1. Arrays Includes Some Review
CIS265/506
Arrays
Includes Some Review
CIS265/506: Chapter 02

2. Introduction
Imagine we have a problem that requires us to process 20 integers. We could put every number in a different variable:
Number_0
Number_1
Number_2
Number_19
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3. Introduction In Java it will simply be something like:
int number1, number2, number3, number4, number5,
number6, number7, number8, number9, number10,
number11, number12, number13, number14, number15,
number16, number17, number18, number19, number20;
Easy, but that looks like it could be troublesome to manage.
Well, maybe not for 20 integers, but what about 20,000?
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4. Introduction
What if we make one variable that can hold all our integers? Then we only have one name to remember… that might make it easier.
For this, we use a powerful structure called an array.
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5. What is an Array?
An array is a fixed size, sequenced collection of elements of the same data type
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6. What is an Array? Elements scores scores[0] scores[1] scores[2]
Indexes
scores[0]
scores[1]
scores[2]
scores[3]
scores[4]
scores[5]
scores[6]
scores[7]
scores[8] 23 45 12 67 95 56 34 83
Elements
Name of the array
scores
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7. Sept 3, 1998
Arrays
An array’s name is a symbolic reference for the address to the first byte of the array. The index represents an offset from the beginning of the array being referred to.
elementAddress = arrayAddress + (sizeof(element) * index)
Let us say that this spot is address location “A21”
Imagine this is an array of integers. If we want the address of element 4, we would say:
Address of E[4] = A21 + (2 * 4) = A = A29
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8. What is an Array?
An array must be declared and defined before it is used
Declaration & definition tell the compiler the name of the array, the type of each element, and the size or number of elements in the array
The size is constant and must have a value at compile time
These are called “Static Arrays”
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9. A small difference Java supports Dynamic Arrays
The size can be given at compile or run time
Use the new operator
Arrays are objects in Java
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10. How do we declare an array?
We can declare and define in two steps or one.
Two steps
One step
int[ ] scores;
scores = new int[9];
int[ ] scores = new int[9];
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11. Declaring Arrays char [] vowels; // Declare a character array variable
vowels = new char[5]; // Define an array of 5 characters
The declaration statement declares the array name. It does not allocate any space in memory
The definition statement will create enough space in memory to store a character array of length 5.
The vowels will have every element initialized to ‘\u0000’ (Unicode null character).
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12. Initial Values Java arrays are initialized to a default value
A good practice is to initialize them to your own value(s)
All numeric arrays are initialized to zero
All boolean arrays are initialized to false
All character arrays are initialized to ‘\u0000’
All class-type arrays are initialized to null
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13. Storing Values in the array
We can store (or place) values in our array in two different ways
Initialize the array
Input values during execution of the program
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14. Initializing the Array
Method One: When the array is declared
Method two: One element at a time
int[ ] scores = { 23, 45, 12, 67, 95, 45, 56, 34, 83};
scores[0] = 23;
scores[1] = 45;
scores[2] = 12;
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15. Initializing the Array
Method three: Using Loops
Initializing the array using a loop is useful if the array values are sequential or dependant on some function (i.e. a random set of numbers)
int[ ] scores = new int[9];
for (int z = 0; z < 9; z++) {
scores[z] = z; }
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16. Array Length
Once you have created the array, you can use the length attribute (a data member of the array object).
Why? Knowing the length will prevent you from going past the ‘end’ of the array – trying to access elements that are not there
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17. Initializing the Array with Array Length
We use length, a data member of the array object:
int[] scores = new int[9];
for (int z = 0; z < scores.length; z++) {
scores[z] = z; }
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18. Array Length double[] samples = new double[50];
for (int L1 = 0; L1 < 50; L1 ++) {
samples[L1] = * Math.random(); // random values }
double average = 0.0;
for (int L2 = 0; L2 < samples.length; L2++) {
average += samples[L2];
average /= samples.length;
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19. How do we look at each element?
Java uses an index to access the individual elements
The index is usually some numeric constant, and is always an integer i
i -1
i + 1
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20. Accessing Array elements
Refer to an element of an array by the array name followed by the element’s index in square brackets
Remember that the array starts with index zero!
vowels[0]
vowels[1]
vowels[2]
vowels[3]
vowels[4] 1 2 3 4
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21. Accessing Array elements
What happens if you attempt access an array element that does not exist?
For instance vowels[10] ?
Java will throw an EXCEPTION – or generate an error.
This exception is called IndexOutOfBounds
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22. Working with the array public class scores {
public static void main(String[] args) {
int[ ] scores = { 23, 45, 12, 67, 95, 45, 56, 34, 83};
int sum = 0;
for (int i = 0; i < scores.length; i++) {
sum += scores[i]; }
System.out.println("The sum of the scores is: " + sum);
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23. Sept 3, 1998
Arrays
To copy one array to another, you must copy each element individually:
for (j = 0; j < 25; j++) { second[j] = first[j]; }
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24. Arrays of Objects
Now that we have made arrays of primitive data types, you can start to think to yourself that we should be able to make arrays of anything
You're right
Well… there may be some things we can't make arrays from, but at least for today, there are probably no limits
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25. Book class public class Book { // class variables
private String title;
private int pages;
// constructor
public Book(String title, int pages) {
this.title = title;
this.pages = pages; }
// mutators
public Book() {
this.title = "";
this.pages = 0;
public int getPages() {
return pages;
public void setPages(int p) {
pages = p;
public String getTitle() {
return title;
public void setTitle(String t) {
title = t;
public void showBook() {
//user defined method to show data
Book class

26. public class Book_Driver { public static void main(String[] args) {
// reserve memory space for 4 Book objects
Book[] theBooks = new Book[4];
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27. // Actually create each book
theBooks[0] = new Book(); // Call the constructor
theBooks[0].setPages(450);
theBooks[0].setTitle("The Shining");
theBooks[1] = new Book();
theBooks[1].setPages(900);
theBooks[1].setTitle("Java By Example");
theBooks[2] = new Book();
theBooks[2].setPages(225);
theBooks[2].setTitle("100 Years of Solitude");
theBooks[3] = new Book();
theBooks[3].setPages(51);
theBooks[3].setTitle("The McGuffey Reader");
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28. /*******Show results *******/ for (int i = 0; i < 4; i++) {
System.out.println("Book " + (i+1) + " is " +
theBooks[i].getTitle() + " with " +
theBooks[i].getPages() + " pages." ); }
Book 1 is The Shining with 450 pages.
Book 2 is Java By Example with 900 pages.
Book 3 is 100 Years of Solitude with 225 pages.
Book 4 is The McGuffey Reader with 51 pages.
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29. Searching Arrays
To search through an array, we combine a "for" loop and (usually) an "if" statement
We look at each element in the array (iteration), and ask if that element meets our criteria (condition testing)
If so we do something, if not we (usually) skip it
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30. for (int i = 0; i < prices.length; i++ ) { sum += prices[i];
public class priceChecker {
public static void main(String[] args) {
// declare & initialize the array
double[] prices = {2.34, 3.11, ,9.32, 4.00, 7.11,
5.01, 6.43, 2.11, 0.32, 21.21, 32.11,
11.65, 1.12, 0.88, 1.13, 5.12, 6.99, 7.99, 1.88};
// declare and initialize sum, average
double sum = 0.0;
double average = 0.0;
// Column Heading for the first thing we need to print
System.out.println("The values less than 5.00 are: ");
// loop thru the array
for (int i = 0; i < prices.length; i++ ) {
sum += prices[i];
if (prices[i] < 5.00) {
System.out.println("\t" + prices[i]); }
… Code continues…
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31. Arrays & Methods How do you pass an array to a function?
Sept 3, 1998
Arrays & Methods
How do you pass an array to a function?
Individual elements are passed to a function like any ordinary variable.
To pass the entire array - in the calling function, use the array name as the actual parameter.
In the called function, you need to say that the corresponding formal parameter type is an array.
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32. Passing Arrays to Methods
When we pass an entire array to a method, we pass the address of the array
This means our method not only has access to every element in the array, but can change each element as well
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33. changeArray(myArray);
public class passingArrays {
public static void changeArray(int[] newArray) {
System.out.println("In Method \n\n\nOld Value\tNew Value");
for (int i=0; i < newArray.length; i++) {
System.out.print(newArray[i] + "\t\t");
newArray[i] += 3;
System.out.println(newArray[i]); }
System.out.println("\n\nReturning from method\n\n");
public static void main(String[] args) {
int[] myArray = {1, 2, 3, 4, 5};
System.out.println("In Main \n\n\nValue");
for (int i=0; i < myArray.length; i++) {
System.out.println(myArray[i]);
System.out.println("\n\nGoing to method\n\n");
changeArray(myArray);
System.out.println("In Main After Method\n\n\nValue");

34. In Main
Value 1 2 3 4 5
Going to method
In Method
Old Value New Value
1 4
2 5
3 6
4 7
5 8
Returning from method
In Main After Method 6 7 8

35. Arrays of Arrays
Just as we had arrays with one index, we can have arrays with multiple indices.
We call these multi-dimensional arrays
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36. An array of arrays 1 2 3 4 0 1 2 3 4 First dimension (rows)1 2 3 4
Second dimension (columns)
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37. An array of arrays (row-wise)
table[0][0] table[0][1] table[0][2] table[0][3]
table[0]
table[1][0] table[1][1] table[1][2] table[1][3]
table[1]
table[2][0] table[2][1] table[2][2] table[2][3]
table[2]
table
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38. Working with two-dimensional arrays
// declare & initialize the array
int[ ][ ] table = {
{ 0, 1, 2, 3},
{10, 11, 12, 13},
{20, 21, 22, 23} };
// printing the array
for (int i = 0; i < table.length; i++) {
for (int j=0; j < table[i].length; j++) {
System.out.println(
" i = " + i + " , j = " + j +
" and the array value is " +
table[i][j]); }
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39. Data Structures
Searching
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40. Introduction
Consider the problem of looking up a word to see if it is spelled correctly.
How would we do this?
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41. Introduction
We could start out by making a list of all the words known to us.
This could be a huge list… right?
How would we manage the list?
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42. Introduction First, the obvious things: Now, the not-so-obvious:
Maintenance:
Inserting, deleting, updating
Now, the not-so-obvious:
How do we EFFICIENTLY find anything in a list so large?
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43. What we know... We could store this in a list
How do we find things in a list?
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44. A few terms... a table or file contains groups of elements
each group is called a record
COBOL File:
xxxxxx yyyyyyy zzzz aa qq  a record
xxxxxx yyyyyyy zzzz bb qq  a record
xxxxxx yyyyyyy zzzz cc qq  a record
xxxxxx yyyyyyy zzzz dd qq  a record
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45. A few terms... Each record has a key keys can be simple or complex
If the key is part of the record, it is internal or embedded
If there is a separate list of keys (for example, a table of items that point to the records), these are called external keys
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46. Keys: Examples
Your address book collection: <Last name, First name>
What if each person has a home phone, business phone, fax, cell phone, …… ?
Maybe we need to assign each a number to each person, and another id for the type of phone.
Person PhoneType Person PhoneType 1 H 2 H 1 W 2 W 1 C 2 C 1 F 2 F
That might work….
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47. Keys: Examples Would these be internal or external keys? It depends.
1 H 1 W 1 C 1 F
Bill Smith Bill Smith Bill Smith Bill Smith
these are ……._______________?
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48. Keys: Examples
1 H Bill Smith W Bill Smith C Bill Smith F Bill Smith
these are ……._______________?
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49. Keys
Why did we go to so much trouble to make sure our key pointed to only a single record? What is wrong with using just last name?
What if Bill Smith has a son, who is also Bill Smith? And Junior also has four phone numbers? Wow. How do we keep track?
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50. Keys
We call the key or set of keys that makes each record unique the primary key.
Generally speaking, a primary key is always unique.
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51. Keys We can also have a key that is used to sort items
Example: Suppose you want to sort your phone list by state, so you can plan a trip to visit everyone.
“State” is not unique - many people live in one state.
We call this key a secondary key - it does not have to be unique.
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52. Now what?
We now have a pretty good idea how our data elements are organized.
We can now start to think of a search algorithm that will be optimized for our data.
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53. A few more terms…
A search algorithm is a methodology to find a requested value. (Note we never mention how - that is still a ways away.)
The algorithm can return an entire record, a pointer to the record, or nothing (The requested item was not found, so NULL was returned).
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54. A few more terms…
An algorithm that inserts a new record whenever the search value indicates it was not found, is called a placement or search & insertion algorithm
A search process is called a retrieval.
A table of records in which a key is used for retrieval is called a search table, index or dictionary
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55. A few more terms…
Searches in which the entire table is constantly kept in main memory are called internal searches
Searches which use auxiliary storage (disks, tapes,…) are called external searches
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56. Performance Predication and the “Big O” Notation.
One way of deciding what algorithm is “better” is to figure out how the running time of the algorithm will vary or grow as a function of the “problem size”.
Problem size takes into account things like the number of elements in the array, the number of records in the file and so forth.
Your algorithm may work well & quickly for a small file, but may take an extraordinarily long time when running on a large data set.
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57. Performance Predication and the “Big O” Notation.
An example: What if you have a program that takes
1 second on a block holding10 records,
4 seconds on 2 blocks (each holding 10 records),
100 seconds on 10 blocks (each holding10 records).
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58. Performance Predication and the “Big O” Notation.
An example: continuation
Observe the relationships are:
1sec:1b lock, 4sec:2bloks, 100sec:10block
The running time of this program varies with the square value of the sample size
time ≈ numberBlocks2
Therefore 1000 records (fitting in 100 blocks) will predictably take 10,000 seconds (about 3 hours!) and 10,000 records (1000 blocks) will take two weeks!!
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59. Performance Predication and the “Big O” Notation.
We will look at a few ways to determine growth rate of algorithms. This growth rate is often called the “Big O (‘oh’) Notation” - where the ‘O’ is “order of magnitude”.
For the previous example we write the order formula
O(2 n)
Where n represents the number of blocks in the file.
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60. Performance Predication and the “Big O” Notation.
How do we try & predict the growth rate?
We try and write a formula for the computational time in terms of the program size n.
This formula takes into account programming language, compiler, and computer.
The formula allows for a estimate of complexity that can be used for comparison of growth rate from one problem to another.
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61. Performance Predication and the “Big O” Notation.
The common growth rates you will encounter include: (from highest to lowest)
O(n!) - factorial growth rate
O(n3) - cubic growth rate
O(n2) - quadratic: proportional to the square of N
O(n * log(n)) - usually written as O(nlogn)
O(n) - linear growth rate
O(log(n)) - logarithmic growth rate
O(K) - constant growth rate
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62. Performance Predication and the “Big O” Notation.
O(n) - linear
O(logn) -
logarithmic
O(K) - constant
O(nlogn) - logarithmic
O(n2) - quadratic
O(n3)
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63. Performance Predication and the “Big O” Notation.
OBSERVATION
Fast algorithms have lower orders (constant, linear, …)
Slow algorithms have higher orders (exponential, factorial…)
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64. Performance Predication and the “Big O” Notation.
How do we estimate the growth rate of an algorithm?
If you have a simple statement - like an assignment statement, or some other statement without any function calls - the growth rate of this statement is O(K) or constant.
The growth rate of a (nested) counting loop is some function of N - either constant, O(N), O(N2), O(N3), etc.
The growth rate of a multiplicatively-controlled loop is some function of logN - either O(logN), O(NlogN), etc.
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65. Performance Predication and the “Big O” Notation.
A counting loop is something like:
for (i=1; i< 10; i++) { some activity; }
A multiplicatively-controlled loop is something like:
for (i=1; i< 100; i=i*2) { some activity; }
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66. Performance Predication and the “Big O” Notation.
We’ll leave the proofs & further discussion of this topic for the algorithm class.
However, you will need some understanding of this to see why one searching/sorting algorithm is more efficient than another.
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67. Sequential Searching
A sequential search starts at the beginning of an array, and goes from one cell to the next until the item is found, or the end of the array is reached.
A sample code fragment:
for (i = 0; i < n; i++) if (searchItem == array[i]) return i; return (-1); //Not found!
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68. Sequential Searching searchItem1 = 21 searchItem2 = 22 17 19 21 23 251 2 3 4 5 6 7 8 9 10 11 12 13 15 17 19 21 23 25 27 29 31
searchItem1 = 21
searchItem2 = 22
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69. Sequential Searching
If we search an array for a record, and do not find it, what next?
Exit Routine
Report message to user
Add the Element
Must insure no two records have the same key
Can not go past the upper bound of the array
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70. Sequential Searching
We can eliminate some of these problems by changing the supporting data structure to a linked list, rather than an array.
Why linked lists will be better?
No worries about upper bounds checking
Can insert in-order and uniqueness checks will not be as difficult.
Deleting an element from a list is very simple.
The efficiency of a sequential search is O(n)
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71. Important Points
It is (obviously?) more efficient to search an ordered group of elements vs. an unordered group
It is “easier” to work with lists vs. arrays
The data structures and actual search techniques are application specific
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72. Indexed Sequential Search
The indexed sequential search can speed searching in a sorted file
An auxiliary table, called an index, is built.
The index is held in addition to the sorted file
We find where our item would fall in the index & search only that section of the sorted file.
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73. Indexed Sequential Search
Imagine a phone book:
Your friend’s last name starts with “S”. Rather than start at the beginning of the phone book, and search the entire book for your friend’s number, you start at the section beginning with “S”.
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74. Indexed Sequential Search
key Record Able Amos Baker Blue Charlie Delta Dumas Echo . . .
key index pointer index A B C D E . . .
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75. Indexed Sequential Search
The algorithm:
Search the index table until you find the place where the record might be located.
Follow the pointer pointerIndex to reach the correct record location on the main sorted file.
Search the area between the pointerIndex where you started and the next pointerIndex.
Record found: return the key
Record not found: Either insert record, or return message to user.
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76. Indexed Sequential Search
Things to watch out for:
If there are multiple records with the same key, your search may not always return the first one!
Application specific
If the index table is very large, a secondary index table can be built
Insert & delete not as trivial as they may seem
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77. Binary Search Very efficient Does not involve auxiliary tables.
Can be used with auxiliary tables, not not necessary.
Can be either recursive or non-recursive
Most algorithms require this search to be used on an array.
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78. Binary Trees 1 1 = 2 - 1 2 3 = 4 - 1 4 7 = 8 - 1 8 15 = 16 - 1 2n
Level
Nodes at
this level
Total nodes
in the tree 1
1 = 2 - 1 2
3 = 4 - 1 4
7 = 8 - 1 3 8
15 = n 2n
2n+1 – 1
Binary Trees
Level 0
0.1
Level 1
1.1
Level 2
2.1
2.2
1.2
2.3
2.4
A search is done by traversing the tree from one level to the next.
A data set of size n that is arranged as a balanced binary tree has log2(n) levels.
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79. Binary Search Insertions & Deletions
Not trivial to insert or delete items from arrays and still maintain order.
Several algorithms exist for this purpose
The efficiency of a binary search is O(logn)
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80. Binary Search
Assume you have a sorted list. You are looking for an item in the list.
1. Choose the center of the list.
2. Is your item greater than, equal to or less than the center point?
2a. Greater - Repeat items 1 & 2 with the upper half of the list
2b. Equal - Exit routine, returning the index of the array
2c. Less - Repeat items 1 & 2 with the lower half of the list
3. If not found, exit with message to user
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