Introduction to Sorting Algorithms

1. Introduction to Sorting Algorithms • Sort: arrange values into an order • Alphabetical • Ascending numeric • Descending numeric • Two algorithms considered here • Bubble sort • Selection sort

2. Selection Sort Algorithm • Locate smallest element in array and exchange it with element in position 0. • Locate next smallest element in array and exchange it with element in position 1. • Continue until all elements are in order.

3. Selection Sort Example Array numlistcontains • Smallest element is 2. Exchange 2 with element in 1st array position (i.e. element 0). Now in order

4. Now in order Now in order Selection Sort – Example(continued) • Next smallest element is 3. Exchange 3 with element in 2nd array position. • Next smallest element is 11. Exchange 11 with element in 3rd array position.

5. Selection Sort Tradeoffs • Benefit • Easy to understand • Disadvantage • Best and Average case same as Worst case

6. Selection Sort Algorithm • On the first pass through the outer loop of the insertion sort • the inner loop compares the second element to the first element • If the second element is smaller, it is swapped with the first element. • During the second pass through the outer loop • the third element is compared to the second element • if smaller than the second element, it is swapped with the second element. • Then the second element is compared to the first element, and swapped if smaller. • Continue for remaining elements.

7. Insertion Sort Example Array numlistcontains • Second element 2 is smaller than first element 11. Exchange 2 with element in 1st array position (i.e. element 0). • Next compare third element 29 to second element 11. 29 is larger than 11, so move on to fourth element. Now in order

8. Insertion Sort – Example(continued) • Next look at fourth element 3. Exchange 3 with element in 3rd array position. • Next compare 3 to 11. Exchange 11 with 3 array position.

9. Insertion Sort: Linked List-Based • The insertion sort algorithm can also be applied to linked lists • In a linked list, traversal is in only one direction starting at the first node

10. Analysis: Insertion Sort • The average number of comparisons and the average number of item assignments in an insertion sort algorithm are: 1/4 n2 + O(n) = O(n2)

11. Average Case Behavior for a list of length n

12. Quick Sort: Array-Based Lists • The quick sort algorithm uses the divide-and-conquer technique to sort a list • The list is partitioned into two sublists, and the two sublists are then sorted and combined into one list in such a way that the combined list is sorted

13. Quick Sort: Array-Based Lists • The general algorithm is: if (list size is greater than 1) { 1. Partition the list into two sublists, say lowerSublist and upperSublist. 2. Quick sort lowerSublist. 3. Quick sort upperSublist. 4. Combine the sorted lowerSublist and sorted upperSublist. }

14. Analysis of Quick Sort Algorithm for List of length n

15. Merge Sort: Linked List-Based • Merge sort uses the divide-and-conquer technique to sort a list • It partitions the list into two sublists, and then combines the sorted sublists into one sorted list • It partitions the list into nearly equal sizes • For example, consider the list: List: 35 28 18 45 62 48 30 38 • Merge sort partitions this list into two sublists as follows first sublist: 35 28 18 45 second sublist: 62 48 30 38

16. Merge sort algorithm

17. Divide and Merge • Divide • Because the data are stored in a linked list, we do not know the length of the list • To find the middle of the list we traverse the list with two pointers, say middle and current • Merge • Once the sublists are sorted the next step in the merge sort is to merge the sorted sublists • Sublists are merged by comparing the elements of the sublists and adjusting the pointer of the nodes with the smaller info