CPS120: Introduction to Computer Science

Sorting

Basics of Sorting

• When you rearrange data and put it into a certain kind of order, you are sorting the data. • You can sort data alphabetically, numerically, and in other ways. • Often you need to sort data before you use searching algorithms to find a particular piece of data.

Key Fields

• The key field is the field upon which the data is sorted. • A key value is a specific value that is stored within the key field. • The input size is the number of elements in a list that will eventually be sorted.

Approaches to Sorting

• ·There are two basic approaches to sorting data – The incremental approach – The divide and conquer approach. • Using the incremental approach, one sorts the whole list at once using loops • The divide and conquer approach splits the list up into parts and sorts each part separately. Then this approach manages to join the sorted parts together into a large sorted list

Sorting Algorithms

• There are a number of different sorting algorithms that are widely used by programmers. • Each algorithm has its own advantages and disadvantages.

Selection Sort

• Sorting a List of names manually – Put them in alphabetical order • Find the name that comes first in the alphabet, and write it on a second sheet of paper • Cross out the name on the original list • Continue this cycle until all the names on the original list have been crossed out and written onto the second list, at which point the second list is sorted

Understanding the Selection Sort

• The selection sort is an incremental one • Every key value is examined starting at the beginning of the list. • A temporary variable to "remember" the position of the largest key value • By the time you have examined every key value, you swap the key value that was the largest with the last key value in the list • Next, you repeat the process again from the beginning of the list, however, you will not need to compare anything to the new last key value in the list since you know it is the largest

Selection Sort

Example of a selection sort (sorted elements are shaded)

Coding the Selection Sort

• This algorithm uses nested loops and is easy to code. • It is quite inefficient since it continues processing even if the list is already sorted • Whether the original data is close to being sorted or not, this algorithm takes quite awhile since a lot of loop iterations and comparisons must be made.

The Insertion Sort

• The insertion sort is incremental in nature. • This is similar to the way a person usually organizes a hand of playing cards. • The insertion sort is relatively quick for small lists that are close to being sorted

Mary Terry Gerri Kari Harry Barry

Insertion Sorting

Mary Gerri Kari Harry Barry Terry Gerri Kari Harry Barry Mary Terry

Bubble Sort

• A sort that uses a different scheme for finding the minimum value – Starting with the last list element, we compare successive pairs of elements, swapping whenever the bottom element of the pair is smaller than the one above it

Understanding the Bubble Sort

• The bubble sort is an incremental sort which is usually faster than the insertion and selection sorts. • A bubble sort works similarly to the release of CO 2 carbonated soda in • The use of the Boolean variable causes this sort to only sweep the list one extra time after it has been fully sorted. This makes the bubble sort more efficient than a number of other incremental sorts

Bubble Sort

Example of a bubble sort

Coding a Bubble Sort

• Beginning at one end of a list, adjacent key values are compared • Assuming that you are sorting the list into ascending order, these two key values would be swapped if the first was larger than the second • Next you compare the larger of the two to the next adjacent key value in the list, swapping if necessary. • By the time that you compare the last two key values in the list, you know that the largest key value from the whole list will be in the last position

Quicksort

Based on the idea that it is faster and easier to sort two small lists than one larger one

Understanding the Quick Sort

• The quicksort is a divide and conquer algorithm and is more efficient than incremental sorts. It can be difficult to code though since it uses recursion or stacks. • The original list is partitioned into two lists. – One of the lists contains elements that are greater than the first original element. – The second list contains elements that are less than or equal to the first original element.

Pages 292 –293

Quicksort