The document discusses various sorting and searching algorithms: - Bubble sort, selection sort, merge sort, quicksort are sorting algorithms that arrange data in a particular order like numerical or alphabetical. - Linear search and binary search are searching algorithms where linear search sequentially checks each item while binary search divides the data set in half with each comparison. - Examples are provided to illustrate how each algorithm works step-by-step on sample data sets.

2. An algorithm is a finite collection of well defined steps
to solve
A particular problem. An algorithm Is a finite sequence
of instructions,
Logic, step by step process for solving a problem.

5. Sorting technique to arranging data in a
particular format. Sorting algorithm specifies
the
Way to arrange data in a particular order. Most
common are numerical or lexicograpical order.
Sorting is also used to represent data in more
readable formats.

6. Telephone Directory – Telephone directory keeps
telephone No. of people sorted on their
Names. So that names can be searched.
Dictionary – Dictionary keeps words in
alphabetical order so that searching of any work
becomes easy.

7. Bubble Sort is a simple sorting algorithm. This
sorting algorithm is comparison
Based algorithm in which each pair of
adjacent elements is compared & elements
Are swapped if they are not in order. This
algorithm is not suitable for large data
Sets as its average and worst case complexity.

8. We take an unsorted array for our example:
14 33 27 35 10
14
14
14
14
14
14
14
14
1433
33
33
27 33
27
27
27
35
35
35
35
10
10
10
10
27
27
27
27
27
33
33
33
33
10
35
35
35
10
35
10
10
10
35
33

9. 14
14
10
10
27
27 33
33
35
35

10. This is a in-place comparison based sorting
algorithm. Here, a sub-list is always sorted.
For example, the lower part of an array is
maintained to be sorted. The array is
searched
Sequentially and unsorted items are moved
and inserted into sorted sub-list.

11. 14 33 27 3510
14
14
14
14
14
14
14
14
1433
33
33
33 27
27
27
27
10
10
10
10
35
35
35
35
27
27
27
27
27
33
33
33
10
10
10
10
10
33
35
35
35
35
35
33
We take an unsorted array for our example.

12. 14
14
14
10
10
10
27
27
27
33
33
33
35
35
35

13. Selection sort is a simple sorting algorithm .
This sorting algorithm is a in-place
Comparison based algorithm in which the
list is divided into two parts, sorted
Part at left end and unsorted part at right
end. intially end sorted part is empty
And unsorted part is entire list.

14. We take the depicted array for our example :
14 33 27 10 35
14
10
10
10
10
10
10
10
1033
33
33
33 27
27
27
27
10
14
14
14
35
35
35
35
14
14
14
14
14
27
27
27
19
19
33
33
33
33
35
35
35
35
35
33
19 19
19
19
27
27
19
19
19
19

15. 10
10
10
10
10
14
14
14
14
14
19
19
19
19
19
27
27
27
27
33
35
35
35
33
27
33
33
33
35
35

16. Merge Sort is a sorting technique based
on divide & conquer technique. With
worst case time complexity being
respected algorithms. Merge Sort first
divides the array into equal halves &
Then combines them in a sorted manner.

17. To understand merge sort, we take an unsorted array as depicted below.
14 33 27 10 35 19 42 44
35 19 42 4414 33 27 10
14 33 27 10 35 19 42 44
14 33 27 10 35 19 42 44
14 33 10 27 19 35 42 44
Combine Them into another list

18. 10 14 33 27 19 35 42 44
After final merging, the list should look like this :
10 14 19 27 33 35 42 44

19. Quick sort is a highly efficient sorting
algorithm and is based on partitioning of array
Of data into smaller arrays. The quick sort
partitions an array and then calls itself
recursively twice to sort the resulting two sub
arrays. This algorithm is quite efficient for
large size data sets its average & worst case
complexity are of 0.

20. The below given image representation explains how to find
pivot value in the way.
10 42 35 33 31 27 26 19 14 44
10 14 19 26 27 31 33 35 42 44

22. Linear search is a very simple search algorithm. In
this type search, a sequential
search is made over all items one by one. Every
items is checked & if a match founds them
Particular item is returned otherwise search
continues till the end of the data collection.

23. Suppose that we find 33 in array element
Linear Search
10 14 19 26 27 31 33 35 42 44
=
33
10 14 19 26 27 31 33 35 42 44

24. Binary search is a fast search algorithm
with run-time complexity of 0 (log n) .
This search algorithm works on the
principle of divide & compare. For this
algorithm to work properly the data
collection should be in sorted form.

25. The below given is our sorted array and assume that we need to search location
Of value 31 using binary search.
10 14 19 26 27 31 33 35 42 44
0 1 2 3 4 5 6 7 8 9
First, we shall determine the half of the array by using this formula-
Mid = low + (high – low) / 2
Here it is, 0+(9-0) / 2 = 4(integer value of 4.5). So 4 is the mid of array.
10 14 19 26 27 31 33 35 42 44
0 1 2 3 4 5 6 7 8 9

26. We change our low to mid + 1 and final the new value again.
Low = mid + 1
Mid = low + (high – low) / 2
Our new mid 7 now. We compare the value stored at location 7 with our target value 31.
10 14 19 26 27 31 33 35 42 44
0 1 2 3 4 5 6 7 8 9
The value stored at location 7 is not match, rather it is less that what we are looking for.
So the value must be in lower part from this location.
10 14 19 26 27 31 33 35 42 44
0 1 2 3 4 5 6 7 8 9

27. So we calculate the mid again. This time is 5.
10 14 19 26 27 31 33 35 42 44
0 1 2 3 4 5 6 7 8 9
We compare the value stored ad location 5 with our target value. We find
that is a match.
10 14 19 26 27 31 33 35 42 44
0 1 2 3 4 5 6 7 8 9
We conclude that the target value 31 is stored at location 5.

29. End Of The Moment