1. The document discusses various sorting algorithms like bubble sort, quick sort, and merge sort. It explains their time and space complexities. 2. It describes how to count inversions during merge sort by tracking the number of elements a back element passes during the merging process. Pseudocode for the merge-and-count and sort-and-count functions is provided. 3. Related problems on sorting and inversion counting from online judges like UVA are listed along with references for further reading.

1. Sorting Prepared by Anis

3. Sorting

4. Types Of Sorting

5. Using Predefined Header File

6. Inversion Counting (Merge Sort)

7. Related Problem (UVA online-judge)

10. To introduce notion of algorithm as means of specifying how to solve a problem.

12. Types Of Sorting Bubble Sort Speed: O(n^2), extremely slow but stable sorting algorithm Space: The size of initial array Coding Complexity: Simple Quick Sort Speed: O(nlogn), one of the best sorting algorithm for unsorted data Space: The size of initial array Coding Complexity: Complex, Divide and Conquer Merge Sort Speed: O(nlogn) , one of the best stable sorting algorithm Space: The size of initial array Coding Complexity: Complex, Merging Heap Sort Speed: O(nlogn) , one of the best unstable sorting algorithm Space: The size of linked list used Coding Complexity: Complex, Uses Tree Data structure

13. Using Predefined Header File Sometimes it is needed to reduce the hassle of recoding same thing over and over again. Sometimes it is needed to sort a more complex stuffs, such as record, structure etc. where these record / structure might be sorted based on key present in the record/structure. Quick Sort header for C++ Language. qsort(<arrayname>,<size>,sizeof(<elementsize>),compare_function);

14. Compare function intcompare_function(const void *a,const void *b) { // The comparison Code goes here. } Return type of the compare_function 1. negative, if a comes before b Ž 2. 0, if a == b Ž 3. positive, if a comes after b Using Predefined Header File

15. Using Predefined Header File Comparing a list of integers 1. simply cast a and b to integers 2. x < y, x-y is negative x == y, x-y is zero x > y, x-y is positive

16. Using Predefined Header File Comparing a list of strings Comparing floating point numbers

17. Using Predefined Header File Multi field sorting Before Sorting After Sorting

18. Using Predefined Header File

19. Inversion Counting (Merge Sort)

20. Inversion Counting (Merge Sort) 4 7 6 2 1 5 8 3 Divide into front and back halves 4 7 6 2 1 5 8 3 4 3 2 4 6 7 1 3 5 8 Count inversions within each half, and sort each half Then, count inversions between front and back half

21. Inversion Counting (Merge Sort) 2 4 6 7 front: 1 3 5 8 back: Merge. Whenever a back item is pushed up, count how many it goes past

22. Inversion Counting (Merge Sort) 2 4 6 7 front: 1 3 5 8 back: skips over 2, 4, 6 and 7 Inversions: 4 Merge. Whenever a back item is pushed up, count how many it goes past

23. Inversion Counting (Merge Sort) 2 4 6 7 front: 1 3 5 8 back: from front, nothing to count Inversions: 4 Merge. Whenever a back item is pushed up, count how many it goes past

24. Inversion Counting (Merge Sort) 4 6 7 front: 1 2 3 5 8 back: from front, nothing to count Inversions: 4 Merge. Whenever a back item is pushed up, count how many it goes past

25. 4 6 7 3 5 8 Inversion Counting (Merge Sort) front: 1 2 back: 3 skips over 4, 6, and 7 Inversions: 4 Inversions: 7 Merge. Whenever a back item is pushed up, count how many it goes past

26. 4 6 7 3 5 8 Inversion Counting (Merge Sort) front: 1 2 back: 4 is in front: no change Inversions: 4 Inversions: 7 Merge. Whenever a back item is pushed up, count how many it goes past

27. 4 6 7 3 5 8 Inversion Counting (Merge Sort) front: 1 2 back: 5 moves past 6 and 7 Inversions: 4 Inversions: 7 Merge. Whenever a back item is pushed up, count how many it goes past

28. 4 6 7 3 5 8 Inversion Counting (Merge Sort) front: 1 2 back: 6 is in front: no change Inversions: 4 Inversions: 9 Merge. Whenever a back item is pushed up, count how many it goes past

29. 4 6 7 3 5 8 Inversion Counting (Merge Sort) front: 1 2 back: 7 is in front: no change Inversions: 4 Inversions: 9 Merge. Whenever a back item is pushed up, count how many it goes past

30. 4 6 7 3 5 8 Inversion Counting (Merge Sort) 1 2 back: 8 just moves out Inversions: 4 Inversions: 9 Merge. Whenever a back item is pushed up, count how many it goes past

31. 4 6 7 3 5 8 Inversion Counting (Merge Sort) 1 2 Inversions: 4 Inversions: 9 Merge. Whenever a back item is pushed up, count how many it goes past

32. merge-and-count(A,B) ; A,B two input lists (sorted) ; C output list ; i,j current pointers to each list, start at beginning ; a_i, b_j elements pointed by i, j ; count number of inversion, initially 0 while A,B != empty copy min(a_i,b_j) to C if b_j < a_i count += number of element remaining in A j++ else i++ ; now one list is empty copy the remainder of the list to C return count, C Inversion Counting (Merge Sort)

33. sort-and-count(L) if L become less then 2 return 0 else divide L into A, B copy first to mid to A copy from mid to last to B (rA, A) = sort-and-count(A) (rB, B) = sort-and-count(B) (r, L) = merge-and-count(A,B) return r = rA+rB+r, L Inversion Counting (Merge Sort)

34. Related Problem (UVA online-judge) Sorting 299 612 10327 11462 Record based Sorting 482 10194 11804 Inversion Counting 299 10810 11495

35. References Art of Programming Contest by Ahmed ShamsulArefin http://en.wikipedia.org/wiki/Sorting_algorithm

36. While(1) { if(any questions pops) { printf(“Shout”); process(); } else break; }

37. THANK YOU