Chapter11 sorting algorithmsefficiency

Sorting Algorithms
and their Efficiency
Chapter 11
Data Structures and Problem Solving with C++: Walls and Mirrors, Carrano and Henry, © 2013

Contents
• Basic Sorting Algorithms
• Faster Sorting Algorithms
• A Comparison of Sorting
Algorithms

Basic Sorting Algorithms
• Sorting is:
 A process
 It organizes a collection of data
 Organized into ascending/descending order
• Internal: data fits in memory
• External: data must reside on secondary
storage
• Sort key: data item which determines order

The Selection Sort
FIGURE 11-1 A selection sort of an array of five integers

The Selection Sort
• View implementation of the selection sort,
Listing 11-1
• Analysis
 This is an O (n2
) algorithm
• If sorting a very large array, selection sort
algorithm probably too inefficient to use
.htm code listing files
must be in the same
folder as the .ppt files
for these links to
work
.htm code listing files
must be in the same
folder as the .ppt files
for these links to
work

The Bubble Sort
FIGURE 11-2 The first two passes of a bubble sort
of an array of five integers

The Bubble Sort
• View an implementation of the bubble sort,
Listing 11-2
• Analysis
 Best case, O(n) algorithm
 Worst case, O(n2
) algorithm
• Again, a poor choice for large amounts of
data

The Insertion Sort
• Take each item from unsorted region, insert
into its correct order in sorted region
FIGURE 11-3 An insertion sort partitions
the array into two regions

The Insertion Sort
FIGURE 11-4 An insertion sort of an
array of five integers

The Insertion Sort
• View implantation of insertion sort,
Listing 11-3
• Analysis
 An algorithm of order O(n2
)
 Best case O(n)
• Appropriate for 25 or less data items

The Merge Sort
FIGURE 11-5 A merge sort with an
auxiliary temporary array

The Merge Sort
FIGURE 11-6 A merge sort of an array of six integers

The Merge Sort
• View implementation of the merge sort,
Listing 11-4
• Analysis
 Merge sort is of order O(n × log n)
 This is significantly faster than O(n2
)

The Merge Sort
FIGURE 11-7 A worst-case instance of the
merge step in a merge sort

The Merge Sort
FIGURE 11-8 Levels of recursive calls to mergeSort ,
given an array of eight items

The Quick Sort
FIGURE 11-9 A partition about a pivot

The Quick Sort
FIGURE 11-10 Partitioning of array during quick sort

The Quick Sort
FIGURE 11-11 Median-of-three pivot selection:
(a) The original array; (b) the array with its
first, middle, and last entries sorted

The Quick Sort
FIGURE 11-12 (a) The array with its first, middle, and
last entries sorted; (b) the array after positioning the
pivot and just before partitioning

The Quick Sort
• Note function that performs a quick sort,
Listing 11-5
• Analysis
 Worst case O(n2
)
 Average case O(n × log n)
 Does not require extra memory like merge sort

The Quick Sort
FIGURE 11-13 kSmall versus quickSort

The Radix Sort
• Uses the idea of forming groups, then
combining them to sort a collection of data.
• Consider collection of three letter groups
ABC, XYZ, BWZ, AAC, RLT, JBX, RDT, KLT, AEO, TLJ
• Group strings by rightmost letter
(ABC, AAC) (TLJ) (AEO) (RLT, RDT, KLT) (JBX) (XYZ, BWZ)
• Combine groups
ABC, AAC, TLJ, AEO, RLT, RDT, KLT, JBX, XYZ, BWZ

The Radix Sort
• Group strings by middle letter
(AAC) (A B C, J B X) (R D T) (A E O) (T L J, R L T, K L T) (B W Z) (X Y Z)
• Combine groups
AAC, ABC, JBX, RDT, AEO, TLJ, RLT, KLT, BWZ, XYZ
• Group by first letter, combine again
( A AC, A BC, A EO) ( B WZ) ( J BX) ( K LT) ( R DT, R LT) ( T LJ) ( X YZ)
• Sorted strings
AAC, ABC, AEO, BWZ, JBX, KLT, RDT, RLT, TLJ, XYZ

The Radix Sort
FIGURE 11-14 A radix sort of eight integers

The Radix Sort
• Analysis
 Has order O(n)
 Large n requires significant amount of memory,
especially if arrays are used
 Memory can be saved by using chain of linked
nodes
• Radix sort more appropriate for chain than
for array

Comparison of Sorting
Algorithms
FIGURE 11-15 Approximate growth rates of time
required for eight sorting algorithms

End
Chapter 11

Chapter11 sorting algorithmsefficiency

More Related Content

Viewers also liked

Similar to Chapter11 sorting algorithmsefficiency

More from Gopi Saiteja

Recently uploaded

Chapter11 sorting algorithmsefficiency