1. Sorting and Searching -- Introduction
Two common programming tasks are sorting a list of items and searching for an item in a list
Chapter 13 focuses on:
Selection Sort
Insertion Sort
A generic sort for objects
Linear Search
Binary Search
Hashing
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

2. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Sorting
Sorting is the process of arranging a list of items into a particular order(순서대로 배치)
There are many algorithms for sorting a list of items
These algorithms vary in efficiency
We will examine two specific algorithms:
Selection Sort and
Insertion Sort
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

3. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Selection Sort
The approach of Selection Sort:
select one value and put it in its final place in the sort list
repeat for all other values
An expanded version:
scan the list to find the smallest value
put it in the first position
find the next smallest value
put it in the second position
repeat until all values are placed
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

4. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Selection Sort
An example:
original:
smallest is 1:
smallest is 2:
smallest is 3:
smallest is 6:
See Selection_Sort_Test.java
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

5. Example: Selection_Sort_Test
public class Selection_Sort_Test {
public static void main (String[] args) {
int[] numbers = {3, 9, 6, 1, 2};
Selection_Sort.sort (numbers);
for (int index = 0; index < numbers.length; index++)
System.out.println (numbers[index]);
} // method main
} // class Selection_Sort_Test
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

6. Example: Selection_Sort_Test
class Selection_Sort {
public static void sort (int[] numbers) {
int min, temp;
for (int index = 0; index < numbers.length-1; index++) {
min = index;
for (int scan = index+1; scan < numbers.length; scan++)
if (numbers[scan] < numbers[min])
min = scan;
// swap the values
temp = numbers[min];
numbers[min] = numbers[index];
numbers[index] = temp; }
} // method sort
} // class Selection_Sort
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

7. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Insertion Sort
The approach of Insertion Sort:
Pick any item and insert it into its proper place in a sorted sublist
repeat until all items have been inserted
An expanded version:
consider the first item to be a sorted sublist (of one item)
insert the second item into the sorted sublist, shifting items as necessary to make room to insert the new addition
insert the third item into the sorted sublist (of two items), shifting as necessary
repeat until all values are inserted into their proper position
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

8. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Insertion Sort
An example:
original:
insert 9:
insert 6:
insert 1:
insert 2:
See Insertion_Sort_Test.java
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

9. Example: Insertion Sort
public class Insertion_Sort_Test {
public static void main (String[] args) {
int[] numbers = {3, 9, 6, 1, 2};
Insertion_Sort.sort (numbers);
for (int index = 0; index < numbers.length; index++)
System.out.println (numbers[index]);
} // method main
} // class Insertion_Sort_Test
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

10. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
class Insertion_Sort {
public static void sort (int[] numbers) {
for (int index = 1; index < numbers.length; index++) {
int key = numbers[index];
int position = index;
// shift larger values to the right
while (position > 0 && numbers[position-1] > key) {
numbers[position] = numbers[position-1];
position--; }
numbers[position] = key;
} // method sort
} // class Insertion_Sort
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

11. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Comparing Sorts
Both Selection and Insertion Sorts are similar in efficiency
Outer loops that scan all elements, and
inner loops that compare the value of the outer loop with almost all values in the list
That is approximately n2 number of comparisons for a list of size n
We therefore say that these sorts are of order n2
Other sorts are more efficient: order n log2 n
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

12. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Sorting Objects
Integers have an inherent order
But the order of a set of objects must be defined by the person defining the class
Recall that a Java interface can be used as a type name and guarantees that a particular class has implemented particular methods
We can use this to develop a generic sort for a set of objects
See Object_Sort_Test.java
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

13. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Searching
The goal is to find a particular target value
In an unsorted list, a linear search is a simple technique
Scan through the list one item at a time in order looking for the target value
7, -3, 7, 2, 8, -1, 3, 2, 5, 6, 7
If the list is sorted, not all items need to be examined
As soon as you encounter a value greater than the target value, you know the target is not in the list
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

14. Example: Linear Search
public class Linear_Search_Test {
public static void main (String[] args) {
int numbers[] = {7, -3, 7, 2, 8, -1, 3, 2, 5, 6, 7};
System.out.println ("The index of 6 is " +
Linear_Search.search (numbers, 6));
} // method main
} // class Linear_Search_Test
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

15. Example: Linear Search
class Linear_Search {
public static int search (int[] numbers, int target) {
int index = 0;
while (index < numbers.length) {
if (target == numbers[index])
return index; // target found
index++; }
return -1; // target not found
} // method search
} // class Linear_Search
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

16. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Binary Search
If the list is sorted, we can use a binary search to find the target value
Strategy: examine the item in the middle of the list, eliminating half of the items from consideration
The target value will either be found, or
will be in one half or the other
Continue the process
Example : Search 9
[2, 3, 5, 7, 7, 8, 9]
[7, 8, 9]
[9]
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

17. Example: Binary Search
public class Binary_Search_Test {
public static void main (String[] args) {
int[] numbers = {2, 3, 5, 7, 7, 8, 9};
System.out.println ("The index of 5 is " +
Binary_Search.search (numbers, 5));
} // method main
} // class Binary_Search_Test
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

18. Example: Binary Search
class Binary_Search {
public static int search (int[] numbers, int target) {
int index;
int left = 0, right = numbers.length - 1;
while (left <= right) {
index = (left + right) / 2;
if (target == numbers[index])
return index; // target found
if (target > numbers[index])
left = index + 1;
else right = index - 1; }
return -1; // target not found
} // method search
} // class Binary_Search
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

19. Recursive Binary Search
The binary search algorithm can be implemented recursively
It has the same general strategy as the iterative version
Each recursive call narrows the search section
See Binary_Search_Test2.java
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

20. Example: Recursive Binary Search
public class Binary_Search_Test2 {
public static void main (String[] args) {
int[] numbers = {2, 3, 5, 7, 7, 8, 9};
System.out.println ("The index of 5 is " +
Binary_Search2.search (numbers, 5));
} // method main
} // class Binary_Search_Test2
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

21. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
class Binary_Search2 {
public static int search (int[] numbers, int target) {
int left = 0, right = numbers.length - 1;
return recursive_search (numbers, target, left, right);
} // method search
private static int recursive_search (int[] numbers, int target,
int left, int right) {
int index = (left + right) / 2;
if (left > right) return -1; // target not found
else if (target == numbers[index]) // target found
return index;
else if (target > numbers[index])
return recursive_search (numbers, target, index+1, right);
else return recursive_search (numbers, target, left, index-1);
} // method recursive_search
} // class Binary_Search2
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

22. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Hashing
Hashing is another technique for storing and finding information
A hash function produces an integer hash code for any given item
The hash code is scaled to a hash index relative to the size of the hash table
The item is stored in hash table at the hash index
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.

23. Copyright 1997 by John Lewis and William Loftus. All rights reserved.
Hashing
Collisions may occur, resulting in a list of values at a particular index
Therefore a small search may be necessary
Because hashing is based on calculations, it is simple and efficient
Storing and searching involve the same amount of effort
Chapter 13
Copyright 1997 by John Lewis and William Loftus. All rights reserved.