1. Principles of Computing – UFCFA3-30-1
Searching and Sorting
Instructor : Mazhar H Malik
Global College of Engineering and Technology

2. Today’s Lecture Sorting Searching Linear Search Binary Search
Selection Sort
Insertion Sort
Bubble Sort
Searching & Sorting

3. Learning Objective
Explain algorithmic behaviour of programs in appropriate formal terms. LO[3] Component B

4. Linear Array
A linear array is the list of finite number of data elements (i.e. same type of data).
Data Store in the array identify by the index numbers.

5. Searching
A search algorithm is a method of locating a specific item of information in a larger collection of data. This section discusses two algorithms for searching the contents of an array.
Linear Search
Binary Search

6. The Linear Search This is a very simple algorithm.
It uses a loop to sequentially step through an array, starting with the first element.
It compares each element with the value being searched for and stops when that value is found or the end of the array is reached.

7. The Linear Search-Algorithm
Initialize the elements of the array
Input “X” number to search
while i<length of array
if(array[index] == X):
print("%d found at %dth position"%(X,i))
break
i=i+1

8. Efficiency of the Linear Search
The advantage is its simplicity.
It is easy to understand
Easy to implement
Does not require the array to be in order
The disadvantage is its inefficiency
If there are 20,000 items in the array and what you are looking for is in the 19,999th element, you need to search through the entire list.

9. Binary Search
The binary search is much more efficient than the linear search.
It requires the list to be in order.
The algorithm starts searching with the middle element.
If the item is less than the middle element, it starts over searching the first half of the list.
If the item is greater than the middle element, the search starts over starting with the middle element in the second half of the list and it continues halving the list until the item is found.

10. 1 11 2 22 3 33 4 44 5 55 6 66 7 77 8 88 9 99
Item := 33
Mid
Beg := 1 End : = 9
Mid := Int (( Beg + End ) / 2)

11. 1 11 2 22 3 33 4 44 5 55 6 66 7 77 8 88 9 99
Mid
Item := 33
Beg := 1 End : = 4
Mid := Int (( Beg + End ) / 2)

12. 1 11 2 22 3 33 4 44 5 55 6 66 7 77 8 88 9 99
Item := 33
Mid
Beg := 3 End : = 4
Mid := Int (( Beg + End ) / 2)

13. 1 11 2 22 3 33 4 44 5 55 6 66 7 77 8 88 9 99
Item := 33
Mid
Mid := 3

14. Efficiency of the Binary Search
Much more efficient than the linear search.
Array should be in sorting condition before applying binary search

15. How Fast is a Binary Search?
Worst case: 11 items in the list took 4 tries
How about the worst case for a list with 32 items ?
1st try - list has 16 items
2nd try - list has 8 items
3rd try - list has 4 items
4th try - list has 2 items
5th try - list has 1 item

16. How Fast is a Binary Search? (con’t)
List has 512 items
1st try items
2nd try items
3rd try - 64 items
4th try - 32 items
5th try - 16 items
6th try - 8 items
7th try - 4 items
8th try - 2 items
9th try - 1 item
List has 250 items
1st try items
2nd try - 63 items
3rd try - 32 items
4th try - 16 items
5th try - 8 items
6th try - 4 items
7th try - 2 items
8th try - 1 item

17. What’s the Pattern? List of 11 took 4 tries List of 32 took 5 tries

18. Since binary algorithm is very efficient (e. g
Since binary algorithm is very efficient (e.g. it requires only about 20 comparisons with an initial list of 1,000,000 elements) but observe that algorithm requires two conditions
The list must be sorted
One must have direct access to middle element in sub list

19. Sorting
Sorting — arranging items in order — is the most fundamental task in computation. Sorting enables efficient searching algorithms such as binary search.
Selection Sort
Insertion Sort
Bubble Sort

20. Sorting
Selection sort: repeatedly pick the smallest element to append to the result.
Insertion sort: repeatedly add new element to the sorted result.
Bubble sort: repeatedly compare neighbor pairs and swap if necessary.

21. Selection Sort
Selection sort is to repetitively pick up the smallest element and put it into the right position:
Find the smallest element, and put it to the first position.
Find the next smallest element, and put it to the second position.
Repeat until all elements are in the right positions.

22. Selection Sort

23. Insertion Sort
Insertion sort maintains a sorted sub-array, and repetitively inserts new elements into it. The process is as following:
Take the first element as a sorted sub-array.
Insert the second element into the sorted sub-array (shift elements if needed).
Insert the third element into the sorted sub-array.
Repeat until all elements are inserted.

24. Insertion Sort

25. Bubble Sort
Bubble sort repetitively compares adjacent pairs of elements and swaps if necessary. :
Scan the array, swapping adjacent pair of elements if they are not in relative order. This bubbles up the largest element to the end.
Scan the array again, bubbling up the second largest element.
Repeat until all elements are in order.

26. Bubble Sort

27. Bubble Sort
Apply Bubble sort on the following array
{38, 27, 43,9, 82, 10} 

28. Home Work {38, 27, 43, 3, 9, 82, 10} Using above dataset, perform
{38, 27, 43, 3, 9, 82, 10} 
Using above dataset, perform
Searching
Linear Search
Binary Search
Sorting
Insertion Sort
Selection Sort
Bubble Sort
Due Date:

29. Lab Work: Linear Search Python Implementation
Write a program that will input a number from user and will check whether number exist in the array or not using Linear Search Algorithm. After execution display suitable message (i.e Input number not exist or Input number is at index[n] of array.

30. Summary
In This lecture we discussed about the array searching and Sorting techniques.
Searching Techniques?
Sorting Techniques?

31. Reference
Chapter 6, Page Hein J H (2010). Discrete Structures, Logic, and Computability, 4th ed. Jones and Bartlett

32. Questions?