CIS3023: Programming Fundamentals for CIS Majors II Summer 2010 Ganesh Viswanathan Sorting Course Lecture Slides 24 May 2010 “The real focus here is bringing some sort of order.” --Janet Hubbell

Sorting 1.Rearrange a[0], a[1], …, a[n-1] into ascending order. 2.When done, a[0] <= a[1] <= … <= a[n-1] 3.a[0], a[1],…a[n] could be integers, doubles, characters, or objects

Sorting Algorithms 1.Selection-based Selection sort Heap Sort 2.Insertion-based Insertion Sort Shell Sort 3.Exchange-Based Bubble Sort Quick Sort 4.Merge-based Merge Sort All these are comparison-based sorting algorithms.

Selection Sort Algorithm List is sorted by selecting a list element and moving it to its proper position. Algorithm finds position of smallest element and moves it to the top of unsorted portion of list. Repeats process above until entire list is sorted.

Selection Sort Algorithm (Cont’d) Figure 1: An array of 10 elements Figure 2: Smallest element of unsorted array

Selection Sort Algorithm (Cont’d) Figure 3: Swap elements list[0] and list[7] Figure 4: Array after swapping list[0] and list[7]

Selection Sort Algorithm (Cont’d) In-class exercise: Complete Selection Sort and get the array fully sorted! Show at each step: # array elements, # comparisons required, and # exchanges performed.

Insertion Sort Algorithm Based on technique of card players to arrange a hand Player keeps cards picked up so far in sorted order When the player picks up a new card Makes room for the new card Then inserts it in its proper place

Example Steps in Insertion Sort: Inserting the Fourth Array Element:

Bubble Sort Algorithm Compares adjacent array elements Exchanges their values if they are out of order Smaller values bubble up to the top of the array Larger values sink to the bottom

Bubble Sort Algorithm (Cont’d) Figure 1: Elements of array list during the first iteration Figure 2: Elements of array list during the second iteration

Bubble Sort Algorithm (Cont’d) Figure 3: Elements of array list during the third iteration Figure 4: Elements of array list during the fourth iteration

“ To iterate is human, to recurse divine. ” --L. Peter Deutsch

Merge Sort

Merging two sorted lists