Transcript Searching and Sorting Copyright Prentice Hall Modified by Sana odeh, NYU Road Map  Search – Linear search – Binary search  Sort – Selection sort – Bubble sort (not.

Searching and Sorting
Copyright Prentice Hall
Modified by Sana odeh, NYU
Road Map

Search
– Linear search
– Binary search

Sort
– Selection sort
– Bubble sort (not covered in the book)

Reading:
– Liang 4: chapter 5, 5.7 & 5.8
– Liang 5: chapter 5, 5.6 & 5.7
– Liang 6: chapter 6, 6.7 & 6.8
Searching Arrays
Searching is the process of looking for a
specific element in an array; for example,
discovering whether a certain score is included
in a list of scores. Searching, like sorting, is a
common task in computer programming. There
are many algorithms and data structures
devoted to searching. In this section, two
commonly used approaches are discussed,
linear search and binary search.
Linear Search
The linear search approach compares the key
element, key, with each element in the array
list[]. The method continues to do so until the
key matches an element in the list or the list is
exhausted without a match being found. If a
match is made, the linear search returns the
index of the element in the array that matches
the key. If no match is found, the search
returns -1.
Example 5.10
Testing Linear Search
 Objective:
Implement and test the linear search
method by creating an array of 10 elements of
int type randomly and then display this array.
Prompt the user to enter a key for testing the
linear search.
LinearSearch
Run
http://www.cosc.canterbury.ac.nz/people/mukundan/dsal/appldsal.
html
Searching
Linear Search is not very efficient.
 In the worst case, the target we are searching
could be placed at the very end of the array,
requiring that we search every single element in
the array.
 On average, the target might be somewhere in the
middle of the array, requiring that we search half
of all the elements in the array.
 For example, if we had a 1000 element array:
– worst case: we must search 1000 elements
– on average: we search about 500 elements

Binary Search



Binary Search is a more efficient option for searching
arrays.
There are two tricks to using Binary Search:
– First, the array must be sorted. (Before you use Binary
Search, you might first sort the array.)
– Second, Binary Search works by dividing the search
area in half after each comparison (more on this soon.)
Binary Search is used very commonly in computer science,
and there is a related concept called Binary Search Trees.
– If you take an Algorithms course, you will definitely
spend time researching Binary Search Trees.
Binary Search Pseudo Code
1.
2.
3.
4.
Create a sorted array of sample data.
Prompt user for a search target.
Locate the middle of the array.
Compare the middle element with the search target:
a) If the search key is equal to the middle element, we
have a match! Exit Loop
b) If the search key is less than the middle element,
search the first half of the array (back to Step 4)
c) If the search key is larger than the middle element,
search the second half of the array (back to Step 4)
Binary Search Applet
 Search
/ Sort Applets:
– http://www.cosc.canterbury.ac.nz/people/muku
ndan/dsal/appldsal.html
 Blue:
indicates that these elements have been
eliminated from the search.
Example 5.11
Testing Binary Search
Implement and test the
binary search method. The
program first creates an array
of 10 elements of int type. It
displays this array and then
prompts the user to enter a key
for testing binary search.
 Objective:
BinarySearch
Run
Binary Search, cont.
key = 1 1
[0 ] [1 ] [2 ] [3 ] [4 ] [5 ] [6 ] [7 ] [8 ] [9 ] [1 0 ] [1 1 ] [1 2 ]
list
2
4
7
10
11
45
key < 5 0
m id
[0 ] [1 ] [2 ] [3 ] [4 ] [5 ]
2
key > 7
4
7
10
11
45
m id
[3 ] [4 ] [5 ]
10
key = 1 1
50
11
m id
45
59
60
66
69
70
79
Binary Search Efficiency



Binary Search is very efficient.
For example, if you have 1024 elements in you array, in
the worst case, binary search only requires 10
comparisons.
– Linear Search Worst Case: 1024
– Binary Search Worst Case: 10
If you have 1 billion elements, binary search only requires
30 comparisons!
– Linear Search Worst Case: 1 billion
– Binary Search Worst Case: 30!
Sorting
Sorting data is one of the most important
computing applications.
 Examples:

– Banks sort all checks by account number in order to
prepare individual bank statements.
– Telephone companies sort accounts by last name, first
name in order to create phone books.
Sorting data has attracted intense research efforts
in computer science.
 In this lecture, we explore the two of the simplest
known sorting algorithms.

Selection Sort Applet
Before examining any code, let us first try out a
Java applet for Selection Sort.
 The Applet lets you step through each step in the
algorithm, so that you can gain an intuitive sense
of how it works.
 Just go to:
http://math.hws.edu/TMCM/java/xSortLab/

– Click the “Start Again” Button to get a new set of
random numbers.
– Click “Go” to sort.
– Click “Step” to step through the algorithm.
Example 5.12: (Cont) Using
Arrays in Sorting
int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted
Find the largest element in myList and swap it with the last
element in myList.
2, 9, 5, 4, 8, 1, 6 => 2, 6, 5, 4, 8, 1, 9 (size = 7)
2, 6, 5, 4, 8, 1 => 2, 6, 5, 4, 1, 8 (size = 6)
2, 6, 5, 4, 1 => 2, 1, 5, 4, 6 (size = 5)
2, 1, 5, 4 => 2, 1, 4, 5
2, 1, 4 => 2, 1, 4,
2, 1 => 1, 2
Sort it to produce 1, 2, 4, 5, 6, 8, 9
Example 5.12
Using Arrays in Sorting

Objective: Use the selectionSort method to write a
program that will sort a list of double floating-point
numbers.
int[] myList = {2, 9, 5, 4, 8, 1, 6}; // Unsorted
Sort it to produce 1, 2, 4, 5, 6, 8, 9
2, 9, 5, 4, 8, 1, 6
SelectionSort
Run
Bubble Sort
Bubble sort is another option for sorting a list of
numbers.
 It’s called bubble sort because

– larger values gradually “bubble” their way upward to
the end of the array like air bubbles rising in water.

The technique is to make several passes through
the array.
– On each pass, pairs of elements are compared.
– If the pair is in increasing order, we leave the values as
they are.
– If the pair is in decreasing order, we swap the values.
Bubble Sort Applet
Before examining any code, let us first try out a
Java applet for Bubble Sort.
 The Applet lets you step through each step in the
algorithm, so that you can gain an intuitive sense
of how it works.
 Just go to:
http://math.hws.edu/TMCM/java/xSortLab/

– Click the “Start Again” Button to get a new set of
random numbers.
– Click “Go” to sort.
– Click “Step” to step through the algorithm.
Advantages / Disadvantages of
Bubble Sort and Selection Sort
The main advantage of these two sorting
algorithms is that it is easy to program.
 The main disadvantage is that it is very slow.
 Much work in computer science has been geared
towards creating more efficient sorting algorithms.


For example:
– Merge Sort
– Bi-directional Bubble Sort
– Quick Sort

For another quick demo, check out:
http://java.sun.com/applets/jdk/1.4/demo/ap
plets/SortDemo/example1.html