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

2. OutlineOverview on Algorithm

3. Sorting

4. Types Of Sorting

5. Using Predefined Header File

6. Inversion Counting (Merge Sort)

7. Related Problem (UVA online-judge)

8. ReferencesOverview on AlgorithmComputing devices are dumb !!!!!

9. How to solve a problem ???? “a small, basic set of primitive instructions”.Complexity of Solving Problems.Goals of Algorithm StudyTo develop framework for instructing computer to perform tasks.

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

11. To introduce and appreciate approaches for defining and solving very complex tasks in terms of simpler tasks.SortingDefinition of SortingSorting makes life easy for searching, eg. Binary SearchThings to be considered for SortingSize / MemoryStabilityMethodPerformance Measure

12. Types Of SortingBubble Sort Speed: O(n^2), extremely slow but stable sorting algorithm Space: The size of initial array Coding Complexity: SimpleQuick Sort Speed: O(nlogn), one of the best sorting algorithm for unsorted data Space: The size of initial array Coding Complexity: Complex, Divide and ConquerMerge Sort Speed: O(nlogn) , one of the best stable sorting algorithm Space: The size of initial array Coding Complexity: Complex, MergingHeap 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 FileSometimes 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 functionintcompare_function(const void *a,const void *b) { // The comparison Code goes here. }Return type of the compare_function1. 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 FileComparing 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 FileComparing a list of stringsComparing floating point numbers

17. Using Predefined Header FileMulti field sortingBefore SortingAfter Sorting

18. Using Predefined Header File

19. Inversion Counting (Merge Sort)

20. Inversion Counting (Merge Sort)47621583Divide into front and back halves476215834324671358Count inversions within each half, and sort each halfThen, count inversions between front and back half

21. Inversion Counting (Merge Sort)2467front:1358back:Merge. Whenever a back item is pushed up, count how many it goes past

22. Inversion Counting (Merge Sort)2467front:1358back:skips over 2, 4, 6 and 7Inversions: 4Merge. Whenever a back item is pushed up, count how many it goes past

23. Inversion Counting (Merge Sort)2467front:1358back:from front, nothing to countInversions: 4Merge. Whenever a back item is pushed up, count how many it goes past

24. Inversion Counting (Merge Sort)467front:12358back:from front, nothing to countInversions: 4Merge. Whenever a back item is pushed up, count how many it goes past

25. 467358Inversion Counting (Merge Sort)front:12back:3 skips over 4, 6, and 7Inversions: 4Inversions: 7Merge. Whenever a back item is pushed up, count how many it goes past

26. 467358Inversion Counting (Merge Sort)front:12back:4 is in front: no changeInversions: 4Inversions: 7Merge. Whenever a back item is pushed up, count how many it goes past

27. 467358Inversion Counting (Merge Sort)front:12back:5 moves past 6 and 7Inversions: 4Inversions: 7Merge. Whenever a back item is pushed up, count how many it goes past

28. 467358Inversion Counting (Merge Sort)front:12back:6 is in front: no changeInversions: 4Inversions: 9Merge. Whenever a back item is pushed up, count how many it goes past

29. 467358Inversion Counting (Merge Sort)front:12back:7 is in front: no changeInversions: 4Inversions: 9Merge. Whenever a back item is pushed up, count how many it goes past

30. 467358Inversion Counting (Merge Sort)12back:8 just moves outInversions: 4Inversions: 9Merge. Whenever a back item is pushed up, count how many it goes past

31. 467358Inversion Counting (Merge Sort)12Inversions: 4Inversions: 9Merge. Whenever a back item is pushed up, count how many it goes past