The document discusses various sorting algorithms. It describes how sorting algorithms arrange elements of a list in a certain order. Efficient sorting is important as a subroutine for algorithms that require sorted input, such as search and merge algorithms. Common sorting algorithms covered include insertion sort, selection sort, bubble sort, merge sort, and quicksort. Quicksort is highlighted as an efficient divide and conquer algorithm that recursively partitions elements around a pivot point.

1. Sorting Algorithms
Trupti Agrawal 1

2. Sorting Algorithms
• A sorting algorithm is an algorithm that
puts elements of a list in a certain order.
• Efficient sorting is important for optimizing
the use of other algorithms (such
as search and merge algorithms) which
require input data to be in sorted lists
Trupti Agrawal 2

3. Why Sorting?
 “When in doubt, sort” – one of the principles of
algorithm design. Sorting used as a subroutine in
many of the algorithms:
 Searching in databases: we can do binary search on
sorted data
 A large number of computer graphics and
computational geometry problems
 Closest pair, element uniqueness, frequency distribution
Trupti Agrawal 3

4. Why Sorting? (2)
 A large number of algorithms developed representing
different algorithm design techniques.
 A lower bound for sorting W(n log n) is used to prove
lower bounds of other problems
Trupti Agrawal 4

5. Sorting Algorithms so far
 Insertion sort, selection sort, bubble sort
 Worst-case running time Q(n2); in-place
 Merge sort
 Worst-case running time Q(n log n); but requires
additional memory
Trupti Agrawal 5

6. Insertion sort
• Card players all know how to sort …
– First card is already sorted
– With all the rest,
Scan back from the end until you find the first card larger than
the new one,
Move all the lower ones up one slot
insert it

Q

2

9

A

K

10

J

2

2

9



Trupti Agrawal 6

7. Insertion Sort
To insert 12, we need to
make room for it by moving
first 36 and then 24.
Trupti Agrawal 7

8. 8
Insertion Sort
Trupti Agrawal

9. Insertion Sort
Trupti Agrawal 9

10. Insertion Sort
input array
5 2 4 6 1 3
at each iteration, the array is divided in two sub-arrays:
left sub-array right sub-array
sorted unsorted
Trupti Agrawal 10

11. Insertion Sort
Trupti Agrawal 11

12. Insertion Sort - Summary
• Advantages
– Good running time for “almost sorted” arrays
Q(n)
• Disadvantages
– Q(n2) running time in worst and average case
–  n2/2 comparisons and exchanges
Trupti Agrawal 12

13. Selection Sort
• Idea:
– Find the smallest element in the array
– Exchange it with the element in the first
position
– Find the second smallest element and exchange
it with the element in the second position
– Continue until the array is sorted
• Disadvantage:
– Running time depends only slightly on the
amount of order in the file
Trupti Agrawal 13

14. Example-Selection Sort
8 4 6 9 2 3 1
1 4 6 9 2 3 8
1 2 6 9 4 3 8
1 2 3 9 4 6 8
1 2 3 4 9 6 8
1 2 3 4 6 9 8
1 2 3 4 6 8 9
1 2 3 4 6 8 9
Trupti Agrawal 14

15. Bubble Sort
• Idea:
– Repeatedly pass through the array
– Swaps adjacent elements that are out of order
i
1 2 3 n
8 4 6 9 2 3 1
j
• Easier to implement, but slower than Insertion
sort
Trupti Agrawal 15

16. Example - Bubble Sort
Trupti Agrawal 16

17. Quicksort
 Efficient sorting algorithm
 Discovered by C.A.R. Hoare
 Example of Divide and Conquer algorithm
 Two phases
 Partition phase
 Divides the work into half
 Sort phase
 Conquers the halves!
Trupti Agrawal 17

18. Quicksort  Partition / Divide
 Choose a pivot
 Find the position for the pivot so that
 all elements to the left are less
 all elements to the right are greater
< pivot pivot > pivot
Trupti Agrawal 18

19. Quicksort
 Conquer
 Apply the same algorithm to each half
< pivot > pivot
< p’ p’ > p’ pivot < p” p” > p”
Trupti Agrawal 19

20. Quicksort - Example
Trupti Agrawal 20

21. Review of Algorithms
 Selection Sort
 An algorithm which orders items by repeatedly looking through remaining items to
find the least one and moving it to a final location
 Bubble Sort
 Sort by comparing each adjacent pair of items in a list in turn, swapping the items if necessary, and
repeating the pass through the list until no swaps are done
 Insertion Sort
 Sort by repeatedly taking the next item and inserting it into the final data structure in its proper order with
respect to items already inserted.
 Merge Sort
 An algorithm which splits the items to be sorted into two groups, recursively sorts each group, and merges
them into a final, sorted sequence
 Quick Sort
 An in-place sort algorithm that uses the divide and conquer paradigm. It picks an element from the array
(the pivot), partitions the remaining elements into those greater than and less than this pivot, and
recursively sorts the partitions.
Trupti Agrawal 21

22. THANK YOU….. !!!
Trupti Agrawal 22