] = temp;
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6. How many assignments are done?
Another Challenge
private void mystery(int left, int right) {
int temp = a[right];
for (int j = right; j > left; j--)
a[j] = a[j-1]; }
a[left] = temp;
How many assignments are done?
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7. Feeling Out of Sorts?
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8. Sorting Data processing / information processing
one of the earliest computing domains
often simple, repetitive calculation
payroll, inventory, etc.
Critical was the ability to
store and search for info
prepare reports
Fundamental to this was sorting
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9. Sorting Sorting was critical Much effort went into for reports
for more effective searching
Much effort went into
finding better ways to sort
comparing ways to sort
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10. To Understand Sorting An array of values
with positions/indices
that we can separate into “regions”
Criterion for ordering given two values
either they are equal
or one comes before the other in order
[0] [1] [2] [3] [4]] 5 9 17 11 12
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11. In the to sort region, find the minimum and swap with next to fill
Selection Sort
Simple sort
Think of regions
next to fill
[0] … …
sorted
to search
In the to sort region, find the minimum and swap with next to fill
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12. Selection Sort 11 9 17 5 12 11 9 17 5 12 5 9 17 11 12 Ready for pass 1
to search
Search for min 11 9 17 5 12 5 9 17 11 12
Ready for pass 2
to search
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13. Selection Sort 5 9 17 11 12
Ready for pass 2
to search 5 9 17 11 12
Ready for pass 3 5 9 11 17 12
Ready for pass 4 5 9 11 12 17
Ready for pass 5
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14. In the sorted region, find the place to insert the next to place
Insertion Sort
Simple sort
Think of regions
next to place
[0] … …
sorted
In the sorted region, find the place to insert the next to place
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15. Insertion Sort 11 9 17 5 12 11 9 17 5 12 9 11 17 5 12 Initial state
sorted 11 9 17 5 12
Begin first pass
1st pass begins at pos 1
to sort 9 11 17 5 12
Begin second pass
2nd pass begins at pos 2
sorted
Sort the region by placing and shifting
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16. Insertion Sort 9 11 17 5 12 5 9 11 17 12 5 9 11 12 17 Begin third pass
3rd pass begins at pos 3
Begin fourth pass 5 9 11 17 12
4th pass begins at pos 4 5 9 11 12 17
Final state
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17. In the sorted region, find the place to insert the next to place
Bubble Sort
Simple sort
Think of regions
next to place
[0] … …
sorted
unsorted
In the sorted region, find the place to insert the next to place
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18. Bubble Sort
Compare the first two elements of the array. If the first element is larger than the second
Then swap them
Otherwise, leave them alone.
Repeat this step
for the second and third element
then the third and fourth
and so on.
At the end of the first pass the last number in the array is the largest.
Repeat for as many times as elements in the array
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19. Bubble Sort 11 9 17 5 12 11 9 17 5 12 9 11 5 12 17 Initial state
Begin first pass
1st pass compare pattern: 9 11 5 12 17
Begin second pass
2nd pass compare pattern:
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20. Bubble Sort 9 5 11 12 17 5 9 11 12 17 5 9 11 12 17 Begin third pass
3rd pass compare pattern: 5 9 11 12 17
Begin forth pass
4th pass compare pattern: 5 9 11 12 17
Final state
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21. Profiling 9 5 11 12 17 5 9 11 12 17 5 9 11 12 17 Begin forth pass
3rd pass compare pattern: 5 9 11 12 17
Begin forth pass
4th pass compare pattern:
Begin third pass 5 9 11 12 17
Final state
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22. Comparing Sort Approaches
Historically, sorting was
Critical
Costly
Studied
What is the efficiency of the sort algorithms?
Which is the best to use?
Approaches
Profiling
Algorithm analysis
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23. Profiling Use a “stopwatch” approach
Use the system clock to get time of execution in milliseconds
The steps
Get CPU clock time (t1)
Run sort method
Get CPU clock time (t2)
Sort time (approximately) is t2 – t1
Time
numbers
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24. Profiling Elements Bubble Selection Insertion 2,560 31 15 5,120 125 47
Sort time in milliseconds for various array sizes
Elements
Bubble
Selection
Insertion
2,560 31 15
5,120
125 47
20,480
1,969
875
563
81,920
31,391
14,047
9,125
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25. Analyzing Sort Algorithms
Analyze how many times each array element is “visited” during search.
Number of visits for selection sort (n numbers): ½ n2 + 5/2 n – 3
As n gets bigger, fastest growing term is n2
So rest of equation can be ignored.

26. Analyzing Sort Algorithms
Selection sort considered O(n2) algorithm - this is called Big-Oh notation
Selection sort, Bubble sort, and Insertion sort are all O(n2)algorithms

27. Searching When there are a large number of items to search
There are different strategies for finding a specific item:
Ordered or not
Where to look next

28. Linear Search
A linear search looks through list from the beginning until it encounters the desired item. Very simple, yet very inefficient.
If the list is sorted, the search process can end when a value greater than the one sought out is found.
int foundIt = -1;
for (int i = 0; i < array.length; i++) {
if (array[i] == searchValue)
foundIt = i;
break; // out of for loop }
// when done, foundIt holds position of item or –1
Linear search is O(?) algorithm

29. Binary Search A binary search assumes you start with a sorted list.
Algorithm:
The list is divided in half to find the mid-point.
At this mid-point, one of three states exist:
You have found the item.
The item is less than the mid-point.
The item is greater than the mid-point.
If the value sought is not found, divide the remaining space in half and find a new mid-point.
Repeat until you find the item or run out of space to divide.
Binary search is O(logn)

30. A View of Variables count  hgt1  score int count; Height hgt1;
count
primitive value
Height hgt1; 
hgt1
object reference
int[] score; 
score
array reference
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31. A View of Variables 5 count hgt1 score count = 5; hgt1 = new Height();
primitive value
hgt1 = new Height();
feet 
inches
hgt1
object reference
int[] score = new int[3];
[0] 
[1]
[2]
score
array reference
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32. A View of Variables 9 count hgt1 score count = 9; hgt1.setFeet(5);
primitive value
hgt1.setFeet(5);
feet 5 
inches
hgt1
object reference
score[1] = 10;
[0] 
[1] 10
[2]
score
array reference
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33. A View of Variables 10 count hgt1 score count = count + 1;
primitive value
this.inches = 4;
feet 5 
inches
hgt1
object reference
score[2] = score[1] - 1;
[0] 
[1] 10
[2] 9
score
array reference
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34. So What Is An Array? An array has a name has a type has a length
and is a reference to a collection of indexed …
values?
variables?
slots?
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35. classes can have instance fields that are arrays
Variations
classes can have instance fields that are arrays
an instance of Gradebook
“J. Doe”
name 
[0]
[1] 10 
[2] 9
score
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36. arrays can have class types
Variations
arrays can have class types
Height[] tall = new Height[3]; 5 10
feet
inches
[0] 
[1] 
[2]  6 4
feet
inches
tall[1] = new Height(5,10);
tall[2] = new Height(6,4);
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37. Some Examples
On BlueJ
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38. Array Algorithms You can calculate with numbers
You can manipulate Strings
What can you do with arrays?
count the elements
count the elements matching a condition
find element an element matching a condition
calculate min, max, sum average, etc.
and much more …
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39. Array Lists Arrays have some limitations Array lists
While we don’t need to fill them
They have a maximum number of elements
We have to program the operations (except for ….????)
Array lists
Can grow and shrink as needed
Provide useful methods
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40. ArrayLists All element of same type
Must be a class type (not primitive type)
Starts out empty
Has a size (starts out zero)
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41. Examples Constructing Adding Accessing
ArrayList<Customer> store1 = new ArrayList<Customer> ();
// newly created list, size is 0
Adding
store1.add( new Customer(“William Dodds”, ));
// size is 1 now
store1.add( new Customer(“Martha Shavers”, ));
// size is 2 now
Accessing
Customer cust = store1.get(1); // retrieves second object
int store1Size = store1.size(); // returns size (2)
Customer newCust = new Customer(“Lee Cash”, );
store1.set(1, newCust); // overwrites Martha with Lee
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42. Accessing Use get method Index starts at 0
BankAccount anAccount = accounts.get(2); gets the third element of the array list
Bounds error if index is out of range
Most common bounds error:
int i = accounts.size();
anAccount = accounts.get(i); // Error
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43. Adding Before
add(i,a)
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44. Removing remove removes an element at an index accounts.remove(i)
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45. Wrappers primitive types are not objects
so can’t use directly in ArrayLIst
so Java has wrapper classes
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46. Wrapper Class
  ArrayList<Double> data = new ArrayList<Double>();
data.add(29.95);
double x = data.get(0);
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47. Wrapper Classes Are classes Start with cap
Each contains a single value of corresponding type
Use where objects needed
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48. Auto-Boxing Automatic conversion between
primitive types and the corresponding wrapper classes is automatic. Double d = 29.95; // auto-boxing; same as Double d = new Double(29.95);
double x = d; // auto-unboxing; same as double x = d.doubleValue();
Auto-boxing even works inside arithmetic expressions
Double e = d + 1;
Means:
auto-unbox d into a double
add 1
auto-box the result into a new Double
store a reference to the newly created wrapper object in e
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49. Auto-Boxing A recent feature of Java Automatic conversion between
primitive types
corresponding wrapper class
Double d = 29.95;
Double d = new Double(29.95);
double x = d;
double x = d.doubleValue();
Double e = d + 1;
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50. Enhanced For Loop Recent addition to Java Shortcut for a common loop
for (typevariable : collection) {
statements }
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51. Examples double[] data = new double[100];
… assume that array is then populated
double sum = 0;
for (double e : data) {
sum = sum + e; }
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52. Examples ArrayList<BankAccount> accounts =
new ArrayList<BankAccount>();
… assume that array list is then populated
double sum = 0;
for (BankAccount a : accounts) {
sum = sum + a.getBalance(); }
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53. Two-Dimensional Arrays
int[][] table = new int[2][3];
The array identified by table will have
2 rows (the row is the FIRST subscript)
3 columns (the column is the SECOND subscript).
[0][0]
[0][1]
[0][2]
[1][0]
[1][1]
[1][2]
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54. Examples table[0][0] = 22; table[0][1] = 1301; . . . table[1][2] = 43;
for (int i = 0; i < 2; ++i)
for (int j = 0; j < 3; ++j)
System.out.println(table[i][j]);
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55. Self Check 7.1
What elements does the data array contain after the following statements? double[] data = new double[10];
for (int i = 0; i < data.length; i++) data[i] = i * i;
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56. Answer:
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, but not 100
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57. What do the following program segments print? Or, if there is an
Self Check 7.2
What do the following program segments print? Or, if there is an
error, describe the error and specify whether it is detected at
compile-time or at run-time.
double[] a = new double[10]; System.out.println(a[0]);
double[] b = new double[10]; System.out.println(b[10]);
double[] c; System.out.println(c[0]);
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58. Answer: a run-time error: array index out of bounds
a run-time error: array index out of bounds
a compile-time error: c is not initialized
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