The document discusses and compares linear and binary search algorithms. It describes how linear search sequentially compares an element to all items in a list, while binary search relies on a sorted list and divides the search space in half at each step. Example code is provided for implementing linear and binary search in Java. The document concludes that binary search is more efficient for large sorted data, while linear search can be used for small unsorted data or as a simpler approach.

1. using Java
2015
Data Structure
Prepared by: Mahmoud Rafeek Al-farra
in Java
3. Searching Algorithms

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Contents
Which is best ?
Binary Search approach
Linear search approach
Introduction

3. Introduction
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 Searching for data is a fundamental computer
programming task and one that has been studied for
many years.
There are two fundamental ways to search for data in
a list:
The sequential (linear) search approach.
The binary search approuach.

4. Linear search approach
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The linear search approach compares the key element
sequentially with each element in the data structure.
 It continues to do so until the key matches an
element in the DS or the DS is exhausted without a
match being found.
If a match is made, the linear search returns the
index of the element in the DS that matches the key.
 If no match is found, the search returns -1.

5. Linear search approach
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2 5 81 88 90 997 9 34 55 56 66 79 80
1 2 3 4 5 6 7 8 9 10 11 12 13
Wanted = 80
array
0
==‫؟‬
.... ....
The wanted value at comparison number 10 and position 9
You can see an animated example from the following link:
http://www.cs.armstrong.edu/liang/animation/web/LinearSearch.html

6. Linear search approach
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1. public class LinearSearch {
2. /** The method for finding a key in the list */
3. public static int linearSearch(int[] list, int key) {
4. for (int i = 0; i < list.length; i++) {
5. if (key == list[i])
6. return i;
7. }
8. return -1;
9. }
10. }

7. Binary search approach
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When the records you are searching through are
sorted into order, you can perform a more efficient
search than the sequential search to find a value. This
search is called a binary search.
To use this algorithm, we first need our data stored
in order (ascending, preferably) in an array.
You can see an animated example from the following link:
http://www.cs.armstrong.edu/liang/animation/web/BinarySearch.html

8. Binary Search approach
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9. Binary Search approach
2 5 81 88 90 997 9 34 55 56 66 79 80
1 2 3 4 5 6 7 8 9 10 11 12 13
(0+13) / 2 = 6
If (array[6] == 80)
return 6
Elseif (array[6] > 80)
High = 6 -1
Else
Low = 6+1
Middle = (low + high)/2
Wanted = 80
array
0
(7+13) / 2 = 10
If (array[10] == 80)
return 10
Elseif (array[10] > 80)
High = 10 -1
Else
Low = 10+1
(7+9) / 2 = 8
If (array[8] == 80)
return 8
Elseif (array[8] > 80)
High = 8-1
Else
Low = 8+1
1 2 3
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10. Binary Search approach
2 5 81 88 90 997 9 34 55 56 66 79 80
1 2 3 4 5 6 7 8 9 10 11 12 13
Middle = (low + high)/2
Wanted = 80
array
0
(7+9) / 2 = 8
If (array[8] == 80)
return 8
Elseif (array[8] > 80)
High = 8-1
Else
Low = 8+1
3
(9+9) / 2 = 9
If (array[9] == 80)
return 8
Elseif (array[9] > 80)
High = 9-1
Else
Low = 9+1
4
return 8
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11. Binary Search approach
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1. public class BinarySearch {
2. public static int binarySearch(int[] list, int key) {
3. int low = 0;
4. int high = list.length - 1;
5. while (high >= low) {
6. int mid = (low + high) / 2;
7. if (key < list[mid])
8. high = mid - 1;
9. else if (key == list[mid])
10. return mid;
11. else
12. low = mid + 1;
13. }
14. return –low - 1; // Now high < low, key not found
15. }
16. }

12. Which is best ?
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The
best
Complexity
Data
structure
Suitable
data
Size of
data

13. Which is best ?
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 If an array is sorted, binary search is more efficient
than linear search for finding an element in the array.
 Linear search is useful for finding an element in a
small array or an unsorted array, but it is inefficient
for large arrays.
 Binary search is more efficient, but it requires that
the array be presorted.

14. Which is best ?
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Complexity time of linear approach is: O(n)
Complexity time of binary approach is: O( log(n))
 Supported data structure of linear: ?
 Supported data structure of Binary: ?

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2015
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